1.

The Correct Answer is (B) — We can solve this problem by plugging in the value given for y in order to solve for x. x = 2(x - 2) + 4. Simplify x = 2x - 4 + 4. Simplify further x = 0. The correct answer is (B).

2.

The Correct Answer is (B) — The equation for a line can be represented by f(x) = mx + b where b is the y-intercept (where x equals zero and the line crosses the y-axis). From the table we know when x = 0, f(x) = 3. The y-intercept is 3 so we can eliminate answers (C) and (D). Plug in the next coordinates for answer (A) 4 does not equal 2 + 3, so knock out (A). The correct answer is (B). Double-check that the coordinates make the expression true.

3.

The Correct Answer is (B) — We can set up an algebraic ratio of pigs/acres to solve the problem. Cross multiply 8 pigs/1.5 acres = x pigs/6 acres. 48 = 1.5x. x = 48/1.5 = 32, the answer is (B).

4.

The Correct Answer is (B) — We can cross multiply to get 4(x - 1) = 3(2x - 6). Simplify 4x - 4 = 6x -18. Subtract 4x from both sides of the equations and add 18 to both sides of the equation. 14 = 2x, x = 7. The correct answer is (B).

5.

The Correct Answer is (D) — The population(p) = current population x 2 every 5 years. So, the initial population is 300, in 5 years the population will be 600, in 5 more years the population will be 1200, in 5 more years the population will be 2400. The correct answer is (D).

6.

The Correct Answer is (C) — We know there are 180 degrees in a triangle. Therefore angle ACB = 180 degrees - 30 degrees - 40 degrees = 110 degrees. Angles on one side of a straight line will always add up to 180 degrees. We know angle BCE = 180 degrees - 110 degrees = 70 degrees. Because we know that line BC is parallel to line DE, we know that the value of angle BCE = the value of angle x. Answer (C) is correct.

7.

The Correct Answer is (A) — We can write out 2 equations to represent the word problem: 10b + 7m = $50.95 and m = b - 0.25. Solve for b in terms of m in the second equation: b = m + $0.25. Plug this value of b back into the first equation in order to solve for price of a chocolate milkshake. Simplify 10(m + $0.25) + 7m = $50.95 = 10m + $2.50 + 7m = $50.95 = 17m + $2.50 = $50.95. Subtract $2.50 from both side of the equation. 17m = $48.45, divide each side of the equation by 17, m = $2.85, the correct answer is (A).

8.

The Correct Answer is (B) — We know the 3 angles of a triangle add up to 180 degrees. A right triangle has an angle of 90 degrees so the remaining acute angles must add up to 90 degrees. The problem gives us the ratio of 12/3 so we can set up the equation 12/3 = (90 –x)/x to solve for the value of the smaller acute angle. Cross multiply and we get 12x = 270 – 3x = 15x = 270. Divide each side of the equation by 15 and we get x = 18 degrees which is the smaller acute angle. The larger acute angle = 90 – x = 90 – 18 = 72 degrees. The question is asking for the difference in the two angles measures. Subtract 18 from 72 and we get 54 degrees. The answer is (B).

9.

The Correct Answer is (D) — The fastest way to solve this problem is by plugging in the answer choices to the inequality. Plugging in -3, -2, or -1 to the inequality makes it false. Plugging 0 into the inequality we get 0 times 0 – 1 < 0 times 0 times 0. 0 multiplied by any number is 0. This inequality is true -1 < 0. The correct answer is therefore (D).

10.

The Correct Answer is (C) — We can solve for y by plugging in 12 as the value for x in the second equation. 3(12) = 4y^2. Multiply 3 and 12 and we get 36 = 4y^2. Divide both sides of the equation by 4 and we get 9 = y^2. Take the square root of each side of the equation and we get 3 = y. The question is asking for the value of x^2y. Plug in x =12 and y =3 and we get 12 times 12 times 3 = 432. The correct answer is (C).

11.

The Correct Answer is (B) — The likelihood of choosing any one of the three numbers on the first selection is 3/5. When choosing the second number, 2 out of 4 of the remaining numbers are the correct ones, so the likelihood of selecting 1 of the 2 is 2/4. The likelihood of selecting the last number from the remaining 3 numbers is then 1/3. We can calculate the likelihood of all 3 of these events occurring to be (3/5)(2/4)(1/3)= 6/60 = 1/10. This means that (B) is correct.

12.

The Correct Answer is (B) — The ratio of d:c can be rewritten as d/c = 3/1. The second sentence tells us that d + c = s. We are looking for d in terms of s, so we are looking to get rid of the variable c. We can isolate c in the first equation and substitute its value into the second equation. Substituting c=d/3, we get d + d/3 = s. Adding the terms on the left side, we get (4d/3)= s, and dividing both sides by 4/3, we get d= (3/4)s. (B) is the correct answer.

13.

The Correct Answer is (B) — According to the table, 75.75% of juniors drink 2 or more cups of coffee per day. From here, the simplest thing to do is to estimate the fraction fraction of Seniors who drink 2 or more cups of coffee, in order to determine that it is a higher percentage (94.1%, to be precise). All the other answer choices are true, which makes (B) the only answer choice not supported by the table.

14.

The Correct Answer is (C) — When we model this like a linear function, we see that the y-intercept is 1500. We can then eliminate (A) and (B), which do not have this y-intercept. The number of passengers increase by 100 with each month, so we know m is multiplied by 100 in the function, which gives us (C) as the correct answer.

15.

The Correct Answer is (C) — We can solve this question by setting up a system of equations with the information given in the question. A ratio of (j + n):k = 1:3 can be written as the fraction (j+n)/k=1/3. The ratio of n:(j +k) can also be written as a fraction, but this time we can set the proportion of (j + n) to 100, giving us n/(j+n)=x/100, where x is n expressed as a percentage of j + n. Plugging in our given values for j and k into equation 1, we get (925+n)/5550=1/3. We can then multiply both sides by 5550 and subtract both sides by 925 to solve for n. This gives us n = 925. Plugging in the values of n and j into equation 2, we get 925/(925+925)=x/100. Multiplying both sides by 100 to solve for x, we get x = 50, which means n is 50% of (j + n). (C) is thus the correct answer.

16.

The Correct Answer is (A) — We can first find the average number of languages offered across the 20 schools, which is ((1×0)+(3×1)+(5×2)+(8×3)+(2×4)+(1×5))/20 = 2.5. This means that any school offering 2 languages or less offer fewer than the average. We can see from the graph that 1 school offers 0 languages, 3 offer 1, and 5 offer 2. This makes it a total of 1 + 3 + 5 = 9 schools that offer fewer languages than the average. (A) is the correct choice.

17.

The Correct Answer is () — We can first expand the brackets to get –30 – 15n = –16n + 112. Isolating all the terms containing n to one side, we get –15n + 16n = 112 + 30. Simplifying this, we get n = 142.

18.

The Correct Answer is () — We know that the angles within the rectangle are all right angles, so the larger triangles created by the diagonal lines are right-angle triangles. If 2 of the sides are 3 and 4, this makes the triangle with the diagonal line as its hypotenuse a 3:4:5 triangle. We can extrapolate from this that the length of the diagonal line is 5. There are 2 solid lines with a length of 3 and 2 solid lines with a length of 5. Therefore, the total length of the solid lines is 2 × 3 + 2 × 5 = 16.

19.

The Correct Answer is (117) — First, plug the initial values for P and V into the equation PV = k to find that k = 78 kPa × 30 cm3 = 2,340. Using the same equation, plug in the new volume (20 cubic centimeters) and the k value to solve for P:

P × 20 = 2,340
P = 117 kPa

20.

The Correct Answer is (80) — First, calculate the k value for the gas in each syringe by using the formula PV = k. For syringe A, k = 50 × 15.6 = 780. For syringe B, k = 40 × 15.6 = 624.

Now, plug the new volume (30 cubic centimeters) for each syringe into their respective equations to solve for pressure:

Therefore, the new pressure in B as a percent of A is 20.826 × 100% = 80%.