The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the Official SAT Study Guide.

It would be best that you go through the SAT practice test questions in the Study Guide first and then look at the worked solutions for the questions that you might need assistance in. Due to copyright issues, we are not able to reproduce the questions, but we hope that the worked solutions will be helpful.

11. Correct answer: (B)

Given:
Line m is a reflection of line l about the x-axis
Slope of line m is

To find:
Slope of line l

Solution: Topic(s): Coordinate geometry

Line l is a reflection of line m about the x-axis.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is changed to the opposite sign.

This means that the slope will also be changed to its opposite sign.

Line m has a slope of so line l would have the slope of

Answer: (B)

12. Correct answer: (A)

Given: n = 3p

To find:
The value of p such that n = p

Solution:
Given n = 3p, the only way that n can be equal to p would be when both n and p are both 0

Answer: (A) 0

13. Correct answer: (D)

Given:
The figure z = 30

To find: x + y

Solution: Topic(s): Supplementary angles

a = 180 – y (supplementary angles) b = 180 – x (supplementary angles) a + b + 30 = 180 (sum of angles in a triangle = 180) ⇒
180 – y + 180 – x + 30 = 180 ⇒
x + y = 180 + 30 = 210

Answer: (D) 210

14. Correct answer: (E)

Given: f(x) = x^{2} + bx + c, where b and c are positive constants

To find:
Which of the folllowing could be the graph of f

Solution: c is the intercept at the y-axis and it is positive.

The only given diagram that has a positive intercept at the y-axis is (E)

Answer: (E)

15. Correct answer: (D)

Given:
A cube with sides = 2 A and B are midpoints of two of the edges

To find:
Length of

Solution: Topic(s): Pythagoras theorem

To get AB, we first AC

Using Pythagoras theorem, AC^{2} = 1^{2} + 2^{2 }= 5

Answer: (D)

16. Correct answer: (C)

Given:

To find:
The value of a

Solution: Topic(s): Symbol problems

Answer: (C)

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