## 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).

## 1.

The Correct Answer is (C) — (C) is the correct answer. The passage states that Mrs. Honeychurch “wanted to show people that her daughter was marrying a presentable man” (lines 4−5), indicating that she wants to show her neighbors that her daughter has made a respectable match. Furthermore, “it pleased her” (line 11) to be congratulated on this match; she likes feeling the approval of others. Together these reactions suggest that she is concerned with her image in her society, giving support to (C). Although Mrs. Honeychurch has positive feelings about her daughter’s engagement to Cecil, the passage does not give any indication that she feels particularly warmly toward him for his own sake; thus, (A) is incorrect. Although the passage refers briefly to Mrs. Honeychurch thinking back on a dress (lines 28−30), there is no specific indication that she sews dresses or anything else particularly well; thus, (B) is incorrect. Mrs. Honeychurch is the one who insists on their attendance at the garden-party (lines 1−3), so she is the opposite of disinterested in it; thus, (D) is incorrect.

## 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) — We can solve for x first. Subtract 4 from both sides of the equation 8x + 4 = 48, 8x = 44, x = 5.5. Plug the value for x in to 2x + 1 = 2(5.5) + 1 = 12. The correct answer is (D).

## 6.

The Correct Answer is (B) — The slope of a line is calculated by rise over run. Look carefully at the graph. The y-axis is marked by a 9 and -9 and delineated by units of 3. The x-axis is marked by -6 and 6 and delineated by units of 2. Look at the y intercept. The coordinates are 0, -3. The x intercept is 2,0. You can calculate the rise (3) over run (2) from these two points. The slope of the function is 3/2, the correct answer is (B).

## 7.

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).

## 8.

The Correct Answer is (B) — If we write out an algebraic expression from the word problem we get $0.05v +$0.10t = $3.10, so we know (I) is true. The word problem also tells us that v + t = 54, so we know (II) is also true. v = 54 - t and t = 54 - v. We can see that (III) has misplaced the variables in the equation.$0.05t + $0.10v does not equal$3.10. Therefore, we know (III) is incorrect. The correct answer is (B); only (I) and (II) are true.

## 9.

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.

## 31.

The Correct Answer is (18) — Setting up the equation as described in the question, we get 2x = 11 + 12 + 13. Adding the right side and dividing both sides by 2, we get x = 18.

## 32.

The Correct Answer is (142) — 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.

## 33.

The Correct Answer is (18) — To make this statement easier to understand, we can set up equations that describe the relationships. 60% of y is x, so x = 0.6y. 30% of z is y, so y = 0.3z. To find x as a percentage of z, we want to get rid of y. We can substitute the second equation into the first and solve for x, giving us x = 0.6(0.3z) = 0.18z. This means that x is 18% of z.

## 34.

The Correct Answer is (3) — We can start by multiplying both sides by , which gives us . We can then rewrite all the bases in terms of base 2, giving us . Then, applying exponent rules, we can simplify the left side to , then . We can then take only the exponents from both sides to solve for x, giving us the equation 15x – 45 = 0. Adding 45 to both sides and dividing both sides by 15, we get x = 3.

## 35.

The Correct Answer is (16) — 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.

## 36.

The Correct Answer is (4) — We can see that the equation given is similar to the standard form for the equation of a circle, which is x^2 + y^2 = r^2 . Adding 7 to both sides, we get x^2 + y^2 = 16. We can see now that 16 should equal r^2. This means that r^2 = 16 and r = 4.

## 37.

The Correct Answer is (12) — We see that the question asks for us to compare times for “each mile,” so we can set our calculations up as seconds per mile instead of miles per second. In Week 3, she took 68 min × 60 s/min = 4080 seconds to run 8 miles, meaning she took 4080/8 = 510 seconds to run each mile. In Week 4, she took 5220 seconds to run 10 miles, so it took her 522 seconds to run each mile. Compared to Week 3, it took her 12 more seconds to run each mile.

## 38.

The Correct Answer is (8) — Again this question asks for her speed in terms of minutes per mile, so we’ll set up our questions likewise. We can start by getting her desired speed in terms of her current speed. 3 hours and 54 minutes translates into 234 minutes, so that’s a rate of 234 minutes/26 miles = 9 minutes/mile. She currently runs 11 minutes/mile, so she will have to improve by 2 minutes/mile in total, or 120 seconds/mile. If she improves at 15 seconds/mile every week, and she needs to improve by a total of 120 seconds/mile. That means it will take her (120 seconds/mile )/(15 seconds/mile)=8 weeks to get to her desired speed.