1.
The Correct Answer is (B) —
Combining like terms gives 3x + 6 = 5x. You can subtract 3x from each side of the equation to get 6 = 2x, so x = 3.
2.
The Correct Answer is (B) —
The question asks you simply to add the two expressions. Combine like terms to get a2 – a + 6.
3.
The Correct Answer is (A) —
The absolute value function in the graph has been shifted to the right by 2 units, so it is |x – 2|. Since the function is drawn with a solid line and the shaded values are above it, you know the y values are greater than or equal to the function, so y ≥ |x – 2|.
4.
The Correct Answer is (C) —
Let m represent the amount of money that Sophia and Jazmin had originally. Then 2(m – 15,000) = m + 15,000 after Sophie gives Jazmin $15,000. Rearranging gives 2m = m + 45,000, so m = 45,000.
5.
The Correct Answer is (B) —
The graph is of a parabola, so (C) and (D) cannot be correct, since they are equations of lines. The graph is shifted to the left by 5 units, meaning that 5 is added to rather than subtracted from x in the equation for this function. Therefore, (B) is correct.
6.
The Correct Answer is (A) —
Because Luca pays the same amount in rent every month, the value 1,195 should not be multiplied by x. However, the $0.10 he pays for electricity does vary according to how many kilowatt-hours he uses, so that value must be multiplied by x. Adding the two together gives you 1,195 + 0.1x dollars.
If you chose (C), you may have forgotten that the electricity cost was ten cents, not dollars, per kWh.
7.
The Correct Answer is (B) —
If two lines are parallel, it means that their slopes are equal. It may be helpful to put the equations in slope-intercept form: y = –ax + 5 and y = -3x + 5/2. It is now clear that a = 3.
If you chose (D), you may have forgotten to divide the second equation by 2.
8.
The Correct Answer is (A) —
By the Alternate Interior Angles Theorem, if a transversal intersects two parallel lines, then the alternate interior angles are congruent. This means that angle AFD is 30° because it is the same as angle CAF. The angle y must be 90° since it forms a triangle with F and D. Similarly, we know that angle ABD is 60° because it is equal to angle BDF, and because BD is parallel to CE, angle BCE is also 60°. This means that angle x is 180° – 60° = 120°, so x – y = 120° – 90° = 30°.
If you chose (C) or (D), you may have found either the value of y or x and stopped there.
9.
The Correct Answer is (D) —
Rearranging the equation above the question gives you:
Plugging this into the other given equation gives you:+4x&space;&=&space;36&space;%5C%5C&space;12x&space;&=&space;36&space;%5C%5C&space;x&space;&=&space;3&space;%5Cend%7Balign*%7D "\begin{align*} 2(4x)+4x &= 36 \\ 12x &= 36 \\ x &= 3 \end{align*}")
Plugging this into the other given equation gives you:
You know that y = 4x = 4(3) = 12. Finally, x + y = 3 + 12 = 15.
If you got (A) or (C), you found the value of x or y and stopped there.
10.
The Correct Answer is (B) —
By looking at the equation given, you can see that as h increases by 1, C decreases by 2. This means that after an hour, Niki has two fewer cars remaining to test drive, meaning that he test drives cars at a rate of 2 per hour.
11.
The Correct Answer is (B) —
You can factor (x2 – 1) = (x + 1)(x – 1), and then cancel out the (x + 1) from the numerator and denominator (since you know that x is positive, this expression cannot equal zero). You are then left with (x – 1)(x – 1) = (x – 1)2.
12.
The Correct Answer is (B) —
You can expand the binomials to get f(x)=cx2 – 9c. From here, you can see that the equation is now in the quadratic standard form f(x)=ax2 + bx + c. When considering the graph of a parabola, the constant a affects its width, the constant b affects its horizontal shift, and the constant c shows its y-intercept. In this case, the equation is missing its middle term, so b=0. This means that the graph has no horizontal shift. So, the axis of symmetry is the y-axis. The vertex lies on this line of symmetry, so its x-value is 0. This means that the vertex of the parabola is (0, -18), and plugging that point into the given equation and solving for c gives you c=2.
13.
The Correct Answer is (D) —
You can rewrite the left side of the equation as:
By comparing this with the right side of the equation, you can see that a = –4.
14.
The Correct Answer is (A) —
Rewrite the sentence as 5x = x2 – 14. This can be rearranged to give 0 = x2 – 5x – 14, which factors as (x + 2)(x – 7). Of the solutions, –2 and 7, only –2 is negative.
15.
The Correct Answer is (B) —
Since each circle has an area of π, you know that each circle has a radius of 1. If you draw a square connecting the centers of the circles, that square will have an area of 4, since each side has length 1 + 1 = 2. That square covers the shaded area, but the shaded area does not include the four quarter-circles also covered by the square. Subtracting those four quarter-circles leaves you with an area of 4 – 4(π/4) = 4 – π.
16.
The Correct Answer is (63) —
Rearranging the first equation gives you y = 16 – x. Plugging this in for y in the second equation:
&space;&=-2&space;%5C%5C&space;x+x-16&space;&=-2&space;%5C%5C&space;2x&space;&=14&space;%5C%5C&space;x&space;&=7&space;%5C%5C&space;%5Cend%7Balign*%7D "\begin{align*} x-(16-x) &=-2 \\ x+x-16 &=-2 \\ 2x &=14 \\ x &=7 \\ \end{align*}")
Substitute this value of x into the first equation to get y = 16 – 7 = 9. Therefore, the value of xy is (7)(9) = 63.
17.
The Correct Answer is ($$ \frac 15 \le x \le 1 $$) —
The correct answers is anything in the range ⅕ ≤ x ≤ 1. First, substitute y = 2x into the first inequality to get |3x - 1| ≤ 2x. Split this absolute value expression into two cases and solve the first case:
Next, solve the second case:
You can see that x ≤ 1 and x ≥ ⅕. Combining these conditions tells you that a possible value for x is anything in the range ⅕ ≤ x ≤ 1.
18.
The Correct Answer is (7) —
The slope of the line that passes through these points is equal to the difference in y-values divided by the difference in x-values: 
. You can cross-multiply and simplify to find that a = 7.
19.
The Correct Answer is (3) —
You know that the width of the rectangle is 6, so to have an area of 24 it must have a height of 24/6 = 4. Since you are given one y-value, –1, the other y-value must be 3 for the rectangle to have a height of 4.
20.
The Correct Answer is (18) —
Notice that you can square both sides of the first equation to get:%5E2&space;&=&space;(-6)%5E2&space;%5C%5C&space;x%5E2&space;+&space;2(x)(%5Cfrac%7B9%7D%7Bx%7D)&space;+&space;%5Cfrac%7B81%7D%7Bx%5E2%7D&space;&=&space;36&space;%5C%5C&space;x%5E2&space;+&space;18&space;+&space;%5Cfrac%7B81%7D%7Bx%5E2%7D&space;&=&space;36&space;%5C%5C&space;x%5E2&space;+&space;%5Cfrac%7B81%7D%7Bx%5E2%7D&space;&=&space;18&space;%5Cend%7Balign*%7D "\begin{align*} (x+\frac{9}{x})^2 &= (-6)^2 \\ x^2 + 2(x)(\frac{9}{x}) + \frac{81}{x^2} &= 36 \\ x^2 + 18 + \frac{81}{x^2} &= 36 \\ x^2 + \frac{81}{x^2} &= 18 \end{align*}")
