1.

The Correct Answer is (B) — To find 6x + 4y, all you need to do is multiply both 3x and 2y by 2, and then add them to get (3x)(2) + (2y)(2) = (15)(2) + (10)(2) = 50.

2.

The Correct Answer is (C) — Looking at the answer choices, you can see that all of the coefficients of i are different, so you can find the answer just by finding the coefficient of i. By using FOIL to expand the binomials, you can find that the coefficient of i is equal to (2i)(4) + (i)(3) = 11i. Since none of the other answer choices include the term 11i, you have found the answer.

3.

The Correct Answer is (D) — You can find the solution to this question by determining the slope of the line. The values for two points on the line are (2, 3) and (5, 9), so the slope is equal to (9 – 3) / (5 – 2) = 2. There is only one answer choice with this slope.

4.

The Correct Answer is (B) — First, find the number of tank tops that the printer can produce in one hour:

$\frac{40\;tank\;tops}{5\;hours}=\frac{8\;tank\;tops}{hour}$

Next, multiply this by the number of hours to get:

$\frac{8\;tank\;tops}{hour} \times 7\;hours = 56\;tank\;tops$

10.

The Correct Answer is (A) — The correct answer is (A). First, you can see that the equation is reflected about the y-axis, so the absolute value function must be for x-values; you can eliminate (D). Next, when x is zero, y is –1. Plugging in values, you can see that only equation that gives you this result is $y= \left | x \right | - 1$

11.

The Correct Answer is (A) — The fastest way to solve this is by plugging in values. Start with when x is equal to 0. Plugging this into (A) gives you 6, (B) gives you 7, (C) gives you 6, and (D) gives you 4. Since 6 is the value in the table, either (A) or (C) is correct. When x = 1, (A) gives you 7 and (C) gives you 8, meaning that (A) is correct. You can check the other values in the table to verify that (A) matches the values of all of them.

12.

The Correct Answer is (C) — First, simply square both sides of this equation to get 5x - 5 = y2 + 1. Next, isolate for a variable — in this case x is easier to isolate:

\begin{align*}5x-5=y^2+1\\ x=\frac{y^2+6}{5}\end{align}

You can plug in the given values for x and y and see which one satisfies this equation. (A) gives -1 = 7/5, so it is incorrect. (B) gives 1 = 2, so it is incorrect. (D) gives 4 = 7/5, so it is incorrect. However, (C) gives 3 = 3, so it is correct.

13.

The Correct Answer is (B) — You can use FOIL to expand the binomials on the right side as (ax + 3)(x – 4) = ax2 + (3 – 4a)x – 12. By comparing this to the equation given in the question, you know that 3 – 4a = –5, or a = 2.

14.

The Correct Answer is (C) — First, solve for the missing angle in the upper triangle in the diagram. This is 180 – (75)(2) = 30. Next, since you know this angle, you know that the opposite angle at the top of the lower triangle is also 30 degrees. Now, you can solve for the missing angle of the lower triangle, which is 180 – 30 – 90 = 60. The lower triangle is a 60-30-90 triangle, so you know that the side measurements are in the ratio of 1-2-3 . You can now determine that the hypotenuse of this triangle is 5 x 2 = 10 m.

15.

The Correct Answer is (D) — You can write the numerator as (x + 4)(x – 1) – 6, and so you can rewrite the expression as $\frac{(1+4)(x-1)}{x+4}-\frac{6}{x+4}=x-1-\frac{6}{x+4}$

16.

The Correct Answer is (10) — You want to determine how many rain barrels Jeff and Liz need, and you are given a ratio of 2 barrels per 7 square feet of land. If you multiply this by the total number of square feet in their yard you get $\frac{2\;barrels}{7\;square\;feet}\times 35\;square\;feet=10\;barrels$

17.

The Correct Answer is (5) — Notice that you are given a difference of squares as the first equation. This means that this simplifies to (xy)(x + y) = 20. You know that xy = 4, so x + y must equal 20/4 = 5. Substituting a for x and b for y gives you a + b = 5.

18.

The Correct Answer is (0) — You are dealing with two equations and two unknowns, so you must solve for one variable. In this case, just substitute the second into the first equation: x = 2(–2x – 3) + 6. Simplifying gives 5x = 0, so x=0. Since x = 0, xy = 0 no matter what y is.

19.

The Correct Answer is (16) — You can set up two ratios — the original value of 1/d2 and the new value of 1/d2, and the original force and the new force — since distance is the only factor that changes.

\begin{align*} Original: \frac{1}{d^2} = \frac{1}{4^2} = \frac{1}{16}\\ New:\frac{1}{d^2} = \frac{1}{8^2} = \frac{1}{64}\\Ratio\;of\;\frac{1}{16}\;to\;\frac{1}{64}=4:1\end{align}

Since you know that the original force and the new force must be in the ratio 4:1 = 64:16, the new force must be 16 exanewtons.

20.

The Correct Answer is (48) — You need to find the x-intercept since you can determine that the y-intercept is (0,16) from the equation. Substituting 0 in for y, you get $0=-\frac{4}{3}x + 16$  . Solving for x gives you:

\begin{align*} \frac{4}{3}x = 16\\x=12\end{align}

Now that you have the triangle’s two intercepts, (12,0) and (0,16), you can solve for its perimeter since you know that the two lines x = 0 and y = 0 constitute two of its sides. The base of the triangle is 12, and the height of the triangle is 16. Using the Pythagorean Theorem, you can find that the third side (the hypotenuse) of the triangle has length $\sqrt{12^2+16^2}=20$  . Therefore, the perimeter of the triangle is 12 + 16 + 20 = 48.