1.

The Correct Answer is (B) — You can solve the first equation by subtracting 4 from both sides to get a = 8, and then 4a = 4(8) = 32.

2.

The Correct Answer is (A) — The one-hour package is $100 per hour; the two-hour package is $190/2 hours or $95 per hour. $100 – $95 = $5.

3.

The Correct Answer is (B) — When evaluating a chain of functions, it is helpful to work from the inside out. First evaluate f(c), then plug this into g(x): g(f(c)) = g(2c) = 5(2c) + 1 = 10c + 1.

If you chose (A), you may have evaluated f(c) and stopped there.

4.

The Correct Answer is (B) — You are told that U is 75% of T, so U = 0.75T. You can plug this into the equation for V to get V = 0.05U = 0.05(0.75T) = 0.0375T.

5.

The Correct Answer is (B) — Without numbers on the pie chart, you must recognize that ¼ is too small (“Miscellaneous” takes up ¼ of the chart, and “Sleep” and “Classes” combined take up more area than “Miscellaneous”) and ½ is too large (“Classes” and “Homework” combined take up half the chart). “Sleep” and “Classes” together take up 1/3 of the chart.

6.

The Correct Answer is (A) — Multiplying f(x) by 4 is the same as multiplying every y-value on the graph by 4, meaning that the slope will be four times greater. You can see this for yourself: 4f(x) = 8x + 8, which has a slope of 8 compared to the old slope of 2.

7.

The Correct Answer is (B) — The equation must have a negative slope, which eliminates (C) and (D). Because the y-intercept is greater than zero, a positive value must have been added to the right side of the equation, eliminating (A) and leaving you with the correct answer choice, (B).

8.

The Correct Answer is (A) — The probability of selecting one student from the junior class who wants to enter finance is 6/30 or ⅕. After you have chosen the first student, the probability that the next student you pick will also want to enter finance is 5/29. Multiplying these together gives .

9.

The Correct Answer is (B) — If the average across the four classes is 5 students, then there must be a total of 20 students who want to enter finance. As there are 15 such students currently choosing finance in the table, 5 freshmen students must have changed their preference.

10.

The Correct Answer is (C) — The mean of the five integers given is . If a number equal to the mean is added to a set of numbers, the mean will not change, so the sixth number must be equal to 65.

11.

The Correct Answer is (A) — From the line of best fit, about 10 businesses are added every two years. The year 2015 is four years from the last data point, so 20 new businesses should be added by then. In 2011, there were 100 businesses, so there will be 100 + 20 = 120 businesses in total in 2015.

12.

The Correct Answer is (A) — Substitute the expressions for x, y, and z into the final equation, xy + 2z:

13.

The Correct Answer is (D) — The horseshoe crab population is growing linearly, since a constant number of crabs is being added each year. The Dungeness crab population is growing exponentially, since the number of crabs in increasing by a fixed percentage each year. Of the choices, only (D) represents these growth rates accurately.

If you chose (C) you may have confused which line corresponded to which crab.

14.

The Correct Answer is (A) — Simply add up 35 + 40 + 35, the points on the graph from 2000, 2001, and 2002.

15.

The Correct Answer is (B) — In 2001, there were more psychology students than biology students, so (A) is incorrect. (C) is also incorrect, because enrollment in the biology class increased by about 5 students per year in the period specified. Finally, (D) is incorrect because in 2003 there were more students in the psychology class than in the biology class. You are left with the correct answer, (B), which you can confirm by calculating the slope of the line as .

16.

The Correct Answer is (A) — The fastest way to solve this question is to plug the three simplest points into all four expressions. All of the answer choices satisfy (0,–3), but only (A) gives f(x) = –4 when x = 1.

If you chose (B) you may have forgotten the negative sign and solved for the equation of the parabola outright.

17.

The Correct Answer is (A) — Plugging in the given values gives 45 + 2y2 = 333. Simplifying gives 144 = y2, so y = 12 or y = –12. Of these, only 12 is an option.

If you chose (C), you most likely found the value of y2.

18.

The Correct Answer is (A) — Since N(p) doubles each time p increases by 1, you know that this data can be represented by an exponential equation with a base of 2. Furthermore, when p = 0, N(p) = 1250, so (A) is correct.

19.

The Correct Answer is (C) — Eight cubic centimeters of ethanol weighs (0.789)(8) = 6.312 grams, and four cubic centimeters of water weighs 4 grams. Their sum is 10.312, and dividing by the 12 total cubic centimeters gives approximately 0.859 g/cm3.

20.

The Correct Answer is (C) — Cross-multiply and then simplify to solve:

You have found that x can be either 3 or –2. Remember that x cannot be –5 or 1, because either of the original denominators cannot equal zero.

21.

The Correct Answer is (D) — Since the square has an area of A, each of its sides has length . The figure on the right is made up of some full sides, which have length , and some half sides, which have length . Adding these up, you can find that the perimeter is .

22.

The Correct Answer is (A) — After one hour, the colony will be 2 times its original size. After 2 hours, it will be 4 times its original size. After 3 hours, it will be 8 times its original size. After 4 hours, it will be 16 times its original size. After 5 hours, it will be 25 = 32 times its original size.

23.

The Correct Answer is (B) — Arrange the numbers in ascending order: 72, 84, 87, 90. If the median is 85, then x = 85, so (A) is true. The mean is 83.6, so B) is not true and is therefore the correct answer. This calculation also confirms that (C) is true, and that (D) is true, because the new median would be 85.5.

24.

The Correct Answer is (D) — If the first person chosen is from England, that leaves 6 English travelers and 10 travelers total, so the probability of choosing another English person is 6/10 = 60%.

25.

The Correct Answer is (B) — In order to figure out when Isabella and Tom will be 693 km apart, we need to calculate how quickly they are moving apart from one another. Because Isabella and Tom are travelling in opposite directions, we can simply add the speeds at which they are each travelling to figure out how quickly they are moving apart. Isabella is moving at 65 km/h, and Tom is moving at 77 km/h, so they are moving apart at a combined rate of 142km/h. Next, we just divide the total distance we're interested in by their speed: 639/142 = 4.5. It will take 4.5 hours for Tom and Isabella to be 639 km apart. We just need to add that to their departure time to figure out when they will reach that distance. At this point, we need to be careful not to mix fractional values for a single unit of time (like 4.5 hours) and measures in mixed units of time (9 hours and 45 minutes). We can convert 4.5 hours to 4 hours and 30 minutes, and add that to their departure time: 45 minutes + 30 minutes = 1 hour and 15 minutes. Carrying the extra hour, 9 hours + 5 hours = 14 hours. That comes to 14:15, which is another way of writing 2:15 PM. Thus, the correct answer is (B).

26.

The Correct Answer is (B) — You can set up the equation j = 15x where x is time in hours since 7:45, and j is Jorge’s distance from start in kilometers. Similarly, i = 65(x – 2) for Isabella, since she leaves two hours later, at 9:45 AM. You can set i = j and solve for x:

This means that Jorge will have been running for 2.6 hours before Isabella catches up to him, after she and Tom have been driving for 2.6 – 2 = 0.6 hours. In that time, Tom has driven (77)(0.6) = 46.2 kilometers; in 2.6 hours, Jorge has gone 39 kilometers. Therefore, the distance between them is approximately 39 + 46 = 85 kilometers.

If you chose (A), you may have found the distance Jorge travelled and stopped there.

27.

The Correct Answer is (B) — The question tells you that x is between 1 and 9. I is false because it is only true for –x. II is true because it simply combines the inequalities given in the question. III is true because for any number between 1 and 9, it will be at most 4 units away from 5 on a number line.

28.

The Correct Answer is (C) — Since you are told that the total of the House column is 78, you know that y + z = 78 – 22 – 18 = 38 kJ. Since the New Mexico Chile outside (x) absorbs as much light as the Creeping Fig in the house (z) and the Lavender in the house (y) combined, you know that x = z + y = 38 kJ. Therefore, the total energy absorbed by the plants if they are all in the shed is 15 + 8 + 9 + 5 = 37 kilojoules, and the total energy absorbed if they are outside is 25 + 38 + 32 + 38 = 133 kilojoules. The difference between these is 133 – 37 = 96 kilojoules.

If you chose (B), you most likely found the total energy absorbed if all the plants were in the shed. If you chose (D), you most likely found the total energy absorbed if all the plants were outside.

29.

The Correct Answer is (C) — Since the angle at B is a right angle, and everything is symmetric, you know that AB = BC, and since line AC = 8, this means BC = 4. Also, since the circle has a diameter of 10, its radius is 5, so OC = 5. You now have a right-angled triangle (OBC) with a hypotenuse of length 5 and another side of length 4. You can use the Pythagorean Theorem to find that the remaining side, BO, has length 3.

30.

The Correct Answer is (B) — When the ball reaches the ground, h(t) = 0, so 0 = –2t2 + 10t + 100. Factoring gives –2(t – 10)(t + 5), so t must be 10 or –5 seconds. Since time cannot be negative, it took ten seconds for the ball to reach the ground.

If you chose (A), you may have forgotten the minus sign and thought that t = 5.

31.

The Correct Answer is (8) — Subtracting one equation from the other cancels out 2x, leaving you with 7 – (–1) = 8.

32.

The Correct Answer is (32) — Expand to get 3x – 12 – 16 + 2x = 4x + 4, and combine like terms to get 5x – 28 = 4x + 4 or x = 32.

33.

The Correct Answer is (1.5) — You can translate the word equations in the question as 4b = 10 and c = 0.2b. Then c = (0.2)(10/4)= 0.5. Three times 0.5 is 1.5.

34.

The Correct Answer is (15) — Square both sides to get 2x + 10 = x2 + 10x + 25, then simplify and solve: .

This tells you that x = –3 or x = –5. Make sure to plug these solutions back into the original equation to ensure that they are indeed solutions. Finally, the product of –3 and –5 is 15.

35.

The Correct Answer is (0) — Rewriting the second equation gives –2x + y = –b; rearranging gives y + b = 2x. Since y + b = 5x and y + b = 2x, you know that 5x = 2x so x = 0.

36.

The Correct Answer is (40) — The two triangles are similar; all their angles are the same, so their sides are proportional. To find the unknown leg of the larger triangle, use the Pythagorean theorem: 602 + b2 = 1002. Then b = 80, and since the ratio of the smaller triangle to the larger is 1:2, you know that x = b/2 = 40.

37.

The Correct Answer is (10) — If Jennifer has six cages at maximum capacity, she has (6)(5) = 30 mice in total. If she has twice as many female mice as male mice, she has 20 female mice and 10 male mice.

38.

The Correct Answer is (17) — Halving the price per day of cage maintenance means each cage costs $0.625 per day. If the student has 102 mice, she needs at least 21 cages (20 cages could only house 100 mice). Those 21 cages cost $13.125 per day, so if she has $225, she can run the experiment for = 17.143 days. Rounding to the nearest day gives 17 days.