1 When factored, the expression x3 – 36x is equivalent to
Solution: First, we need to factor out the greatest common factor. In this case, it is x. We get x(x2−36) Next we recognize the difference of squares, we get x(x-6)(x+6). Choice 3 is the correct answer.
2 Which equation represents the line that passes through the points (-1,8) and (4,-2)?
Solution: Let’s use the slope intercept form y=mx+b where m is slope and b is y-intercept. To get slope we use the formula m=(y2−y1)/(x2−x1) = (−2−8)/(4–1) = -2. Next we use y−y1=m(x−x1), plugging in one of the points such as (-1, 8) and slope m=−2. We get y−8=−2(x+1) y−8=−2x−2 y=−2x+6 Choice 1
3 A geometric sequence is shown below. 1/2 , 2, 8, 32, … What is the common ratio?
Solution: To find the common ratio in a geometric sequence, we need to divide any term by the previous term. 2 divided by 1/2 is equal 4. Similarly 8 divided by 2 is 4 and so on. Choice 4 is the correct answer.
4 What is the constant term of the polynomial 2x3– x + 5 + 4x2? (1) 5 (3) 3 (2) 2 (4) 4
Solution: The constant term is the term without any variables, which is 5 in this case. Choice 1 is the correct answer.
5 A landscaping company charges a set fee for a spring cleanup, plus an hourly labor rate. The total cost is modeled by the function C(x) = 55x + 80. In this function, what does the 55 represent? (1) the set fee for the cleanup (2) the hourly labor rate for a cleanup (3) the profit earned by the company for one cleanup (4) the number of hours of labor required for one cleanup
Solution: We can notice that 55 is times X which means that this is an hourly rate. X is the number of hours. 80 is without x and would be the set fee. Choice 2 is the correct answer.
6 Which expression is equivalent to (5x2 – 2x + 4) – (3x2 + 3x – 1)?
Solution: Distribute the minus sign to the second group: (5x2 – 2x + 4) – 3x2 – 3x +1 Combine like terms: 2x2-5x + 5. Choice 2 is the correct answer.
7 A system of inequalities is graphed on the set of axes below.
Solution: A solution is within the region that is shaded for both lines. Choice 4 is the correct answer.
8 In an arithmetic sequence, the first term is 25 and the third term is 15. What is the tenth term in this sequence? (1) -20 (3) 70 (2) -25 (4) 75
Solution: An arithmetic sequence has the following formula: an=a1+(n−1)d where an is the nth term and a1 is the first term. We get 15=25+(3-1)d d= -5 Now, we can plug in d and first term to find the tenth term an = 25+(10-1)(-5) = -20. Choice 1 is the correct answer
9 When the formula p = 2l + 2w is solved for w, the result is
Solution: Lets solve p = 2l + 2w. We need to isolate w. We get p-2l= 2w. Then we need to divide by 2 and get (p-2l)/2=w. Choice 2 is the correct answer.
10 Market Street Pizza kept a record of pizza sales for the month of February. The results are shown in the table below.
Of all the pizzas sold in February, what percent were plain, deep-dish pizzas? (1) 20% (3) 40% (2) 30% (4) 50%
Solution: First, we need to find the number that represents plain, deep-dish pizzas which is 200. Next, we have to divide it by the total number of pizzas and multiply by 100% to find percent. We will add all of the numbers in the table to find the total number. We get 1000 pizzas. % = (200/1000)*100% = 20%. Choice 1 is the correct answer.
Solution: First we can multiple both sides of the equation by 2 to get rid of the denominator. We get: -4(3x-5)=9x-4. Next we can open parenthesis and then group like terms with one another. -12x+20 = 9x-4 -12x-9x = -4-20 -21x = -24 x= -24/-21 = 8/7. Choice 1 is the correct answer
12 The expression x2a + b is equivalent to
Solution: The expression x2a + b is equivalent to xa*xa+b. Choice 3 is the correct answer
13 The inputs and outputs of a function are shown in the table below.
This function can best be described as (1) linear (3) exponential (2) quadratic (4) absolute value
Solution: From x = 0 to 1: the output doubles (0.0625 → 0.125). From x = 1 to 2: 0.125 → 0.25 (doubles again). Then: 0.25 → 0.5 → 1 → 2 (keeps doubling). This is an exponential function. Choice 3 is the correct answer.
14 Stephanie is solving the equation x2 – 12 = 7x – 8.
Solution: This step uses the Addition Property of Equality, which states that you can add the same value to both sides of an equation without changing the equality. Choice 4 is the correct answer
15 What is the sum of 8 √3 and √3 ?
Solution: To find the sum of 8√3+√3, you simply add the like terms (they both have the same radical part, (8+1)√3 = 9√3. Choice 4 is the correct answer.
16 The dot plots below represent test scores for 20 students on a math test.
The mode for this math test is 80 and the median is 85. Which dot plot correctly represents this data? (1) I (3) III (2) II (4) IV
Solution: We are told: Total students = 20 Mode = 80 (most frequent value) Median = 85 (middle value when data is ordered) Let’s first look at the most frequent value (the one with most dots.). We can eliminate choices 2 (mode is 85) and 4 (mode is 85). Median must be the 10th point. Looking at plot 3, 10th point is 80, eliminating choice 3. Choice 1 is the correct answer.
17 A function is graphed on the set of axes below.
Solution:From the graph, the function starts at x=−2x=−2 with an open circle, meaning x=−2x=−2 is not included in the domain. The curve extends indefinitely to the right. So, the domain is:{x∣x>−2}. That corresponds to option (1).
18 Which ordered pair is a solution to the equation
Solution: One way to solve this question is to plug in x value (first number) from each answer choice to see if it corresponds to the correct y value. Choice 2 is the correct answer choice.
19 Elena’s fastest time for the 50-meter dash is 7 seconds. She wants to know how fast this is in inches per minute. Which expression can Elena use for a correct conversion?
Solution: We are told that Elena runs 50 meters in 7 seconds and that is what we need to start with, eliminating choices 1 and 2. Next, to convert seconds to minutes, we will put 60 seconds on top and 1 minute on the bottom. Next, to convert meters to inches, meters need to go on the bottom (to get crossed out) and inches on top. Choice 4 is the correct answer choice.
20 The table below shows the highest temperatures recorded in August for several years in one town.
The interquartile range of these data is (1) 7 (3) 11 (2) 10 (4) 18
Solution: Let’s find the interquartile range (IQR), which is: IQR=(Q3−Q1)I Step 1: Order the temperatures from least to greatest 77, 78, 81, 84, 86, 88, 93, 95 Step 2: Find Q1 and Q3 There are 8 data points. Q1 = median of the lower half (first 4 numbers): 77, 78, 81, 84 Q1=(78+81)/2=159/2=79.5 Q3 = median of the upper half (last 4 numbers): 86, 88, 93, 95 Q3=(88+93)/2=181/2=90.5 Step 3: Calculate IQR IQR=90.5−79.5=11, Choice 3 is the correct answer choice.
21 The function f(x) = x2 is multiplied by k, where k <- 21. Which graph could represent g(x) = kf(x)?
Solution: k<−21 means k is negative and has a large magnitude.The negative sign flips the parabola upside down (opens downward).The large magnitude makes it very narrow (steeper). Choice 4 is the correct answer.
22 Which graph is the solution to the inequality 6.4 – 4x ≥ -2.8?
Solution: First we need to isolate x in the inequality, 6.4 – 4x ≥ -2.8 -4x≥ -2.8-6.4 -4x≥-9.2 x≤2.3 (reverse the sign because we divided by a negative number). Choice 4 is the correct answer because the circle is shaded in because of the equal sign and x is less than or equal to 2.3
23 The number of fish in a pond is eight more than the number of frogs. The total number of fish and frogs in the pond is at least 20. If x represents the number of frogs, which inequality can be used to represent this situation?
Solution:Let x represent the number of frogs in the pond. Since there are eight more fish than frogs, the number of fish is x+8. The total number of frogs and fish is then x+(x+8)==2x+8. Because the total number of animals is at least 20, we write the inequality 2x+8≥20 to represent this situation. Choice 2 is the correct answer choice.
24 Which graph below represents a function that is always decreasing over the entire interval -3 < x <3?
Solution: A function that is always decreasing over −3<x<3means: The slope must be negative everywhere in that interval. As x increases, f(x) must continuously decrease. There can’t be any turning points (no going up then down). Choice 4 is the correct answer choice.
1 Which terms identify two scalar quantities? (1) force and acceleration (2) impulse and distance (3) mass and velocity (4) energy and time
Solution: Neither energy nor time has directions. Therefore, they are both scalar quantities. Choice (4)
2 A motorcyclist, initially traveling east at 15 meters per second, accelerates uniformly at a rate of 3.0 meters per second squared east to a velocity of 21 meters per second east. How far does the motorcyclist travel while accelerating? (1) 1.0 m (2) 2.0 m (3) 36 m (4) 72 m
Solution: Use the formula Vf2=vi2+2ad , we can solve for distance by plugging in initial and final velocities (15m/s and 21m/s, respectively) and the acceleration (3m/s^2). d = 36m. Choice (3)
3 A battery-powered electric motor is used to cause the wheels of a toy car to rotate. In this motor, there is a conversion of (1) mechanical energy to electric energy (2) electric energy to chemical energy (3) thermal energy to electric energy (4) electric energy to mechanical energy
Solution: The point of a battery powered motor is to use the energy stored in the battery and turn something such as wheels. This is a conversion from electric energy to mechanical energy. Choice (4)
4 A projectile is launched horizontally from a height of 65 meters with an initial horizontal speed of 35 meters per second. What is the projectile’s horizontal speed after it has fallen 25 meters? [Neglect friction.] (1) 22 m/s (2) 35 m/s (3) 41 m/s (4) 280 m/s
Solution:Remember, there is no acceleration in the horizontal direction, the horizontal speed must always remain the same. Choice (2)
5 The diagram below represents two forces, F1 and F2, acting concurrently on a block sliding on a horizontal, frictionless surface.
Which statement describes the motion of the block? (1) The block is accelerating to the right. (2) The block is accelerating to the left. (3) The block is moving to the right with constant speed. (4) The block is moving to the left with decreasing speed.
Solution: There is no unbalanced force according to the free body diagram. Remember, Newton’s 2nd law states that a net force of zero will produce zero acceleration so it must be moving at a constant speed. Choice (3)
6 The magnitude of an unbalanced force applied to a 4.0-kilogram crate is 10. newtons. If the magnitude of this applied unbalanced force is doubled, the inertia of the crate is (1) halved (3) doubled (2) unchanged (4) quadrupled
Solution: The inertia of the crate is solely dependent on its mass. Doubling the unbalanced force won’t change the inertia. Choice (2)
7 A 60.-kilogram man is pushing a 30.-kilogram lawn mower. Compared to the magnitude of the force exerted on the lawn mower by the man, the magnitude of the force exerted on the man by the lawn mower is (1) one-quarter as great (3) the same (2) one-half as great (4) twice as great
Solution: According to Newton’s 3rd law, for every action, there is an equal but opposite reaction. Choice (3)
8 The diagram below represents a roller coaster car traveling counterclockwise in a vertical circle.
When the car is in the position shown, what are the directions of the centripetal force acting on the car and the velocity of the car? (1) The centripetal force is directed to the right and the velocity is directed downward. (2) The centripetal force is directed downward and the velocity is directed to the right. (3) The centripetal force and velocity are both directed to the right. (4) The centripetal force and velocity are both directed downward.
Solution: The velocity of an object going through uniform circular motion is always tangent to the circular path and the acceleration must be pointing towards the center of the circular path. Choice (1)
9 An electric motor with a power rating of 6.48 * 104 watts is used to raise an elevator weighing 2.80 * 104 newtons at constant speed. What is the total time required for the motor to raise the elevator a vertical distance of 20.0 meters? (1) 0.116 s (3) 8.64 s (2) 2.31 s (4) 46.3 s
Solution: Use the formula P= Fd/t, we can isolate for the time by plugging in F=2.8*10^4N, d=20m, and P=6.48*10^4 W. t= 8.64s. Choice (3)
10 A person standing on a sidewalk hears the siren of an ambulance as it approaches, passes by, and goes away from the person. Compared to the frequency of the sound emitted by the siren, the frequency of the sound observed by the person during this event is (1) higher, only (2) lower, only (3) first higher and then lower (4) first lower and then higher
Solution: This question deals with Doppler effect, as a source is approaching a stationary observer, the frequency observed will increase as the wave fronts are becoming closer and closer together while the wave fronts will spread apart as the source is moving away from the observer. Choice (3)
11 Which particles exhibit properties of waves in some experiments? (1) photons, only (2) electrons, only (3) both photons and electrons (4) neither photons nor electrons
Solution: Both photons and electrons exhibit wave properties as they can both be diffracted. Choice (3)
12 The direction of the electric fi eld at a point in space is defi ned as the direction of the force exerted by the field on a (1) test mass located at that point (2) magnetic north pole located at that point (3) negative test charge located at that point (4) positive test charge located at that point
Solution: The direction of the electric field is the direction of the force exerted on a positive test charge. Choice (4)
13 A net force of one newton will (1) accelerate a 1-kg mass at 1.0 m/s2 (2) accelerate a 1-kg mass at 9.8 m/s2 (3) lift a l-kg mass vertically at a constant speed of 1.0 m/s (4) lift a 1-kg mass vertically at a constant speed of 9.8 m/s
Solution: Using Newton’s 2nd law, Fnet=ma , we can see that 1N of force will accelerate 1kg of mass by 1m/s^2. Choice (1)
14 The elongation of a spring will be quadrupled if the magnitude of the force elongating the spring is (1) quartered (3) doubled (2) halved (4) quadrupled
Solution:Using the formula Fs=Kx , when x quadruples, the F must quadruple as well. Choice (1)
15 The vector diagram below represents the path and distances run by a student in a cross-country race.
The displacement of the student from start to finish is (1) 1.40 km north (3) 5.00 km north (2) 1.40 km south (4) 5.00 km south
Solution: Displacement is a vector that connects the starting point to the end point. In this case, the end point is exactly 1.4km south of the starting point. Choice (2)
16 The diagram below shows the arrangement of three charged hollow metal spheres, A, B, and C. The arrows indicate the direction of the electric forces acting between the spheres.
What spheres have static charges of the same sign? (1) A and B, only (3) B and C, only (2) A and C, only (4) A, B, and C
Solution: A charge will attract an opposite charge or something neutral while it is always repelled by the same charge. Choice (2)
17 Two small charged spheres are located distance d from each other and experience an electrostatic force of attraction, Fe. If the magnitude of charge of each sphere is tripled and Fe is unchanged, what other change must have occurred? (1) The signs of both charges are changed. (2) The sign of only one charge is changed. (3) Distance d was increased by a factor of three. (4) Distance d was increased by a factor of nine.
Solution: Remember the formula for electrostatic force between point charges is , if both q1 and q2 were tripled and yet the F stayed the same, r must be tripled as well. Choice (3)
18 Compared to the resistance of an aluminum wire at 20°C, the resistance of a tungsten wire of the same length and diameter at 20°C is approximately (1) the same (3) one-half as great (2) twice as great (4) four times as great
Solution: from the table provided in the reference sheet, the resistance of aluminum should be ½ as great as the resistance of tungsten given that two objects have the same dimension. Choice (3)
19 How much energy is expended when a current of 5.00 amperes is in a 5.00 ohm resistor for 5.00 seconds? (1) 25.0 J (3) 625 J (2) 125 J (4) 3130 J
Solution: Using one of the Ohm’s laws, P=IV=I2R and the definition of power P=W/t, we can find the energy dissipated by the resistor by plugging in R=5Ω, t=5s and I=5A. We will get 25J. Choice (1)
20 The amount of electric current through an unknown resistor may be measured by connecting (1) an ammeter in series with the resistor (2) an ammeter in parallel with the resistor (3) a voltmeter in series with the resistor (4) a voltmeter in parallel with the resistor
Solution: To measure the current of a resistor, we must use an ammeter connected in series with the resistor. Choice (1)
21 Which phenomenon represents a wave spreading out behind a barrier as the wave passes by the edge of the barrier? (1) diffraction (3) refl ection (2) refraction (4) interference
Solution: The phenomenon where waves can pass through obstacles (such as a tiny hole) is called diffraction. Choice (1)
22 A 1.00 kilometer length of copper wire, A, with a cross-sectional area of 1.00 * 10−4 meter squared has a resistance of 0.172 ohm at 20°C. Another copper wire, B, is half as long and has twice the cross-sectional area of wire A. What is the resistance of copper wire B at 20°C? (1) 0.0430 Ω (3) 0.172 Ω (2) 0.0860 Ω (4) 0.344 Ω
Solution: Using the formula , if L is halved and A is doubled, the R is reduced by a factor of ¼. Choice (1)
23 The magnitude of electric force exerted on a small positive charge located between two oppositely charged parallel plates is (1) smallest near the positive plate (2) smallest near the negative plate (3) greatest midway between the plates (4) the same everywhere between the plates
Solution: The electric field between the parallel plates with the opposite charges is constant everywhere. Therefore the electrostatic force is constant everywhere between the plates as well. Choice (4)
24 An acoustic organ is a musical instrument with pipes. The oscillation of air molecules in the pipes of the organ produces sound waves that are (1) electromagnetic and longitudinal (2) electromagnetic and transverse (3) mechanical and longitudinal (4) mechanical and transverse
Solution: Organs produce sound waves which are mechanical (need the air molecules to propagate) and longitudinal. Choice (3)
25 Which list identifi es portions of the electromagnetic spectrum in order of increasing frequency? (1) gamma ray, infrared, visible, ultraviolet (2) ultraviolet, visible, infrared, gamma ray (3) infrared, visible, ultraviolet, gamma ray (4) gamma ray, ultraviolet, visible, infrared
Solution: Choice 3 is correct based on this chart. Choice (3)
26 A tuning fork is used to produce a sound wave having a frequency of 512 hertz. What is the wavelength of the sound wave in air at STP? (1) 0.646 m (3) 3.31 * 102 m (2) 1.55 m (4) 5.86 * 105 m
Solution: The formula for the speed of a wave is , the speed of sound given in the reference sheet is 331m/s. We can find the wavelength by dividing 331m/s by 512Hz. Choice (1)
27 An amplified sound wave produced by an opera singer shatters a glass. Which phenomenon best explains this event? (1) diffraction (3) refraction (2) reflection (4) resonance
Solution: The phenomenon where the amplitude of vibration is amplified when the object is vibrated at its natural frequency is called resonance. Choice (4)
28 The diagram below represents a wave traveling in a rope in the direction indicated.
Solution: We can find how the point P moves by back tracing along the wave against the direction of the wave. Choice (4)
29 If several resistors are connected in series in an electrical circuit, the potential difference across each resistor (1) varies directly with the resistance of each resistor (2) varies inversely with the resistance of each resistor (3) varies inversely with the square of the resistance of each resistor (4) is independent of the resistance of each resistor
Solution: When resistors are connected in series, they will have the same current. The potential difference across each one is given by Ohm’s law V=IR. Choice (1)
30 In medium X, light with a wavelength of 3.44 * 10−7 meter travels at 2.20 *108 meters per second. In medium Y, this light has a wavelength of 3.12 * 10−7 meter. What is the speed of this light in medium Y? (1) 2.00 * 108 m/s (3) 2.43 * 108 m/s (2) 2.20 * 108 m/s (4) 3.00 * 108 m/s
Solution: Remember that the frequency of the light stays the same no matter which medium you are in. Since the wavelength got shorter in medium Y, we expect Y to have a larger index of refraction than X and therefore a slower speed of light. Choice (1)
31 A nuclear reactor produces 2.7 * 1016 joules of energy per year. How much mass is converted to energy by the reactor in one year? (1) 0.30 kg (3) 9.0 * 107 kg (2) 0.90 kg (4) 2.4 * 1033 kg
Solution: We must use Einstein’s equation E=mc2 , we can obtain the mass by dividing the energy by speed of light in vacuum squared. m=0.3 kg. Choice (1)
32 The diagram below shows the initial charge and position of two identical conducting spheres on insulating stands.
Solution: Once the spheres come into contact with, the charges will evenly distribute between the two spheres. Choice (2)
33 An antimuon neutrino is a (1) lepton with a −le charge (2) lepton with 0 charge (3) meson with a −le charge (4) meson with 0 charge
Solution: An antimuon neutrino is the antiparticle of muon neutrino which happens to have zero charge (hence the same neutrino-little neutron) and is a lepton. Choice (2)
34 The graphs below show the displacement of a certain particle in a medium versus time due to two periodic waves, A and B, traveling through the medium.
The superposition of the two waves will cause the particle of the medium to have a maximum displacement of
(1) 1.0 m (3) 2.5 m (2) 2.0 m (4) 5.0 m
Solution: Wave A has an amplitude of 2m and Wave B has an amplitude of 3m, they are in phase so when they add, the amplitudes will add into 5m. Choice (4)
35 The diagram below represents a wire that is not part of a complete circuit, just above the poles of two magnets.
Moving the wire downward between the poles in the direction shown in the diagram will (1) induce an alternating magnetic fi eld between the poles of the magnets (2) induce a potential difference between the ends of the wire (3) decrease the wire’s resistivity (4) reverse the direction of the magnetic field
Solution: This scenario is where Faraday’s law becomes applicable. Choice (2)
36 Which graph best represents the motion of an object traveling at a constant positive velocity?
Solution: A constant positive velocity will have a graph of displacement vs time graph that is linearly increasing. Choice (1)
37 A cannonball is fi red with an initial velocity of 100. meters per second at an angle of 15.0° above the horizontal. What are the horizontal (vx) and vertical (vy) components of this velocity? (1) vx = 96.6 m/s, vy = 25.9 m/s (2) vx = 25.9 m/s, vy = 96.6 m/s (3) vx = 76.0 m/s, vy = 65.0 m/s (4) vx = 65.0 m/s, vy = 76.0 m/s
Solution: We can find the v_x by 100m/s *cos(30) and v_y by 100m/s*sin(30). Choice (1)
38 A 1200-kilogram car is moving at 10. meters per second when a braking force of 3000. newtons is applied. How much time is required to bring the car to rest? (1) 0.40 s (3) 25 s (2) 2.5 s (4) 4.0 s
Solution: The force of breaking will create an acceleration of 3000N/1200kg= 2.5m/s^2. Keep in mind that this acceleration should be negative and we can use the formula Vf= vi+at, where the final velocity =0m/s and initial velocity = 10m/s. t=4s. Choice (4)
39 Which graph best represents the relationship between the speed of light (f = 5.09 * 1014 Hz) in a transparent medium and the absolute index of refraction of the medium?
Solution: Formula for speed of light is v=c/n , n is inversely proportional to v so graph 1 is the right choice. Choice (1)
40 A student uses a string to whirl a 0.25-kilogram mass in a horizontal circular path that has a 0.80-meter radius. If the magnitude of the centripetal force exerted on the mass with the string is 25 newtons, the speed of the mass is (1) 2.8 m/s (3) 11 m/s (2) 8.9 m/s (4) 80. m/s
Solution: Use the formula , we can plug in 25N into Fc and 0.25kg into m and 0.8m into r. v= 8.94m/s. Choice (2)
41 A deuteron is formed by combining a proton and a neutron. The mass of a deuteron is 2.39 * 10−3 universal mass unit less than the combined masses of a proton and a neutron. This mass difference is equivalent to (1) 2.56 * 10−6 MeV (3) 2.39 MeV (2) 2.23 MeV (4) 2.15 * 1014 MeV
Solution: 1u = 931MeV. We can find the energy equivalent to this mass by doing 2.39*10^-3*931= 2.23MeV
42 A gravitational force of magnitude F exists between Earth and a satellite on Earth’s surface. The satellite is sent into orbit at a distance of three Earth radii above Earth’s surface, as shown in the diagram below.
Solution: Remember that the gravitational force is inversely proportional to square of r (distance between the centers of masses). The distance here increased bdy a factor of 4 so the force is only 1/16 of what it was on the surface of Earth. Choice (1)
43 As part of an investigation on quantization, a student measured and recorded the mass of fi ve identical containers, each holding a different number of pennies. The table shows the student’s data.
Based on the data, what is the most likely mass of one penny? (1) 3.2 g (3) 9.6 g (2) 6.4 g (4) 12.8 g
Solution: The smallest difference between the masses of the boxes is 3.2g so that should be the most likely number. Choice (1)
44 Which graph represents the relationship between the frequency and period of a wave?
Solution: Frequency and period are inversely proportional to each other so graph 4 is correct. Choice (4)
45 What is the current in a conductor if 3.15 * 1018 electrons pass a given point in the conductor in 10. seconds? (1) 0.050 A (3) 0.50 A (2) 2.0 A (4) 0.20 A
Solution: , the charge is 3.15*10^18*1.6*10^-19= 0.504C. I should be 0.504C/10s = 0.0504A. Choice (1)
46 A particle with a charge of +3.0 nanocoulombs is placed in an electric fi eld with a magnitude of 1500 newtons per coulomb. What is the magnitude of the electrostatic force exerted on the particle by the electric field? (1) 4.5 * 10−6 N (3) 4.5 * 1011 N (2) 5.0 * 102 N (4) 5.0 * 1012 N
Solution: Use the formula E=F/q, we can find the force by letting q = 3*10^-9 C and E = 1500N/C. F= 4.5*10^-6N. Choice (1)
47 The graph below represents the motion of an airplane that starts from rest and takes off from a straight runway.
Which quantity is represented by the slope of the graph? (1) total distance traveled (3) average speed (2) displacement (4) acceleration
Solution: For velocity vs time graph, the slope represents the acceleration. Choice (4)
48 The diagram below represents two horizontal platforms that are at different heights above level ground. A ball rolls off the taller platform with a horizontal speed of 15 meters per second and travels through the air, landing on the top of the shorter platform.
What is the total time the ball is in the air? [Neglect friction.] (1) 0.16 s (3) 0.70 s (2) 0.49 s (4) 1.1 s
Solution:
49 Four mechanical waves are created in the same medium over the same time interval. Which diagram represents the wave that transfers the greatest amount of energy?
Solution: Energy of a wave is proportional to the amplitude squared. Graph 2 has the greatest amplitude. Choice (2)
50 Which diagram represents a light ray increasing in speed as it travels from one medium to another?
Solution: If the speed of light increased after going into the 2nd medium, that must mean that the index of refraction is smaller. Based on Snell’s law, it must mean that the angle of refraction is bigger than the angle of incidence. Choice (3)
1 The human body maintains a balanced internal environment. In order to accomplish this, (1) organelles work independently (2) all cells have the same shape and function (3) insulin is produced when protein levels are low (4) stimuli are detected, and actions are taken
Solution: We can answer this by eliminating wrong answer choices. The correct answer is: Choice 1 = Organelles work together, not independently. Choice 2= Cells have different shapes and functions. Choice 3= Insulin responds to high blood sugar, not low protein. Choice 4= stimuli are detected, and actions are taken. This describes how the body maintains balance through homeostasis. Choice 4 is the correct answer
2 Wolves are important predators in some ecosystems. If wolves are removed from their environment, the ecosystem is in danger of becoming unstable due to (1) a reduction of autotrophs when the number of herbivores is not being kept in check by the wolves (2) a decrease in the number of herbivores because they will not be able to reach carrying capacity (3) an increase in the biodiversity of the remaining animal and plant species (4) some species of herbivores taking over the niche the wolves occupied
Solution: Choice 1 is the correct answer choice. Wolves help control herbivore populations. Without them, herbivores may overgraze plants (autotrophs), leading to ecosystem imbalance.
3 Which statement best explains how deforestation that is the result of forest fires can contribute to global warming? (1) Burning the trees adds smoke to the atmosphere and blocks sunlight. (2) Burning the trees adds carbon dioxide to the atmosphere. (3) Deforestation removes trees that produce carbon dioxide through the process of photosynthesis. (4) Deforestation immediately increases ecosystem stability needed in the burned area.
Solution: When trees burn, they release stored carbon as carbon dioxide, a greenhouse gas that contributes to global warming. Choice 2 is the correct answer. The other choices are incorrect because: Deforestation decreases, not increases, ecosystem stability. Smoke may block sunlight temporarily, but it does not cause global warming. Trees absorb carbon dioxide during photosynthesis; they don’t produce it.
4 For centuries, humans have built dams along rivers to redirect water for power, irrigation, and transportation. Dams can prevent migrating fish from swimming upstream to reproduce and can also disrupt the flow of sediments and nutrients. Communities are starting to eliminate some dams, and the health of the river ecosystems is being restored. This best illustrates that (1) technological advances often involve environmental trade-offs (2) when humans modify their environment it always has effects that cannot be reversed (3) industrialization has had a positive effect on the health of river ecosystems (4) the construction of dams affected abiotic factors in the river but not biotic factors
Solution: Building dams provides benefits like power and irrigation but can harm ecosystems. Removing dams shows efforts to reverse those impacts, highlighting the trade-offs between human needs and environmental health. The correct answer is 1. The other choices are incorrect because: Both biotic (fish, plants) and abiotic (sediment flow) factors are affected by dams. Some environmental effects can be reversed, as shown in the passage. The passage describes harm, not benefits, to river ecosystems from industrialization.
5 In humans, lactose is broken down into glucose and galactose in the presence of a particular enzyme. It is most likely that the enzyme that breaks down lactose (1) breaks down several other types of food in the stomach (2) is involved in other reactions when the temperature and pH are ideal (3) helps in the synthesis of complex sugars during autotrophic nutrition (4) is not involved in other types of reactions because enzymes are specific
Solution: Enzymes are highly specific and usually work on only one type of substrate. The enzyme that breaks down lactose is lactase, and it specifically breaks down lactose only. The correct answer is 4. The other choices are incorrect because: Humans are not autotrophs and do not synthesize sugars through autotrophic nutrition. Enzymes are not typically responsible for breaking down many different substances. Temperature and pH affect enzyme activity but don’t change their specificity.
6 The Tdap vaccine can protect adolescents and adults from the serious bacterial diseases tetanus, diphtheria, and pertussis. Another vaccine, called Td, protects against tetanus and diphtheria, but not pertussis. Td does not protect against pertussis because the (1) Tdap vaccine is given to treat pertussis (2) Td vaccine does not contain the antibodies from pertussis to fight the bacteria (3) Tdap vaccine contains a small amount of the bacteria that causes pertussis (4) Td vaccine does not stimulate the immune system of people to recognize pertussis antigens
Solution: Vaccines work by exposing the immune system to antigens from specific pathogens. Since the Td vaccine does not include pertussis antigens, it does not trigger an immune response against pertussis. The correct answer is 4: The other choices are incorrect because: The Tdap vaccine contains inactivated parts of the pertussis bacteria, not live bacteria. Vaccines are used to prevent, not treat, disease. Vaccines contain antigens, not antibodies.
7 Pelagic red crabs living on the ocean floor have been found to eat small bits of plastic. When they are consumed, these small creatures are passing the plastics along the food chain to predators, including fish consumed by humans.
This is of concern because it (1) decreases plastic recycling by primary consumers (2) increases the risk of harmful substances in our food supply (3) decreases the producers in the ecosystem (4) increases the biodiversity of the ocean
Solution: When small ocean animals like pelagic red crabs eat plastic, those plastics can move up the food chain, potentially reaching humans and harming health. The correct answer is 2: The other choices are incorrect because: Plastic pollution harms biodiversity; it doesn’t increase it. Animals do not recycle plastic. Plastic consumption by animals doesn’t directly reduce producers like algae or plants.
8 Duckweed is a small plant that grows on the surface of still bodies of water. Over a nine-week period, scientists monitored the growth of duckweed in three ditches located on the same farm. The number of duckweed plants increased rapidly during weeks one and two. After two weeks, each ditch was completely covered with a layer of duckweed and remained covered for the remaining seven weeks. A valid conclusion based on the data collected over this nine-week study is that (1) animals that eat duckweed have the greatest effect on duckweed population size (2) duckweed populations die off after completing a two-week life cycle in the ditch (3) only changes in temperature affect duckweed population size (4) the size of the duckweed population is kept stable by limited resources in the ditch
Solution: After rapid growth, the population stabilized because the ditch became fully covered, meaning space, nutrients, or other resources became limited, preventing further growth. The correct answer is 4
9 Which statement explains why the organisms in some ecosystems, such as rainforests, deserts, and oceans, are different from each other? (1) The living organisms in each ecosystem have different needs and produce the physical conditions that they require. (2) Each ecosystem contains different types of living organisms that change each of the physical conditions present there. (3) They all have the same physical conditions present, but the living organisms use them in different ways. (4) Each ecosystem contains different physical conditions that determine the type of living organisms present there.
Solution: Different ecosystems (like rainforests, deserts, and oceans) have unique conditions such as temperature, moisture, and light, which influence what organisms can live there. The correct answer is 4 The other choices are incorrect because: Physical conditions are not the same across all ecosystems. Physical conditions influence organisms more than organisms create those conditions. Organisms may influence conditions slightly, but they don’t determine the main physical features.
10 Some green plants secrete acids that dissolve rock, which makes it possible for the plants to absorb phosphorus needed for healthy plant growth. In addition to phosphorus, plants require many other substances. Which substances are required for the production of carbohydrates in green plants? (1) oxygen and nitrogen (2) carbon and glucose (3) carbon dioxide and water (4) hydrogen and starch
Solution: Green plants use carbon dioxide and water during photosynthesis to produce carbohydrates. The correct answer is 3
11 Which statement about competition in ecosystems is correct? (1) Organisms compete most when they occupy different niches and resources are plentiful. (2) Individuals need not compete, because resources such as water and food are always plentiful in ecosystems. (3) Organisms that compete successfully will survive, reproduce, and pass their traits on to their offspring. (4) Competition usually results in the extinction of a species, ensuring the survival of other species
Solution: Successful competition helps organisms survive and reproduce, influencing natural selection. The correct answer is 3. The other choices are incorrect because: Competition rarely causes immediate extinction; it usually affects population sizes over time. Competition is strongest when organisms share the same niche and resources are limited. Resources are not always plentiful; competition often occurs due to scarcity.
12 Human body systems interact with each other. The list below illustrates the results of one body system functioning normally. • Muscle cells receive oxygen. • Nerve cells receive glucose. • Lungs get rid of carbon dioxide. • Some gland cells send chemical signals to organs. Which body system most directly enables all these functions to occur? (1) circulatory system (2) excretory system (3) digestive system (4) immune system
Solution: The circulatory system transports oxygen, glucose, carbon dioxide, and chemical signals throughout the body, enabling these functions. The correct answer is 1
13 The Himalayan rabbit lives in the cold Tibetan mountains. It typically has white fur on its body and black fur on its outer extremities, such as the ears, nose, feet, and tail.
A scientist shaved a patch of white fur off the back of a Himalayan rabbit and applied an ice pack to the area for 30 minutes. The fur in the shaved area grew in black. The best explanation for why black fur grew in the shaved area is that (1) the food the rabbit ate during the experiment influenced fur color (2) the fur in the newly shaved area was younger than the white fur on the rest of the body (3) the ice pack caused a mutation in the genes that regulate fur color (4) warm and cold temperatures activate different genes for fur color
Solution: Himalayan rabbits have fur color that depends on temperature. Cooler areas grow darker fur, while warmer areas grow lighter fur. The ice pack cooled the shaved area, causing black fur to grow. The correct answer is 4
14 Researchers have identified a mutually beneficial relationship between some plant species and specific fungi. The fungi increase the nutrient uptake for these plants, and the plants provide nutrition to the fungi. In order for this relationship to occur, the plant must produce a particular protein. Scientists hope to enable plants that normally do not interact with these fungi to obtain the benefits that the plant-fungi relationship offers. In order to make this possible, which process would scientists most likely use? (1) Treat the plants with chemical fertilizers to stimulate their growth. (2) Provide the fungi with the same molecular bases that are found in plant protein. (3) Identify the gene that codes for the protein and introduce it into plant cells by genetic engineering. (4) Selectively breed a new type of fungus that does not require the nutrients that the plants provide.
Solution: This process would allow plants that don’t normally interact with the fungi to produce the necessary protein and form the beneficial relationship. The correct answer is 3
15 Milkweeds are plants that produce toxic, bitter- tasting chemicals. Some insects have developed the ability to safely feed on milkweed. They accumulate some of the toxin in their bodies, causing them to taste bitter to other animals that may try to eat them. As a result, most animals avoid eating these insects. A possible explanation for this relationship is that (1) eating a toxic plant increases the ability of these insects to survive and reproduce (2) milkweed populations are controlled by many insects (3) the milkweed benefits from the insects that can tolerate the toxin they produce (4) eventually the insects will become immune to the toxin
Solution: By feeding on toxic milkweed and accumulating its toxins, these insects become less likely to be eaten by predators, improving their chances of survival and reproduction. The correct answer is 1 The other choices are incorrect because: The insects tolerate the toxin but becoming immune is not the main point here. The passage doesn’t indicate milkweed populations are controlled by insects. Milkweed does not benefit from insects that tolerate its toxin; often, herbivory harms plants.
16 Which type of cell engulfs pathogens and marks them for killing? (1) red blood cell (3) nerve cell (2) white blood cell (4) muscle cell
Solution: White blood cells engulf pathogens and help mark them for destruction to protect the body from infections. The correct answer is 2 Red blood cells-Carry oxygen from the lungs to body tissues and transport carbon dioxide back to the lungs for removal. Nerve cells (neurons)- Transmit electrical signals throughout the body to enable communication between the brain, spinal cord, and other parts. Muscle cells -Contract and relax to produce movement in the body.
17 Which choice below best completes the diagram with a correct label and definition for the box labeled X?
(1) cell: the basic structural, functional, and biological unit (2) organ: a group of tissues with a common function (3) tissue: a group of cells with a similar structure and function (4) organ system: a collection of organs with a common function
Solution: To solve the question, let’s analyze the diagram step by step: The first image is of organelles. The next image is of a cell. Then comes a box labeled X. Following that is an organ (such as the stomach or intestines). Finally, there is a human body showing an organ system (digestive system).We are looking for what comes between a cell and an organ. That would be:X = tissue, which is defined as a group of cells with a similar structure and function. Choice 3 is the correct answer.
18 Concern is rising that mass extinctions of many species may increase. In the graph below, the risk of extinctions is shown to have risen rapidly from 1850 to 2014.
This loss of different species is a concern because it may (1) lead to an increase in diversity in the ecosystem (2) impact the energy flow and food supply within an ecosystem (3) produce increased nonrenewable resources (4) provide additional sources of potential medicines
Solution: The loss of different species is a concern and something negative. We can eliminate choices 1, 2 and 3 because those are positive. Choice 2 is the correct answer.
19 The American Museum of Natural History has an exhibit called the Ecosystem Sphere. It is a huge glass globe that was assembled in 1999. Populations of algae, bacteria, and little shrimp were sealed with water and air inside. The Ecosystem Sphere is kept in a well-lit area. Although the sphere has never been opened, groups of each kind of organism are still alive inside it. The most likely reason for this is because the populations have (1) remained in separate areas of the sphere and do not interact (2) adapted so that they do not require food (3) a constant source of energy because they cannot recycle gases and materials (4) a constant source of energy and recycle gases and materials
Solution: The Ecosystem Sphere is a closed system—no matter or organisms enter or leave, but energy (like sunlight) can still pass through. In such an environment, for life to persist: Energy must be constantly available, usually from light (which powers photosynthesis by algae). Gases and materials must be recycled. For example, algae produce oxygen through photosynthesis, which the shrimp and bacteria use. In turn, these organisms produce carbon dioxide and waste, which the algae use again. This balance of energy flow and nutrient cycling is what allows the organisms to survive over time without needing anything added or removed from the sphere. Choice 4 is the correct answer.
20 Ebola is a deadly viral disease. Victims of Ebola suffer from massive blood loss and organ failure. Researchers are testing a vaccine on people who have not yet been infected by Ebola, but live in high-risk areas. The vaccine must be given to the subjects before exposure to Ebola because (1) the vaccine will mutate the virus when a person gets infected (2) if a subject is infected with Ebola, it will destroy the vaccine (3) vaccines stimulate the subject’s immune system to react to future exposure to the virus (4) vaccines are only effective for a few days, so the patient must get the vaccine before exposure
Solution: Vaccines are always given before exposure to the virus in order to teach the immune system how to react to future exposure. Choice 2 is the correct answer.
21 A relatively large number of antibodies in a blood sample would most likely indicate that there is (1) an infection in the body (2) a mutation in the lung (3) a deficiency of carbon dioxide in the circulatory system (4) an insufficient amount of a specific vitamin in the diet
Solution: A large number of antibodies usually means the immune system is responding to an infection. The correct answer is 1
22 Ultraviolet light can alter the DNA segments of genes in the skin cells of an individual. Which statement best describes a direct result of these alterations? (1) Any cells produced from the altered skin cells will have the same alterations. (2) All the offspring of the individual will have the same skin cell alterations. (3) These alterations will spread to all the other cells in the body. (4) The sex cells of the individual will have the same alterations.
Solution: Because the DNA change is in skin cells (somatic cells), only the daughter cells from those skin cells will carry the alterations. Offspring and other body cells won’t be affected unless the mutation occurs in sex cells. The correct answer is 1
23 The energy required to assemble proteins and fats is directly supplied to body cells from (1) all the colors of visible light (2) molecules of ATP contained within the cells (3) all the DNA found in sex cells (4) molecules of carbon dioxide produced by chloroplasts
Solution: ATP is the primary energy-carrying molecule in cells. It provides the energy needed for many cellular processes, including the assembly of proteins and fats. Choice 2 is the correct answer.
24 There are over 200 different cell types in the human body. Each type of cell is specialized to carry out a particular function, but they all developed from the same single cell. This is because each type of cell (1) contains different genes than the other types of cells (2) destroys the genes found in the other types of cells (3) expresses some genes not expressed in the other cell types (4) lacks the genes found in the other cell types
Solution: All cells in the human body (except some like red blood cells) contain the same DNA. What makes different cell types specialized is gene expression — different cells turn on (express) different sets of genes depending on their function. For example, a muscle cell expresses genes that produce muscle proteins, while a nerve cell expresses genes that help it transmit signals. They do not destroy or lack the genes found in other cells; they just use different parts of the same genetic code. The correct answer is 3.
25 Coral reefs are vital components of marine ecosystems. They provide shelter and nutrition to many organisms that live on or in them. Some coral reefs in the Pacific Ocean are heavily polluted with plastic objects that provide surfaces where disease-causing microbes are able to grow.
If the amount of plastic present on coral reefs continues to increase, it is likely that the (1) coral will adapt to the presence of the plastic and thrive (2) microbes will adapt to living directly on the coral (3) algae that live on the reef will begin to decompose the dying coral (4) species dependent on the coral will be negatively impacted
Solution: Increasing plastic pollution harms coral reefs, which disrupts the habitat and food sources for many species that depend on them. The correct answer is 4
26 Enzymes, antibodies, and receptor molecules all have different functions. However, they are alike in that they (1) all are involved in cellular respiration (2) have a shape that is specific to their function (3) are classified as carbohydrates (4) are important in animals but not plants
Solution: Enzymes, antibodies, and receptor molecules all have specific shapes that allow them to perform their unique functions effectively. The correct answer is 2
27 Australian quolls are endangered mammals. One factor causing the death of many quolls is that they occasionally consume cane toads, which are poisonous. Scientists have identified a gene that some quolls possess that makes them avoid eating cane toads. By selectively breeding quolls with the “toad-avoiding gene” with other quolls who lack the gene, scientists found that all of the hybrid offspring inherited the survival gene.
Before the survival gene could be passed on to any offspring, the genetic material present in the parent with the “toad-avoiding gene” would have to be (1) mutated to become a different gene (2) accurately replicated (3) genetically engineered (4) changed through recombination
Solution: For a gene to be passed to offspring, the genetic material must be accurately copied during cell division so the gene remains unchanged. The correct answer is 2
28 Scientists have cloned many animals, such as cows, sheep, and chickens, from a single cell. Which natural process is most similar to these cloning techniques? (1) asexual reproduction (2) genetic recombination (3) chromosome mutations (4) gamete production
Solution: Cloning from a single cell is similar to asexual reproduction, where offspring are genetically identical to the parent because they come from one cell without combining genetic material from two parents. The correct answer is 1.
29 Within a sexually reproducing species, the correct chromosome number is maintained by (1) halving the chromosome number in gamete production, followed by fertilization (2) doubling the chromosome number in gamete production, followed by fertilization (3) halving the chromosome number during mitosis, followed by differentiation (4) doubling the chromosome number during mitosis, followed by differentiation
Solution: Meiosis halves the chromosome number in gametes, and fertilization restores the full chromosome number in the offspring. The correct answer is 1
30 The ability of sea otters to find food can be reduced because the environment where they search for food is often dark and murky. It has been recently discovered that the surface of otters’ paws are able to quickly detect a difference of one-quarter of a millimeter when comparing the size of objects, including food sources.
The special characteristics of the otters’ paws can be described as (1) a variation that eliminates the need for other senses otters normally possess (2) a variation that is unlikely to be passed on to offspring because it is not a genetic trait (3) an adaptation that could provide an advantage over the other organisms that they compete with for food (4) an adaptation that is most likely the result of a mutation in body cells of the ancestors of the otter
Solution: Special characteristics that improve an organism’s ability to survive and compete for resources are adaptations that give it an advantage. The correct answer is 3
Part B–1
31 Catalase is an enzyme produced by organisms that breaks down hydrogen peroxide, releasing oxygen and water. The relative enzyme activity, when tested at different temperatures, is shown in the graph below.
Which statement below best explains the decrease in activity of catalase after 35ºC shown in the graph? (1) The structure of the enzyme changes, which slows down the reaction. (2) There is no hydrogen peroxide left for the activity to continue, so it stops. (3) The raw materials permanently bind to the catalase, preventing the reaction. (4) The reaction is no longer needed for survival of the individual.
Solution: Enzymes like catalase have a specific 3D shape that allows them to function. When the temperature goes beyond an optimal level (in this case, around 35ºC), the enzyme starts to denature—its structure changes. This alters the shape of its active site, reducing its ability to bind to hydrogen peroxide and slowing or stopping the reaction. The correct answer is 1
32 Using a microscope, a student observed four different types of cells. For each structure he observed, he placed an X in the chart below to indicate the cells where the structure was observed.
Which of the cells he viewed were most likely from heterotrophs? (1) A and C (3) C and B (2) B and D (4) D and C
Solution: To determine which cells are most likely from heterotrophs, we need to find the ones that do not have chloroplasts, because chloroplasts are used for photosynthesis, a process autotrophs (like plants and algae) use to make their own food. Looking at the chart:
Cell A has chloroplasts → autotroph
Cell B has chloroplasts → autotroph
Cell C does not have chloroplasts → possible heterotroph
Cell D does not have chloroplasts → possible heterotroph
The correct answer is 4.
Part B–1
33 Coleus is a type of plant that has many variations in its leaves. Many coleus plants have chloroplast-rich areas on the edge of the leaf. Other areas in the middle lack chloroplasts. A student exposed the coleus leaf to sunlight. Later, starch indicator was added to the entire leaf. The diagram below shows the result of the experiment
Which statement is a valid claim, supported by evidence from this experiment? (1) Chloroplasts are necessary for the production of starch indicator. (2) Starch indicator causes leaves to produce oxygen. (3) Chloroplasts are necessary for the production of starch. (4) Water is necessary for the production of starch.
Solution: The parts of the coleus leaf that had chloroplasts (the green, outer edges) tested positive for starch after exposure to sunlight. The parts without chloroplasts (usually in the center, which might be white or another color) did not show starch presence. This indicates that starch is only produced where chloroplasts are present, showing that chloroplasts are necessary for photosynthesis, which produces glucose, later stored as starch. The correct answer is 3
34 Breathing vapors produced by e-cigarettes has caused respiratory problems, including coughing, shortness of breath, difficulty breathing, and even some deaths. Medical experts are warning the public and discouraging the use of these devices. The medical issues associated with vaping are an example of (1) organ malfunctions caused by personal behaviors (2) feedback response maintaining homeostasis (3) inherited disorders resulting from inhaling vapors (4) the effects of infectious parasites carried by the vapors
Solution: The correct answer is 1. Vaping is a personal behavior (a choice made by an individual). The health issues like coughing, shortness of breath, and even death are organ malfunctions, particularly of the respiratory system. These problems are not inherited, not caused by parasites, and do not represent a feedback mechanism to maintain homeostasis.
35 The chart below lists some organisms found in a New York ecosystem and their sources of energy.
When constructing an energy pyramid of this ecosystem, which of these organisms would be placed at the top of the pyramid? (1) grasses (3) heron (2) carp (4) leopard frog
Solution: An energy pyramid represents the flow of energy through a food chain, with producers at the base and top predators at the top. Heron eats carp, frogs and salamanders and should be on top. Choice 3 is the correct answer.
Base your answer to question 36 on the information and graph below and on your knowledge of biology. An unusually cool and wet spring prevented certain farmers from planting corn at the usual time. They normally planted their crop on May 1, but the altered weather patterns delayed planting until June 1.
36 Based on the information given, what is the most likely impact of the delayed planting on the production of corn? (1) Corn yield will remain at 100% because higher temperatures in June will make plants grow faster. (2) The corn yield may be reduced by about 20% because of the delay in planting. (3) Corn yield may be reduced by about 80% because of the delayed planting. (4) Crops planted on June 1 will have the same yield as those planted on April 1.
Solution: The farmers delayed planting corn from May 1 until June1 . Looking at the chart on around May 5 , we are at a 100% yield and June 4th at 75%. Choice 2 is the correct answer.
37 An ecologist is studying the biodiversity of beetle species in four different habitats. She counted the number of individuals of each species she observed in each habitat. The results are shown in the data table below.
Which of these habitats displays the most biodiversity of beetle species? (1) Habitat W (3) Habitat Y (2) Habitat X (4) Habitat Z
Solution: Let’s look at each habitat to see how many different beetle species it contains. Habitat W contains C and D only. Habitat X contains all of the species listed. Habitat Y contains only C and habitat Z contain A,D, E. Choice 2 is the correct answer.
38 Hummingbirds, with their long beaks and tongues, are attracted to long, tubular flowers with a lot of nectar. When a hummingbird consumes the nectar from a flower, pollen sticks to the hummingbird and is transferred when the hummingbird feeds from other flowers
This relationship between the flowers and hummingbirds is a result of (1) changes in hummingbirds and flowers in response to their needs (2) inheritance of characteristics acquired during their lifetime (3) natural selection of beneficial variations (4) the environment modifying gene expression
Solution: The relationship between hummingbirds and flowers is an example of coevolution, where both species have developed traits that benefit each other over time. Hummingbirds with longer beaks could access more nectar, and flowers that attracted hummingbirds had better chances of being pollinated. These beneficial traits were passed on through natural selection, not through needs or acquired characteristics. The correct answer is 3
39 The kittens in the photograph below were all born in the same litter.
One possible reason that they all have different fur colors and patterns is that (1) different kittens inherited more chromosomes from one parent than the other (2) there was a random resorting of genes during gamete formation in each parent (3) because there were so many, they did not receive the same amount of nutrients from the mother (4) there were pH differences depending on where in the uterus each kitten developed
Solution: During the formation of eggs and sperm (gametes), chromosomes undergo a process called independent assortment and crossing over, which randomly reshuffles genes. This results in offspring inheriting different combinations of genes, leading to variations in traits like fur color and patterns. This genetic variation explains why kittens from the same litter can look different. The correct answer is 2.
A study was done to determine the effect of a temperature increase on an ocean ecosystem. Panels equipped with heating elements were placed on the ocean floor 50 feet below the surface in the Antarctic Ocean. Some of the panels were heated so that they were 1ºC warmer than the water surrounding them. Others were heated to be 2ºC warmer, and some were not heated. Over a period of nine months, the researchers returned to the site and documented the changes in marine life they observed. They noted that 1ºC of warming resulted in a substantial change in marine life. One species of invertebrate grew rapidly and became the dominant species. It replaced multiple other species typically present in the area. The results were less consistent on the panels that were 2ºC warmer than the water surrounding them. The photographs on the right show the results observed on the three sets of panels.
40 Based on this experiment, one result of the future warming of the Antarctic Ocean could be (1) an increase in the stability of the Antarctic ecosystem (2) the disruption of existing Antarctic marine food webs (3) marine organisms evolving more rapidly in order to compete for resources (4) the need to import predators to eat the tiny invertebrates
Solution: The experiment showed that even a small increase in temperature (1ºC) caused one species of invertebrate to grow rapidly and replace multiple other species. This kind of shift in species dominance can disrupt existing food webs because the balance between predators, prey, and competitors changes. Such disruptions can affect the whole ecosystem’s stability and function. The correct answer is 2.
41 A possible explanation for the differences observed on the panels is that (1) the growth of organisms is dependent on the abiotic factors present in the environment (2) on the warmer panels, organisms reached carrying capacity more rapidly and completely died out (3) on the control panels, wastes built up, poisoning some of the organisms growing there (4) on the warmer panels, there were fewer decomposers present to recycle available energy
Solution: Abiotic factors include non-living environmental conditions like temperature. The experiment showed that even small changes in temperature affected which species thrived or declined. This means that organism growth is influenced by abiotic factors such as temperature, which can change the community composition. The correct answer is 1.
42 These test panels provided scientists with information about (1) how ecological niches influence the rate of mutation (2) the effect of environmental change on the biodiversity of the Antarctic Ocean (3) the variety of producer/consumer relationships in the Antarctic Ocean (4) how the stability of an ecosystem is affected by competition and disease
Solution: The experiment tested how small temperature increases (an environmental change) affected the types and abundance of marine species living on the panels. This directly relates to how environmental change impacts biodiversity—the variety and abundance of species—in the Antarctic Ocean. The correct answer is 2.
43 The kakapo is a small, flightless parrot. Currently there is a small population of kakapos living on four islands off the coast of New Zealand. Scientists are concerned that the kakapo may become extinct due to the introduction of predators and recent infections that have drastically reduced the already small population. During their conservation attempts, scientists made an interesting observation: When food is plentiful, more male offspring survive. Scientists provided the illustration below to explain this observation.
If scientists were going to test this hypothesis, the best way would be to select a test group and develop a research plan that includes collecting data when (1) all of the kakapos are fed a reduced amount of food (2) all of the kakapos are fed an unlimited amount of food (3) the kakapo test group is divided in half, and one-half is fed unlimited food and the other a reduced amount of food (4) the entire test group of kakapos is fed one type of food for one month and a different type of food for the second month
Solution: To test the hypothesis about how food availability affects the survival of male offspring, you need a controlled experiment with at least two groups: one with plentiful food and one with limited food. This allows comparison to see if more males survive when food is abundant versus when it is scarce. The correct answer is 3.
1 Which pair of quantities are both scalar quantities? (1) speed and mass (2) speed and momentum (3) momentum and displacement (4) mass and displacement
Solution: A scalar quantity cannot be expressed as a vector such that it can be oriented at a certain angle (e.g. 45 degrees with respect to x-axis). Momentum and displacement are both vector quantities. On the other hand, mass is a scalar quantity and so is speed (not velocity). Therefore, the correct choice is A Choice (1)
2 In an attempt to get ketchup out of a bottle, a student takes off the cap, turns the bottle upside down, accelerates it downward, and then suddenly stops it. Ketchup is released from the open bottle because the ketchup doesn’t stop moving when the bottle does. The ketchup leaving the bottle illustrates (1) inertia (2) resistivity (3) resonance (4) mass being converted to energy
Solution: The phenomenon being described here is similar to the thrust felt by the driver when he/she suddenly stops the car. According to Newton’s 1st law, things in motion tend to remain in that motion. The reason drivers feel the thrust is because their bodies aren’t moving in the same frame as the car. The tendency to remain in whatever motion there had been called “inertia”. Choice (1)
3 The same net force is applied to object A and object B. The mass of B is three times greater than the mass of A. Compared to the acceleration of A, the acceleration of B is (1) the same (2) one-third as great (3) three times as great (4) one-ninth as great
Solution: According to Newton’s 2nd law, Fnet=ma. For the same Fnet, having 3 more times the mass will mean the acceleration is only 1/3 of the other. Choice (2)
4 What is the mass equivalent of 3.37 × 10−19 joule? (1) 1.26 × 10–54 kg (3) 1.12 × 10–27 kg (2) 3.74 × 10–36 kg (4) 5.08 × 1014 kg
Solution: This problem will require us to use the famous equation introduced by Einstein E=mc2 Choice (2)
5 Which object is in equilibrium? (1) Earth orbiting the Sun (2) a thrown baseball at its highest point above the ground (3) a car moving at a constant speed in a straight line (4) a bicycle skidding to a stop in a straight line
Solution: Something in equilibrium must have no unbalanced force and therefore it must be either stationary or moving at a constant velocity (not speed). While choice 1 seems promising, we must remember that when a planet is orbiting around the star, there is a centripetal force that’s keeping it in moving in a uniform circular motion. Choice 3 mentions that the object is moving at a constant velocity by saying that it’s moving at a constant speed in a linear manner. Choice (3)
6 A race car travels around a flat circular track at constant speed. The net force on the car acts (1) perpendicular to the car’s velocity and toward the center of the circle (2) perpendicular to the car’s velocity and away from the center of the circle (3) parallel to the car’s velocity and in the same direction as the velocity (4) parallel to the car’s velocity and in the opposite direction as the velocity
Solution: If something is undergoing uniform circular motion, the centripetal force must always be pointing towards the center of rotation and is always perpendicular to the velocity. Choice (1)
7 An object is traveling in a horizontal, circular path at a constant speed. If the radius of the path were doubled while the speed remained constant, the centripetal acceleration would be (1) quartered (3) halved (2) doubled (4) quadrupled
Solution: The formula for centripetal acceleration is . When you increase r by a factor of 2 while keeping the velocity the same, the centripetal acceleration is halved. Choice (3)
8 A 600.-newton student pushes on a vertical wall for 20.0 seconds with a constant force having a magnitude of 100. newtons. What is the magnitude of the force that the wall exerts on the student? (1) 0.00 N (3) 100. N (2) 5.00 N (4) 600. N
Solution: This is a problem that we must argue using Newton’s 3rd law, for every action force, there is an equal but opposite reaction force. The action force here is the 100N force that the student is pushing the wall with, so reaction must be also 100N. Choice (3)
9 An unbalanced force of 20. newtons is applied to a mass of 1.0 × 103 kilograms. After 10. seconds, the momentum of the mass will have changed by (1) 2.0 × 102 kg•m/s (3) 1.0 × 104 kg•m/s (2) 2.0 × 103 kg•m/s (4) 2.0 × 104 kg•m/s
Solution: Using the equation , we know that the mass had been rest before the force was applied so P_initial=0. Therefore, P_final=20N*10s=200 kg*m/s Choice (1)
10 To lift a heavy block off the floor, a student pulls with force F on a rope that passes over a pulley, as shown in the diagram below.
Solution:
11 Which graph best represents the relationship between the mass of an object and its distance from Earth’s surface?
Solution: Remember, mass is a quantity that does not depend on the distance with anything such as a planet (Earth). Choice (1)
12 A compass is placed near a strong bar magnet as represented in the diagram below.
Solution: Since opposite poles attract, the south pole of the compass needle will be attracted to the north pole of the bar magnet. Choice (3)
13 As Earth orbits the Sun in its elliptical orbit, the gravitational force between the Sun and Earth is (1) always attractive (2) attractive as the Sun and Earth get closer together and repulsive as the Sun and Earth get farther apart (3) repulsive as the Sun and Earth get closer together and attractive as the Sun and Earth get farther apart (4) always repulsive
Solution: The gravitational force is always attractive. Choice (1)
14 Which unit is used to measure the work per unit charge required to move a charge in an electric field? (1) ampere (3) volt (2) coulomb (4) watt
Solution: Using the equation V= W/q, the unit of W is joules, the unit of q is coulomb, and the unit of V is volt. Choice (3)
15 The diagram below shows a negatively charged sphere and a point, P, located within the electric field produced by the charge on the sphere.
The direction of the electric field at point P is
toward point (1) A (3) C (2) B (4) D
Solution: Remember that the electric field lines of a negative point charge must be radially pointing towards it. Choice (4)
16 Two point charges, q1 and q2, are initially a distance, d, apart. Which change will cause the greatest increase in the electrostatic force between the two point charges, q1 and q2? (1) double q1 (3) double d (2) halve q2 (4) halve d
Solution: Using the equation , if we halve the d, it will cause the force to quadruple whereas doubling d will cause it to be only ¼ of the original amount. On the other hand, if we double q1, it will only double the force and halving q2 will only halve the force. Choice (4)
17 The diagram below represents two identical conducting spheres.
Which statement could be the correct explanation
for the charge distribution on the spheres? (1) A small positively charged object is located between sphere A and sphere B. (2) A small negatively charged object is located between sphere A and sphere B. (3) A small positively charged object is located to the right of sphere B. (4) A small negatively charged object is located to the right of sphere B.
Solution: More positive charges are distributed to the inner sides of the spheres and since opposite charges attract, there must be a negative charge between spheres A and B. Choice (2)
18 The diagram below represents a circuit containing a battery, two operating lamps, A and B, and four closed switches, S1, S2, S3, and S4.
Which switch, when opened, causes both lamps to
turn off? (1) S1 (3) S3 (2) S2 (4) S4
Solution: Opening switch S1 will cause the currents through both light bulbs unable to come back to the battery. Choice (1)
19 What is the resistance of a 100.-watt bulb when operating a potential difference of 120. volts? (1) 1.20 W (3) 120. W (2) 100. W (4) 144 W
Solution: Using Ohm’s law, , we can solve for the resistance R easily by plugging 100W into P and 120V into V, R=144Ω. Choice (4)
20 The interaction that is most responsible for binding three quarks together in a proton is the (1) strong force (3) weak force (2) electromagnetic force (4) gravitational force
Solution: The force that is responsible for holding nucleons (protons and neutrons) and the constituents of nucleons (quarks) is always the strong force. Choice (1)
21 One example of a force doing work is the force exerted by (1) Earth on a high diver falling toward a pool from a platform above (2) a hook on an engine held stationary above a car (3) a frictionless horizontal air hockey table on a puck moving across the table at a constant velocity (4) a weightlifter on a barbell he holds motionless over his head
Solution: The force applied will always do work unless the direction of displacement and the direction of the applied force is perpendicular. Both situations described by choices 2 and 3 have displacement being perpendicular to the force. For choice 4, the situation is that while the weightlifter is simply holding the barbell, the displacement is zero, so no work is done by the applied force (force of holding the barbell). For choice 1, the applied force is the force of gravity, and it is always in the same direction as falling. Choice (1)
22 A ball falls freely from a rooftop to the street below. The ball starts from rest with 20. joules of gravitational potential energy with respect to the street. The total mechanical energy of the ball just before it hits the street is (1) 0 J (3) 10. J (2) 5.0 J (4) 20. J
Solution: The total mechanical energy of the system is always conserved unless there is an external force being applied. Choice (4)
23 Which statement describes the gravitational potential energy (PE), kinetic energy (KE), and internal (thermal) energy (Q), of a wooden crate as it is pushed across a level classroom floor at constant speed? (1) The PE decreases, KE remains the same, and Q decreases. (2) The PE increases, KE increases, and Q decreases. (3) The PE remains the same, KE decreases, and Q increases. (4) The PE remains the same, KE remains the same, and Q increases.
Solution: As a piece of wood is being pulled across a level floor with the same velocity, the PE (due to gravity) will remain constant since the height is not changed, KE will also remain constant since the velocity is constant. However, the Q will increase as there is a friction force acting opposite to the applied force. Choice (4)
24 The oscillation of electrons up and down a metal antenna produces waves. These waves are (1) mechanical and longitudinal (2) mechanical and transverse (3) electromagnetic and transverse (4) electromagnetic and longitudinal
Solution: A charged particle moving under acceleration will always emit electromagnetic radiation. Choice (3)
25 The diagram below shows an incident light ray reflecting from a plane mirror.
What is the angle of reflection?
(1) 96° (3) 48° (2) 84° (4) 42°
Solution:
26 A characteristic common to both sound waves and x rays is that they both (1) travel fastest in a vacuum (2) cause particles to vibrate in a direction parallel to the wave’s direction of motion (3) transmit energy without transmitting matter (4) are mechanical
Solution: Both sound waves and x-ray (EM wave) transmit energy without transmitting matters. Choice (3)
27 The diagram below represents a wave moving to the right through a rope.
Point P in the rope is moving toward the (1) top of the page (3) right (2) bottom of the page (4) left
Solution: If we try to trace back (opposite to the direction of the velocity of the wave) point P along the curve, we see that it must go up. Choice (1)
28 What is the wavelength of a 300.-hertz sound wave in air at STP? (1) 0.906 m (3) 3.00 × 102 m (2) 1.10 m (4) 1.00 × 106 m
Solution: Based on the reference table, the speed of sound is 331m/s and the formula we will use is where the f=300Hz. Solving for λ, we get 331/300=1.10m. Choice (2)
29 In the diagram below, a remote control is aimed at a television.
When the signal from the remote reaches the sensor on the television, the signal will most likely be (1) neither reflected nor absorbed (2) partially absorbed and partially reflected (3) completely reflected (4) completely absorbed
Solution: Under normal circumstances, it is extremely unlikely that an incident (signal emitted out of the remote control) is entirely reflected or absorbed. Choice (2)
30 Compared to waves of blue light traveling in a vacuum, waves of red light traveling in a vacuum have (1) a lower frequency and a lower speed (2) a lower frequency and the same speed (3) the same frequency and a lower speed (4) the same frequency and the same speed
Solution: All EM waves will travel at c=3*10^8 m/s in vacuum. However, the red light has a longer wavelength than the blue light. Longer wavelength will imply that it must have a smaller frequency. Choice (2)
31 Earthquakes often cause buildings between twelve and forty stories high to vibrate at an amplitude high enough to be destructive. Buildings are often designed to absorb this vibrational energy that might cause them to vibrate at their natural frequency. This tendency for an earthquake to cause a building to vibrate at a large amplitude is an example of (1) resonance (3) refraction (2) the Doppler effect (4) diffraction
Solution: When something is being vibrated at a frequency close to its natural frequency of vibration, the amplitude of vibration will keep increasing (e.g. shattering wine glass by voice). This phenomenon is called resonance. (Tacoma bridge https://www.youtube.com/watch?v=XggxeuFDaDU) Choice (1)
32 During the radioactive decay of a uranium-238 atom, a thorium-234 atom and an alpha particle are produced. During this process, there is conservation of (1) charge, only (2) mass-energy, only (3) both charge and mass-energy (4) neither charge nor mass-energy
Solution: During a nuclear reaction (nuclear fission in this case), both the charge and mass-energy must conserve. Choice (3)
33 An antiproton has a charge of
Solution: An antiparticle has the opposite properties as a regular particle. For a proton, the charge is e. So, an antiproton must have -1e. Choice (4)
34 Two pulses approach each other in the same medium. Which pair of pulses will result in the largest magnitude displacement of the medium as the pulses pass through each other?
Solution: Both choices 2 and 4 are ideal since the pulses are on the same side. However, the pulse going to the left in choice 2 is slightly more in amplitude so choice 2 should produce the greatest displacement of the medium Choice (2)
35 Two waves of the same wavelength interfere to form a standing wave pattern as represented in the diagram below.
Which point on the diagram represents a node? (1) A (3) C (2) B (4) D
Solution: A node is where the displacement of the medium is the smallest. Choice (4)
Part B–1
36 A round dinner plate has a diameter closest to (1) 2 × 10–2 m (3) 2 × 100 m (2) 2 × 10–1 m (4) 2 × 101 m
Solution: A dinner plate should have a diameter of a couple of inches. 1 inch = 2.54cm so it should be something around 20cm. Choice (2)
37 Several springs are lying on frictionless tabletops with one end attached to a wall and a variable force F applied to the free end of each spring. The springs have different spring constants, k. The diagram below shows the setup for one of the springs.
The elongation of the springs produced by force F depends (1) directly on both F and k (3) inversely on F and directly on k (2) directly on F and inversely on k (4) inversely on both F and k
Solution:
38 The table below shows the weight of four athletes (A, B, C, and D) and the time required for each athlete to run from the base of a hill to its top
Which athlete ran up the hill with the greatest average power? (1) A (3) C (2) B (4) D
Solution:
39 A copper wire carries 2.8 amperes of current. The total amount of charge that passes a point in the wire in 1.3 milliseconds is (1) 4.6 × 10–4 C (3) 3.6 C (2) 3.6 × 10–3 C (4) 2.2 × 103 C
Solution:
40 The diagram below represents four solid copper wire segments at 20°C with different lengths (L) and cross -sectional areas (A).
Which two segments have the same resistance? (1) A and B (3) B and C (2) B and D (4) A and D
Solution: Using the formula , we see that the resistance of a piece of wire is proportional to the length and inversely proportional to the cross-sectional area. For cylinder A, we see that it is both twice the length and the cross-sectional area of cylinder D. Therefore, cylinders A and D should have the same resistance. Choice (4)
41 In substance X, a ray of light with a frequency of 5.09 × 1014 hertz has a speed of 2.04 × 108 meters per second. Substance X could be (1) diamond (3) zircon (2) water (4) glycerol
Solution: We know the formula for EM wave in a medium is v=c/n, we can calculate the n, index of refraction, by dividing c by v. n=3*108/2.04*108=1.47. Looking up the reference table, this index of refraction is the same as that of corn oil or glycerol. Choice (4)
42 Which could not be the charge on a particle? (1) 3.2 × 10–19 C (3) 4.8 × 10–19 C (2) 4.5 × 10–19C (4) 6.4 × 10–19 C
Solution: Elementary charge = 1.6*10-19 C, a stable particle must always have the integer multiple of this charge. Choice 2 is the only choice which is an integer multiple of the elementary charge. Choice (2)
43 Which graph best represents the relationship between photon energy (Ephoton) and wavelength?
Solution: Using the formula for the energy of a photon, we know that . This indicates that the energy of a photon is inversely proportional to the wavelength. The graph that shows an inversely proportional relationship is 4. Choice (4)
44 Light travels from air into another medium with an index of refraction of n. The light has a wavelength of 6.0 × 10–7 meter in the new medium. Which expression represents the wavelength of this light in air
Solution: When an EM wave enters a medium, the frequency doesn’t change while the wavelength gets shortened by a factor of the index of refraction. Once the ray comes out of the medium, the wavelength will return to the original by being multiplied by a factor of n. Choice (1)
45 If 80. joules of electrical energy is dissipated by a 10.-ohm resistor in 2.0 seconds, the current in the resistor is (1) 5.0 A (3) 8.0 A (2) 2.0 A (4) 4.0 A
Solution: If the dissipated energy is 80 joules over 2 seconds, the power is 40 W. Using the formula P=IV=I2R, we can find the I. I=2A Choice (2)
Base your answers to questions 46 and 47 on the diagrams below, and on your knowledge of physics. The diagrams represent waves W, A, B, C, and D traveling through the same uniform medium.
46 Which wave has a period that is twice that of wave W? (1) A (3) C (2) B (4) D
Solution: Wave W completes two cycles over the length, if there is a wave that has twice the period, it must only complete one cycle over the length. Wave C Choice (3)
47 Which wave is always 180 degrees out of phase with wave W? (1) A (3) C (2) B (4) D
Solution: If a wave is 180 degrees out of phase with wave W, the crest of W must meet the trough of that wave and vice versa. Wave A. Choice (1)
48 Which graph best represents the relationship between acceleration and time for a freely falling object as the object falls near the surface of Earth?
Solution: Everything that is free falling on this planet (Earth) is subject to a gravitational acceleration of 9.81m/s^2 and it’s constant near the surface of Earth. Choice (3)
49 The diagram below represents the forces acting on a skydiver with his parachute.
The total mass of the skydiver with his parachute is 85.0 kilograms. If the magnitude of the gravitational force is 834 newtons, and the magnitude of the force of air friction is 652 newtons, the acceleration of the skydiver at the time shown is (1) 2.14 m/s2 up (3) 7.67 m/s2 up (2) 2.14 m/s2 down (4) 9.81 m/s2 down
Solution: Using Newton’s 2nd law, we know that Fnet=ma. In this case, Fnet=834-652=182N. Given that the mass of the skydiver is 85kg, we can calculate the acceleration by a=182N/85kg= 2.14 m/s2 down Choice (2)
50 A 15.0-gram air hockey puck sliding on a horizontal surface at a velocity of 7.00 meters per second north collides with a 15.0-gram air hockey puck traveling at a velocity of 8.00 meters per second south. The momentum of the system of pucks after the collision is (1) 0.0150 kg•m/s north (3) 0.225 kg•m/s north (2) 0.0150 kg•m/s south (4) 0.225 kg•m/s south
Solution: The total momentum of the system should be conserved after the collision so as long as we can calculate the total momentum of the system before the collision, we should be able to answer the question. Let’s take the north to be positive, Ptotal=0.015kg*7m/s-0.015kg*8m/s= -0.015kg*m/s. So the total momentum is to the south. Choice (2)
1 Which quantity is a vector? (1) electric field (2) electric potential difference (3) electric charge (4) electric power
Solution: A vector quantity must have both directions and magnitude. Although electric potential difference, electric charge and electric power can be positive or negative depending on the case, they cannot be pointed towards a specific direction such as 20 degrees above the x-axis. Therefore, the only choice is electric field. Choice (1)
2 What is the magnitude of the eastward component of the velocity of an airplane flying at 612 kilometers per hour in a direction 40.0° north of east? (1) 393 km/h (3) 799 km/h (2) 469 km/h (4) 952 km/h Solution:
612*cos40=469km/h Choice (2)
3 A car, initially traveling at 25 meters per second, is uniformly brought to rest as the brakes are applied over a distance of 40. meters. The magnitude of the average acceleration of the car while braking is (1) 0.31 m/s2 (3) 7.8 m/s2 (2) 0.63 m/s2 (4) 16 m/s2 Solution:
4 A brick starts from rest and falls freely from the top of a building to the ground. As the brick falls, its acceleration (1) increases and its speed increases (2) increases and its speed is constant (3) is constant and its speed increases (4) is constant and its speed is constant Solution: As everything that is free-falling on this planet, the brick would experience a downward acceleration of 9.8m/s^2. Since it was dropped instead of tossed up, the speed should be constantly increasing at a rate of 9.8m/s^2. Choice (3)
5 Which object has the greatest inertia? (1) a 0.10-kg baseball traveling at 30. m/s (2) a 70-kg sprinter traveling at 10. m/s (3) a 1000-kg car traveling at 50. m/s (4) a 2000-kg truck traveling at 20. m/s Solution: The word “inertia” practically means the tendency to resist being changed. In this context, the more massive an object is, the bigger the inertia. Choice (4)
6 An unbalanced force is always necessary to (1) keep a body at rest (2) keep a body moving with constant velocity (3) change the speed of a body (4) change the position of a body
Solution: According to Newton’s 2nd law, Fnet=ma. If there is an unbalanced force, Fnet is not going to be zero and therefore there will be an acceleration. Once there is an acceleration, there must be a change in either direction or magnitude of the velocity (speed). Choice (3)
7 Space probes launched from Earth send information back to Earth from space in the form of (1) mechanical waves (2) sound waves (3) longitudinal waves (4) electromagnetic waves Solution: Space probes require radio waves to communicate with the people on Earth, radio waves are a part of the spectrum of the EM waves. Choice (4)
8 A ball is thrown from level ground at an angle of 55° above the horizontal and lands on level ground. Neglecting friction, if the ball is thrown again at the same angle but with a larger initial speed, the ball will travel (1) higher and the same distance horizontally (2) to the same maximum height and farther horizontally (3) both higher and farther horizontally (4) to the same maximum height and the same distance horizontally
Solution: The range of a projectile only depends on two things: initial velocity and the angle it makes with the horizontal. Once the initial velocity is increased, the range will be increased. As for the maximum height, it depends on the initial vertical component of the velocity so it will be increased as well. Choice (3)
9 A photon collides with an electron, as represented in the diagram below
After the collision, the electron recoils and the photon is scattered in another direction with a longer wavelength than the incident photon. The increase in photon wavelength results because, during the collision, the photon (1) loses energy to the electron (2) gains momentum from the electron (3) loses some speed (4) generates a magnetic field
Solution:
10 What is the weight of a 60.0-kilogram student on the surface of Earth? (1) 0.164 N (3) 60.0 N (2) 6.12 N (4) 589 N Solution:
11 A 120-newton box is pulled by a 48-newton horizontal force across a horizontal surface at constant velocity. The coefficient of kinetic friction between the box and the horizontal surface is (1) 0.041 (3) 0.67 (2) 0.40 (4) 2.5 Solution:. Since the problem states that the box is being moved at a constant speed over a horizontal surface, we know that Fnormal = Weight = 120N and Ffriction = Fapplied = 48. µ=48N/120N= 0.4. Choice (2)
12 Box A has a mass of 10. kilograms and is at rest on a shelf that is 1.5 meters above the floor. Box B has a mass of 20. kilograms and is at rest on a shelf that is 3.0 meters above the floor. Compared to box A, box B has a gravitational potential energy relative to the floor that is (1) one fourth as great (3) twice as great (2) the same (4) four times as great Solution:. If an object is twice as massive and twice as high compared to another object, it will have 4 times as much of gravitational potential energy. Choice (4)
13 A 0.10-kilogram yo-yo is whirled at the end of a length of string in a horizontal circular path of radius 0.80 meter at a speed of 6.0 meters per second. The magnitude of the centripetal acceleration of the yo-yo is (1) 4.5 m/s (3) 23 m/s2 (2) 7.5 m/s2 (4) 45 m/s2
Solution:
14 A 4.0-kilogram mass is initially at rest on a horizontal, frictionless surface. A constant 2.0-newton force to the east is applied to the mass for a 5.0-second interval. As a result of this action, the mass acquires a (1) velocity of 10. m/s, east (2) velocity of 10. m/s, west (3) momentum of 10. kg•m/s, east (4) momentum of 10. kg•m/s, west
Solution:
The answer is obtained by multiplying 2N*5s=10Ns in the same direction as the force so to the east. Choice (3)
15 A motor lifts a 1.2 × 104-newton elevator 9.0 meters in 15 seconds. The minimum power output of the motor is (1) 8.0 × 102 W (3) 1.0 × 105 W (2) 7.2 × 103 W (4) 1.6 × 106 W
Solution: If the question is asking for the minimum power, the force exerted by the motor should be equal to the weight of the mass to be lifted. Choice (2)
16 A train blows its horn, which emits a uniform sound as the train approaches a stationary observer. The observer hears a sound that has a (1) lower frequency than the emitted sound and is decreasing in amplitude (2) lower frequency than the emitted sound and is increasing in amplitude (3) higher frequency than the emitted sound and is decreasing in amplitude (4) higher frequency than the emitted sound and is increasing in amplitude Solution: If a train is approaching an observer while blowing its horn, the frequency will appear to be higher as the train’s horn’s frequency undergoes Doppler effect. Since the loudness(amplitude) of the sound is inversely proportional to the distance squared, the amplitude will increase as the train approaches the observer. Choice (4)
17 A wood block is pulled at constant velocity across a horizontal wood floor. Which type of energy increases in this block-floor system as the block moves? (1) gravitational potential (3) mechanical (2) kinetic (4) thermal
Solution:As a piece of wood is pulled across the horizontal floor at a constant speed, it must mean that there is a friction force that is there to balance the applied force so that there is no acceleration. The friction between the floor and the wood will create heat energy. Choice (4)
18 A total energy of 5.0 joules is used to move an electron from position A to position B in a uniform electric field. What is the potential difference between positions A and B? (1) 3.1 × 1019 V (3) 3.2 × 10–20 V (2) 8.0 × 10–19 V (4) 3.1 × 1018 V Solution:
19 A 0.14-kilogram lacrosse ball, traveling west at 17 meters per second, is brought to rest with a 0.21-kilogram lacrosse stick. If the force applied by the lacrosse stick on the ball is 220 newtons east, the force applied by the ball on the stick is (1) 150 N east (3) 220 N east (2) 150 N west (4) 220 N west
Solution: According to Newton’s 3rd law, the action and reaction forces should be equal but opposite. If the action force is 220N to the east, the reaction must be 220N to the west. Choice (4)
20 Four wires are tested for electrical conductivity. All the wires have the same length and the same cross-sectional area, but are made of different metals. Which wire has the highest conductivity at 20°C? (1) aluminum (3) gold (2) copper (4) silver
Solution: Conductivity and resistivity are reciprocals of each other. Since silver has the lowest resistivity, it must have the highest conductivity. Choice (4)
21 The angle of incidence for a ray of light striking a plane mirror is 20º. What is the angle between the incident ray and the reflected ray? (1) 20º (3) 70 (2) 40º (4) 90 Solution: The ray will always be reflected at the same angle as the incident angle. So the angle of separation between the incident and the reflected rays is 40 degrees. Choice (2)
22 As shown in the diagram below, mass M slides across a level, frictionless surface with speed vi. The mass strikes a spring at position A, causing the spring to compress. When the mass is at position B, it is moving at a slower speed, vf.
Which statement best describes the energy conversion as the mass moves from position A to position B? (1) Some of mass M’s kinetic energy is converted to elastic potential energy. (2) All of mass M’s kinetic energy is converted to elastic potential energy. (3) Some of mass M’s kinetic energy is converted to gravitational potential energy. (4) All of mass M’s kinetic energy is converted to internal energy. Solution: As the mass is compressing the spring, it will slow down and whatever kinetic energy that is lost will be converted into the elastic potential energy of the spring. Choice (1)
23 The diagram below shows a magnetic compass placed between unlike magnetic poles.
The north pole of the compass needle will point toward (1) A (3) C (2) B (4) D Solution: A compass needle will always point towards the direction of the magnetic south pole so it will point towards point C. Choice (3)
24 Which circuit diagram contains a lamp that will not have current passing through it until switch S is closed?
Solution: For diagram 1, you cannot have an unbroken path between the battery and the lamp unless the switch has been closed so that is the only choice. Choice (1)
25 The diagram below represents an electric circuit.
Solution:
26 An object is thrown vertically upward with an initial velocity of 9.81 meters per second. What is the maximum height reached by the object? [Neglect friction.] (1) 1.00 m (3) 9.81 m (2) 4.91 m (4) 19.6 m
Solution: We know that the object momentarily comes to rest at the maximum height so vf=0. Let a=-9.81m/s^2, we can solve that the d=4.91m Choice (2)
27 Which type of photon has the least amount of energy? (1) ultraviolet (3) infrared (2) visible light (4) radio
Solution:
based on this diagram, the radio waves have the lowest frequency so the photons of radio waves must have the lowest energy. Choice (4)
28 A 7.5-kilogram object moving at 20. meters per second strikes a 60.-kilogram object initially at rest on a horizontal, frictionless surface. The two objects stick together and move off at a speed of (1) 0.33 m/s (3) 2.5 m/s (2) 2.2 m/s (4) 18 m/s
Solution: Using the principle of conservation of momentum, we can derive the formula for the momenta of the objects before and after the collision as
Choice (2)
29 How is the electrostatic force between two positive charges affected as the charges are brought closer together? (1) The force of attraction between them increases. (2) The force of repulsion between them increases. (3) The force of attraction between them decreases. (4) The force of repulsion between them decreases.
Solution:
The same charges always repel each other, as they are brought closer to each other, the force of repulsion increases. Choice (2)
30 What is one difference between magnetic forces and gravitational forces? (1) Magnetic forces are always attractive, whereas gravitational forces are always repulsive. (2) Magnetic forces are always repulsive, whereas gravitational forces are always attractive. (3) Magnetic forces may be attractive or repulsive, whereas gravitational forces are always attractive. (4) Magnetic forces may be attractive or repulsive, whereas gravitational forces are always repulsive.
Solution: The gravitational force is always attractive because we cannot have negative mass in the physics we know so far. However, the magnetic force can be either attractive or repulsive because the same poles repel, and opposite poles attract. Choice (3)
31 A sound wave passes through an opening in a brick wall as represented in the diagram below.
An observer standing behind the wall is able to hear the sound. This spreading out of the sound wave as it passes through the opening is an example of (1) interference (3) refraction (2) reflection (4) diffraction
Solution: Diffraction is a phenomenon where waves can spread around obstacles. Choice (4)
32 A sound wave is emitted by a vibrating tuning fork. What is transferred as the sound wave travels to a student’s ear? (1) mass, only (2) energy, only (3) both mass and energy (4) neither mass nor energy
Solution: Sound is a longitudinal wave where a group of air molecules become compressed or rarified (having low pressure), only packets of energy are travelled along with the wave instead of the matter (air molecules). Choice (2)
33 An electric current passing through a copper wire at constant temperature would result in (1) an increase in the resistivity of the wire (2) a decrease in the resistivity of the wire (3) the emission of protons from the wire (4) the production of a magnetic field around the wire Solution: Using the right hand rule, we know that there must be a magnetic field induced around a current-carrying wire (make a hitchhiker’s sign with your right hand, the thumb is the direction of the current while the rest of the fingers will be the direction of the magnetic field induced by the current). Choice (4)
34 The velocity of an object in uniform circular motion has a (1) constant magnitude and changing direction (2) constant magnitude and constant direction (3) changing magnitude and constant direction (4) changing magnitude and changing direction
Solution: In a uniform circular motion, the velocity’s direction is constantly being changed by the centripetal acceleration while maintaining its magnitude hence the word “uniform”. Choice (1)
35 Tuning fork A starts to vibrate at 320 hertz when it is held near tuning fork B, already vibrating at 320 hertz. Which phenomenon is exemplified by the action of tuning fork A? (1) the Doppler effect (3) diffraction (2) resonance (4) refraction
Solution: When an object is being vibrated close to its natural frequency of vibration, it will start vibrating with increasing amplitude at this frequency. This phenomenon is called resonance. Look up Tacoma Narrow Bridge collapse online for a video of this phenomenon. Choice (2)
Part B–1
36 A light ray with a frequency of 5.09 × 1014 hertz has a wavelength of 2.44 × 10–7 meter in diamond. The wavelength of this light ray in sodium chloride is (1) 1.55 × 10–7 m (3) 3.83 × 10–7 m (2) 2.44 × 10–7 m (4) 5.89 × 10–7 m
Solution:
37 The diagram below shows resistors R1, R2, and R3 connected to a 12-volt source.
The current flowing through resistor R3 is (1) 5.0 A (3) 0.50 A (2) 2.0 A (4) 0.20 A
Solution:The resistors are in series so they must all have the same current passing through them. Using Ohm’s law, we have V=IR. The total resistance of the whole circuit is 15+21+24=60Ω. The current can then be calculated as I=12V/60Ω=0.2A. Choice (4)
38 A charge of 25 coulombs moves past a point in a circuit in 2.5 seconds. What is the current at that point in the circuit? (1) 0.10 A (3) 50. A (2) 10. A (4) 63 A
Solution: Using the formula I=∆q/t, we can calculate the current by I=25C/2.5s = 10A Choice (2)
39 Which statement describes an object with constant kinetic energy? (1) A car accelerates along a straight road. (2) A runner decreases her speed along a curved path. (3) A bicycle travels around a curve at constant speed. (4) A sled travels down a frictionless, steep, straight hill. Solution: The premise of maintaining constant kinetic energy is that the speed cannot change since the formula for kinetic energy is . Choice (3)
40 Which phrase describes a box in equilibrium? (1) box in an elevator slowing down as it rises vertically (2) box at rest on a stationary table (3) box sliding down a frictionless ramp (4) box in free fall Solution: For something to be in equilibrium, we must have no unbalanced force. When there is no unbalanced force, the object must either be stationary or moving at constant velocity (not speed). Choice (2)
41 Quarks may combine to produce a meson of charge
Solution: By definition, a meson is made of a quark and an anti-quark. Since a quark and its anti quark will have the opposite charges, the only possible outcome for the total charge is 0. Choice (4)
42 The diagram below shows waves A and B as they travel through a region in the same medium.
Which wave best represents the superposition of waves A and B?
Solution: The diagram shows that waves A and B are out of phase as in the trough of B matches with the crest of A. However, the amplitude of B is smaller than A. The result of the superposition will result a wave looking like wave A with a reduced amplitude. Choice (3)
43 The diagrams below show the direction of wave travel and the direction of medium particle vibration for different waves. Which diagram best represents the characteristics of a sound wave?
Solution: Sound wave is a longitudinal wave. A longitudinal wave will behave such that the direction of wave traveling is the same as the direction of particles’ vibrations. Choice (1)
44 In a sample of gas, many excited hydrogen atoms are in the n = 4 energy level. What is the maximum number of different photon energies that can be emitted by these atoms as they return to the ground state? (1) 6 (3) 3 (2) 5 (4) 4
Solution:There are a couple of different ways for a particle at n=4 to decay down to n=1. We can go n=4->n=1, n=4->n=3, n=3->n=2,n=2->n1,n=3->n=1,n=4->n=2. So there are six different routes the particle can take to decay and each route represents a photon of different energy Choice (1)
Base your answers to questions 45 and 46 on the information below and on your knowledge of physics. Two students did an experiment to measure the acceleration of a freely falling object. One student dropped an object from rest. The other student measured the distance fallen by the object and the corresponding time of fall. The data for the dropped object are shown below.
distance fallen by object = 2.4 meters time of fall = 0.71 second
45 Based on the data for the dropped object, the experimental value calculated for the object’s acceleration is (1) 11 m/s2 (2) 9.5 m/s2 (3) 6.8 m/s2 (4) 4.8 m/s2
Solution: Use the formula above. Let d=2.4m and vi=0 and t=0.71s, we solve a=9.5m/s^2. Choice (2)
46 The ideal value for the acceleration differs from the one obtained experimentally by the students. What is one possible cause of this discrepancy? (1) The object was given some initial horizontal velocity. (2) The force of gravity was much stronger outside the building than inside. (3) Motion formulas should not be used in an experimental setting. (4) There may have been errors in the measurement of distance and/or time.
Solution: Choices 2 and 3 are simply too ridiculous to be taken seriously. Choice 1 is wrong as well since the time to free fall is not affected by the horizontal component of the initial velocity. Choice (4)
47 Which graph represents the motion of an object falling freely from rest near the surface of the Moon?
Solution: Based on the motion formula, d is proportional to t squared. The graph should have the same characteristics of the graph of y=x^2. Choice (3)
48 The diagrams below represent the initial velocities, vi, of four identical projectiles launched from level ground at various angles above the horizontal. Which projectile will have the longest time of flight? [Neglect friction.]
Solution: Time of flight is dependent on the initial vertical component of the velocity. The diagram 4 should have the biggest initial vertical component. Choice (4)
49 Four forces act on a crate on a level floor, as shown in the diagram below.
At the instant shown, the crate is (1) accelerating to the right (3) moving at constant velocity to the right (2) accelerating to the left (4) remaining at rest Solution: After summing up the forces along the vertical and horizontal directions, we see that there is an unbalanced force of 50N to the right. So the acceleration is to the right. Choice (1)
50 The graph below represents the relationship between the potential energy stored in a spring, PEs, and the elongation of the spring, x.
Solution: Using the formula. Using the values of x=0.04m and PE=0.2J, we get k=250N/m Choice (4)
, if both q1 and q2 were tripled and yet the F stayed the same, r must be tripled as well. Choice (3)
, if L is halved and A is doubled, the R is reduced by a factor of ¼. Choice (1)
, the speed of sound given in the reference sheet is 331m/s. We can find the wavelength by dividing 331m/s by 512Hz. Choice (1)
, we can plug in 25N into Fc and 0.25kg into m and 0.8m into r. v= 8.94m/s. Choice (2)
, the charge is 3.15*10^18*1.6*10^-19= 0.504C. I should be 0.504C/10s = 0.0504A. Choice (1)
. When you increase r by a factor of 2 while keeping the velocity the same, the centripetal acceleration is halved. Choice (3)
, we know that the mass had been rest before the force was applied so P_initial=0. Therefore, P_final=20N*10s=200 kg*m/s Choice (1)
, if we halve the d, it will cause the force to quadruple whereas doubling d will cause it to be only ¼ of the original amount. On the other hand, if we double q1, it will only double the force and halving q2 will only halve the force. Choice (4)
, we can solve for the resistance R easily by plugging 100W into P and 120V into V, R=144Ω. Choice (4)
where the f=300Hz. Solving for λ, we get 331/300=1.10m. Choice (2)
, we see that the resistance of a piece of wire is proportional to the length and inversely proportional to the cross-sectional area. For cylinder A, we see that it is both twice the length and the cross-sectional area of cylinder D. Therefore, cylinders A and D should have the same resistance. Choice (4)
. This indicates that the energy of a photon is inversely proportional to the wavelength. The graph that shows an inversely proportional relationship is 4. Choice (4)
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