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MCAT Section Tests Dear Future Doctor, The following Section Test and explanations should be used to practice and to assess your mastery of critical thinking in each of the section areas Topics are confluent and are not necessarily in any specific order or fixed proportion This is the level of integration in your preparation that collects what you have learned in the Kaplan classroom and synthesizes your knowledge with your critical thinking Simply completing the tests is inadequate; a solid understanding of your performance through your Score Reports and the explanations is necessary to diagnose your specific weaknesses and address them before Test Day All rights are reserved pursuant to the copyright laws and the contract clause in your enrollment agreement and as printed below Misdemeanor and felony infractions can severely limit your ability to be accepted to a medical program and a conviction can result in the removal of a medical license We offer this material for your practice in your own home as a courtesy and privilege Practice today so that you can perform on test day; this material was designed to give you every advantage on the MCAT and we wish you the best of luck in your preparation Sincerely, Albert Chen Executive Director, Pre-Health Research and Development Kaplan Test Prep © 2003 Kaplan, Inc All rights reserved No part of this book may be reproduced in any form, by Photostat, microfilm, xerography or any other means, or incorporated into any information retrieval system, electronic or mechanical without the written permission of Kaplan, Inc This book may not be duplicated, distributed or resold, pursuant to the terms of your Kaplan Enrollment Agreement PHYSICAL SCIENCES TEST EXPLANATIONS Passage I (Questions 1–6) The correct answer choice is B, slightly less than 90° We are looking for the maximum angle the accelerometer pendulum can make with the vertical The passage tells us that the accelerometer pendulum is made up of a small dense body of mass M suspended from a massless rod This mass M is the pendulum bob There are two forces acting on the pendulum bob The first is the force of gravity, or weight, acting vertically downward, and the second is the tension in the rod acting along the rod Since there is no vertical acceleration, the sum of the forces in the vertical direction must equal zero The downward force of gravity, Mg, must equal the upward vertical component of the tension, Ty which should immediately eliminate choice A, for if the rod makes an angle of 90° with the vertical there would be no vertical component to the tension to counteract the force of gravity The fact that tension must be pulling the mass upward means that the rod must be below the horizontal In other words, the angle must be less than 90°, and its maximum value must be slightly less than 90° The correct answer choice is A The passage states in the first paragraph that an acceleration toward the right will cause the pendulum to swing back toward the left This is clockwise from the vertical Therefore, we know that when the pendulum makes a constant angle with the vertical of 2° in the clockwise direction, the system must be accelerating toward the right with a constant acceleration From the note at the end of the passage, we know that the acceleration is positive since it is toward the right Within these two seconds, then, the velocity is increasing This eliminates choices B and C After the first two seconds, the pendulum is described as swinging abruptly to the right, making the same angle as before, except that now it is counterclockwise This indicates that the magnitude of the acceleration remains the same, but the sign (and hence direction) has changed: the system is now decelerating; the velocity decreases Choice D is incorrect because it says that the velocity remains the same after seconds, which would be true if the acceleration changes to zero abruptly, rather than becoming negative Note that the graph in choice C is what the acceleration versus time graph would look like, and would have been an easy mistake to make if we didn’t read the question carefully enough The correct answer choice is C, a equals g tan θ This question asks us to find an equation which relates the acceleration of the system to the angle of displacement of the bob As pointed out in question above, there are two forces acting on the pendulum bob The first is the force of gravity, Mg, and the second is the tension in the rod, T To answer the question, we first resolve the forces into their vertical and horizontal components and then apply Newton's second law in both the horizontal and vertical directions First let's look at the horizontal or x direction The force of gravity, Mg, is vertical The only horizontal force is the horizontal component of the tension, Tx, and this must equal the mass times the acceleration in the horizontal direction, Ma Now look at the vertical or y direction There is no vertical acceleration The forces in the vertical direction must add up to zero The downward force of gravity, Mg, must equal the upward vertical component of the tension, Ty Applying basic trigonometry gives Tx = T sinθ, and Ty = T cosθ Therefore, T sin θ = Ma, and T cos θ = Mg We can eliminate T between these two equations by dividing the first over the second to get a sin θ = tan θ = g cos θ Therefore, a = g tan θ, and choice C is the correct answer choice Tsin θ Tcosθ θ θ Τ Mg Kaplan MCAT Physical Sciences Test Explanations The correct answer choice is B That the accelerometer gives a constant, positive value for seconds means that the car is accelerating at a constant value during this time Its speed is increasing and therefore each subsequent second would see it cover more distance The readings given, and among which we have to choose, correspond to the total distance traveled since start, not the distance traveled per second, and so it is not enough that the readings themselves increase; the difference between one value and the previous one has to increase as well, because this difference is the distance traveled within one second Only choice B conforms to this: in the first second it travels m; in the second m, giving a total distance traveled of m In the third second, it travels a distance of (9 – 4) m = m, etc In fact, even though it is not asked in the question, one can see that the kinetics is what one would observe if 1 the acceleration is m/s2: assuming that the car starts from rest, the kinetics equation would be ? x = v0t + at2 = 2 at2 If a = 2, this would give ? x = t2, which would fit the values given in choice B nicely Even though the readings in choice A increase, they actually describe a scenario in which the velocity is constant (or acceleration is zero): in each second the car travels m; i.e it has a constant velocity of m/s Choice C basically describes a car that is stationary at least for the last three seconds Choice D describes deceleration g , which means that the 2_ L frequency of oscillation is inversely proportional to L The period is just 1/frequency, and so the period is proportional to L If we double the length of the pendulum, then, the period increases by a factor of The correct answer choice is C The frequency of oscillation of a pendulum is The correct answer choice is D, (7/8)Mg Here, the pendulum is submerged in mineral oil, which we are told in the second paragraph of the passage has a density of one eighth the density of the pendulum bob There are now three forces on the pendulum bob The first is the force of gravity, Mg, in the downward or negative y direction; the second is the tension, T, along the rod; and the third is now the buoyant force, B, which is in the upward positive y direction and which is equal to the weight of the displaced oil Since the system is at rest, the angle θ is zero, and the tension, T, will be along the positive y direction Balancing the forces gives T = Mg – B In order to find T, we must find B According to Archimedes' principle, the buoyant force B equals the weight of the displaced oil The mass of the displaced oil equals the density of the oil, ρo, times the volume of the bob, Vb But we already know that ρo equals one eighth the density of the bob, ρb., so the mass of the displaced oil = ρb ∗ Vb But ρb ∗ Vb is just M, the mass of the bob So the mass of the displaced oil equals one eighth the mass of the bob The weight of the displaced oil equals 1 its mass times the acceleration of gravity, g Therefore, the buoyant force B = Mg, and the tension T = Mg – Mg = 8 Mg So choice D is correct Passage II (Questions 7–12) The second passage deals primarily with the energy of activation, kinetics, and the gas laws In addition, you need to be able to read a potential energy diagram for a reaction The correct answer to question is B In Figure 1, the energy differences labeled and are the activation energies of the reaction (2 can be thought of as the activation energy of the reverse reaction); and are the potential energies of the reactants and products; and is the potential energy difference of the reaction A catalyst is a substance that accelerates a reaction by lowering one or more of the activation energies of the reaction; it does not, however, change the ? H of the reaction, which is a state function Since a catalyst can only lower the activation energies of a reaction, only energies and could be affected Their values could be decreased by lowering the energy of the transition states (the “hilltops”) Choice B is the correct response The correct answer to question is choice C Le Châtelier's principle states that if a system at equilibrium is subjected to a stress, it will react in such a way so as to alleviate that stress The stress is alleviated by changes in the concentrations of the reactants and products until equilibrium is once again reestablished Examining choice C, Kaplan MCAT Physical Sciences Test Explanations removal of product D would be responded to by an increase in the rate of the forward reaction in an attempt to replace the product—to put it another way, the rate of the forward reaction increases to keep the equilibrium constant unchanged This would also increase the concentration of C, so choice C is correct All the other choices are incorrect Figure shows that the potential energy of the products is lower than that of the reactants; this means that the reaction is exothermic, so an increase in temperature, choice A, would shift the equilibrium to the left While a lower pH, choice B, if associated with acid smog, might catalyze this reaction, it would not shift the equilibrium to the right since a catalyst does not affect the equilibrium constant An increase in pressure, choice D, will also not affect the reaction, since the three moles of reactant are converted into three moles of product All gases exert an equal pressure per mole so neither side of this reaction is favored by a change in pressure The answer to question is D D is wrong is because the passage states that the slower step of the reaction mechanism follows second order kinetics The slowest step of a reaction mechanism is usually the rate-determining step, and a step that involves second-order kinetics must only involve two reactant molecules Choice D involves three reactant molecules and therefore third order kinetics Although it is often said that the kinetics of a reaction cannot be derived from its stoichiometry, this is true only of the overall reaction When a complex reaction has been broken down into a series of elementary reactions, we can then derive the rate law from the slowest of the elementary reactions In this case, we know that the ratedetermining step must consist of an interaction between two molecules This could be two molecules of A, two of B, or one each of A and B 10 The correct answer to question 10 is A To answer this question correctly, you must understand the concepts of equilibrium and Gibbs free energy, and you must be able to interpret the potential energy diagram in Figure The passage states that the reaction proceeds spontaneously to the right; therefore the equilibrium constant must be greater than one Choice B is incorrect because if ? G were greater than zero, the reaction would not be spontaneous C is incorrect because, according to the graph, the reaction is exothermic If the reaction was endothermic, the potential energy of the products indicated by in Figure would be greater than the potential energy of the reactants-indicated by Choice D is incorrect because we cannot say anything about the potential energy of A alone or of D alone; we know only that the potential energy of 2A + B is greater than that of 2C + D 11 The correct answer is C A reaction's activation energy is a measure of the potential energy difference between the reactants and the transition state The spontaneity of a reaction is determined by the difference in the Gibbs free energy of the products and reactants As has been stated numerous times in the past, whether or not a reaction is possible is determined by thermodynamics; how fast the reaction occurs is determined by kinetics Certainly, if the activation energy of a reaction is very high, even though the energy of the products are lower than that of the reactants, it will proceed very slowly So whether or not a reaction occurs spontaneously has nothing to with the activation energy of the reaction choice C is the correct response The other statements are all correct The activation energy is the energy required to allow particles to react, and a catalyst reduces the amount of activation energy required A far as choice D is concerned, the activation energy is not necessarily related to the change in enthalpy in any way 12 Choice C is the correct response for question 12 This question doesn't really relate to the information in the passage, but this sort of thing is not unusual on the MCAT In cases like this, you just need to pull out your own chemistry knowledge Here, you need to figure out which of the roman numeral choices will change when a substance undergoes a change of phase Roman numeral I is temperature during a change of phase, the temperature remains constant After all of the material has changed phase, and heat is still being added to the system, the temperature will increase So I is wrong, which lets us eliminate choices B and D Number II, density, does change when the phase changes One of the biggest differences between the phases of a substance is the density of the substances in the phase So number II seems correct which points to choice C, the only one with II in it that we haven't eliminated Number III, entropy, also changes with a change in phase Freedom of movement of the individual substance particles is another thing that defines a phase Molecules have the most entropy in the gas phase and the least in solid phase That makes III correct and confirms that fact that choice C is the right answer Passage III (Questions 13–17) 13 The correct answer choice is C, 2000 to 4000 hertz This question tests how well you interpret information presented in graph form Let us examine the graph presented in the passage It is a plot of sound level in decibels as a function of frequency in hertz The frequency is plotted on a log scale so that it can cover three orders of magnitude There are two curves marked on the graph The lower one is labeled "threshold of hearing,” and represents the faintest sound that human hearing can detect as a function of frequency The other curve is labeled "threshold of pain,” and Kaplan MCAT Physical Sciences Test Explanations represents the loudest sound that a human ear can experience without pain as a function of frequency The question gives four frequency ranges and asks which one represents the region of highest sensitivity Therefore, we are concerned with the lower curve, and we would like to find the frequency range over which it is at its lowest If you have forgotten how to read a log scale, the vertical lines have the values 20, 40, 60, 80, 100, 200, 400, 600, 800, 1000, 2000, 4000, 6000, 8000, 10,000, and 20,000 Hz from left to right The lowest region of the bottom curve is between 2000 and 4000 Hz 14 The correct answer choice is A, 30 decibels To answer this question correctly one needs to be able to distinguish between intensity and intensity level Intensity is the power per unit area carried by the sound: since power is itself energy per unit time, intensity is the amount of energy one would absorb per unit area per unit time, e.g the amount of energy that a 1-m2 area would absorb from the sound in one second The intensity level is a measure of the intensity on a logarithmic level In the passage we are given a formula which equates the intensity level, β, to ten times the log of I over I0 I is the intensity of the sound, and I0 is the reference intensity The question asks for βA minus βB I I This equals 10 ∗ log A – 10 ∗ log B To proceed further, we have to remember that the difference of two logs is the I0 I0 log of the quotient, i.e.: I I βA – βB = 10 ∗ log A – 10 ∗ log B I0 I0 IB IA = 10 ∗ (log – log ) I0 I0 IA/I0 = 10 ∗ log ( ) IB/I0 I = 10 ∗ log A IB The I0’s cancel in the quotient, so all we need to know is that IA over IB equals 1000 which is given in the question stem The log of 1000 is since 103 = 1000 Therefore, βA – βB = 10 ∗ = 30 decibels Note that the frequency of the sound does not come into play in this question 15 The correct answer choice is D, meters In order to answer this question, we must realize that a point source emitting sound waves uniformly in all directions will emit spherical wavefronts The intensity, as stated above in question 14, is the power per unit area The intensity of a spherical wave at some point a distance r from the source, therefore, is the power divided by the surface area of a sphere of radius r We are given that the total radiated power is 16 π, and this power is spread out over a surface of area 4πr2 So the intensity of the spherical wave is equal to r The sound level at the threshold of pain is 120 decibels This can be found in the last sentence of the first paragraph in the passage or in the graph The reference intensity, I0, is equal to 10-12 W/m2 as given in the last sentence of the ∞ 1012 passage Using the equation for β given in the passage, we get that 120 = 10 ∗ log ( ∗ -12) = 10 ∗ log ( ) r2 r 10 12 ∞ 10 So first we divide both sides of this equation by 10 to obtain 12 = log ( ) Now taking the anti-log of both r2 ∞ 1012 sides, which implies using each side as an exponent of 10, gives 1012 = (The right hand side is as such r2 because 10(log x) = x.) From this we get that r2 = and therefore r = meters The correct answer choice is C, 1.7 meters In order to answer this question, we must remember that the v wavelength is inversely proportional to the frequency Specifically, λ = ; the wavelength times the frequency of a f wave equals its speed The question presents a tuning fork of wavelength 1.25 meters and frequency 272 Hz Therefore, the speed of sound must equal 272 Hz ∗ 1.25 meters, which equals 340 m/s (A hertz is one inverse second.) We are then asked for the wavelength of another tuning fork with frequency equal to 200 Hz This wavelength is then equal to the speed of sound which we just figured to be 340 m/s divided by the new frequency, 200 Hz So the wavelength is equal to 340 divided by 200 which is 170 divided by 100 or 1.7 meters 16 Kaplan MCAT Physical Sciences Test Explanations 17 The correct answer choice is A, beats In order to answer this question, we must remember that beats are heard when two tones are played simultaneously at slightly different frequencies It is this exact situation that is described in the question Choice B is incorrect since resonance occurs when a driving frequency such as a tone from a tuning fork is the same as a natural frequency of some vibrating system such as a wine glass When the frequency of the tone becomes equal to one of the natural frequencies of the glass, the glass will begin to vibrate and possibly even break This is clearly not the case here Choice C is incorrect since harmonics are vibrations at frequencies of integer multiples of some fundamental frequency Choice D is incorrect since a half tone is the smallest interval between two notes in a major scale Neither of these describes the situation in the question Discrete Questions 18 The correct answer for question 18 is choice D, the magnesium ion This is a straightforward question involving outside knowledge of periodic trends in ionic radii Looking at the answer choices, and with a little help from the Periodic Table, you should be able to deduce that they all have the same number of electrons; in other words, they are isoelectronic So, we have to decide which of these ions is the smallest based on the effective nuclear charge of each Choices C and D, being cations, have lost electrons This will result in a smaller radius because the electrons left occupy shells with smaller principal quantum numbers Because there is a decrease in the total number of electrons, you get a greater average attraction of the nucleus per remaining electron, which is known as an increase in effective nuclear charge The greater the nuclear charge the smaller the ionic radius is in a series of isoelectronic ions and atoms So, knowing that a positive ion is smaller than a negative ion when they are isoelectronic, we can rule out choices A and B Comparing the sodium ion and magnesium ions, the Mg2+ ion has the same number of electrons as Na+ but the Mg2+ has one more proton Thus the electron cloud in Mg2+ is pulled inward more and so it has the smallest ionic radius Thus the correct answer is choice D 19 The correct answer choice is D: the spacing would increase The locations of the dark fringes (minima) in a diffraction pattern are given by the equation: a sinθ = nλ where a is the width of the slit, n is a positive integer (1, 2, 3, …) that indicates which dark fringe we are talking about, λ is the wavelength of the light, and θ is defined as in the following diagram: Second minimum: n = first minimum: n = x θ2 a θ1 central maximum d screen The dashed lines are drawn such that they converge at the midpoint of the slit In any given set-up, a and λ will be constant, while the angle and n would change based on which dark fringe we are talking about In this question we are asked about the second minimum, corresponding to n = The distance between the central maximum and the second minimum, which we shall call x, can be expressed in terms of θ and the distance from the center of the slit to the screen d: x = d sinθ = dnλ/a, or, since n = 2, x = 2dλ/a From this, one can easily see that if the wavelength were increased, the spacing would increase as well 20 The answer to question 20 is A, 11.2 liters You can estimate this answer quickly by approximating the effects of molecular weight, temperature, and pressure on the volume of the gas You could use the equation, PV = nRT and solve for volume, but there is a faster way You know that at STP, one mole of any (ideal) gas occupies a Kaplan MCAT Physical Sciences Test Explanations volume of 22.4 liters You also know that the pressure and volume of a gas are inversely related and that temperature and volume are directly related So, since STP stipulates a temperature of 273K and a pressure of atm, you can see that the temperature and pressure are both double on the gas in the question in relation to STP That means that the volume would be doubled from the effects of higher temperature and halved by the effects of pressure These effects cancel out and the volume of one mole of gas at 546K and atm is also 22.4 liters But don't jump to choice B yet Remember, you only have 14g of N2 gas The molar weight of N2 is 28g, so that means you only have half a mole of gas Therefore, you only have half of your 22.4 L, or 11.2 liters, choice A Multiplying 2, 0.5, 0.5, and 22.4 together is a lot easier than multiplying 0.5, 546, and 0.082 together and then dividing by 2, and you don't have to come up with the universal gas constant from memory It is always easier to take shortcuts like these if you can see them and a good basis of chemical knowledge will make them easy to see Here, you could have saved yourself a lot of calculation simply by remembering the molar volume of a gas at STP and the effects that changing temperature and pressure have on the volume of a gas 21 The correct answer choice is C, the current is halved The formula for the resistance of a resistor in terms of its physical properties is R equals ρ times L over A, where ρ is the resistivity, L is the length of the resistor, and A is the cross sectional area of the resistor Therefore if the length of a resistor doubles, its resistance also doubles Ohm's law says that voltage equals current times resistance Assuming that the voltage across the resistor remains the same, the current will be halved if the resistance is doubled 22 The correct to question 22 answer is B, a silvery-white element that ignites explosively with water The Periodic Table shows that rubidium, element 37, is found in group 1, the alkali metals, so it should be highly reactive You may recall that sodium reacts vigorously, even violently, with water Well, since the alkali metals become more electropositive as you go down the group, rubidium is much more reactive in water than sodium anyway, the point is, that due to periodicity, rubidium will react violently with water much in the same way as does sodium So rubidium is probably too reactive to be used in constructing airplanes as choice D says As one of the heavier alkali metals, you can pretty safely assume that rubidium is not gaseous under normal atmospheric conditions, so choice C is wrong As for choice A, metals in general are good conductors Since rubidium can readily lose an electron, it is a better conductor than semiconductor, so choice A isn't a very likely choice Passage IV (Questions 23–27) This passage deals primarily with enthalpy, entropy, and Gibbs' free energy Essentially, it explores the thermochemistry of photosynthesis Pay special attention to the table and its list of heat or formation values Chances are, you'll be using them in a calculation 23 The correct answer is C The MCAT will sometimes have a problem involving numbers but which simply asks you to identify the correct set-up rather than perform the actual arithmetic It is therefore important to give a brief glance to the answer choices beforehand to make sure you don’t waste any time doing unnecessary calculations Dimensional analysis is always a powerful tool in approaching questions of this type, and especially for ones that are complicated: answer choices can be eliminated if the units not cancel in the right way For this particular question, we first need to convert the amount of water into moles, and then determine the number of moles of sugar that would be produced, then convert it back to a mass quantity The number of moles of a compound is the mass divided by the molar mass (or molecular weight); there is thus 11 g/(18 g/mol) = 11/18 mol of water From reaction 1, we know that moles of water are consumed for every mole of sugar produced 11/18 mol of water will thus yield 11/18 ∗ 1/6 mol sugar To convert this into mass, one multiples by the molar mass of sugar, 180 g/mol 24 B is the correct answer This answer is actually given in the text of the passage A substance which is oxidized loses electrons, while a substance which gains electrons is said to be reduced The passage states that electrons are taken from the hydrogen of the water, so water is oxidized and the correct answer is B 25 The correct answer is B This question requires you to be able to interpret the information given in the passage about Gibbs free energy and different aspects of the chemical equation The sign of ? G tells us whether or not the reaction is spontaneous Here the sign is positive, so the reaction is not spontaneous Thus I is true You can make a good estimate of the change in entropy during the reaction by considering two factors: the number of moles of reactants and products and any phase changes Entropy increases when there is an increase in randomness in a system In this case there are twelve moles of reactants and only seven of products; this would indicate a decrease in entropy Kaplan MCAT Physical Sciences Test Explanations There is also a change in phase from gaseous reactants to a solid in one of the products This also indicates a decrease in entropy, since in a solid there is less movement and therefore less disorder than there is in a gas Taking both these factors together, you can be fairly certain that there is a decrease in entropy; so II is also true Since the reaction clearly is taking in energy in the form of light, it is an endothermic reaction and III is not true The only two correct statements are I and II, so choice B is correct 26 The correct answer choice is A To solve this problem, you must remember several facts concerning ? H The first and most important thing to know is that the ? H for a reaction is equal to the sum of the ? H of formation of the products, minus the sum of the ? H of formation of the reactants For both sums, you must remember that each ? H of formation must be multiplied by the stoichiometric coefficient of the compound in the reaction The second thing to remember is that the ? H of formation of an element in its standard state is always zero Therefore, by substituting the values you are given in the table, and noting that the ? H of formation of O2 is zero, you get the overall ? H equal to +2801.3, or choice A It is interesting to note that this positive ? H coupled with a negative ? S (from the decrease in entropy) indicates that this reaction has a positive free energy change 27 Choice C is the correct answer This question requires you to understand how the light energy in the form of photons affects atoms and compounds Let's go through the four answer choices individually Choice A states that energy absorbed is used to ionize the reactants This can be correct, but isn't necessarily, since there is not always sufficient energy absorbed to actually remove an electron from an atom Choice B states that energy is released from the bonds of the reactants, which you should know is incorrect because energy must be absorbed in order for bonds to be broken Choice C is always correct, because when an atom absorbs energy, its electrons move from their ground state to a higher excited state Choice D states that electrons return to their ground state We know this cannot be true, because electrons are in their most stable, lowest energy state when they are in their ground state Therefore, absorbing energy could not put an electron into its ground state ... and represents the faintest sound that human hearing can detect as a function of frequency The other curve is labeled "threshold of pain,” and Kaplan MCAT Physical Sciences Test Explanations represents... θ, and choice C is the correct answer choice Tsin θ Tcosθ θ θ Τ Mg Kaplan MCAT Physical Sciences Test Explanations The correct answer choice is B That the accelerometer gives a constant, positive... until equilibrium is once again reestablished Examining choice C, Kaplan MCAT Physical Sciences Test Explanations removal of product D would be responded to by an increase in the rate of the forward
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