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: 135

Given:
The figure

To find:
The value of x

Solution: Topic(s): Pairs of angles

a + 90 + 65 = 180 (supplementary angles) ⇒ a = 25

b = a = 25 (vertical angles)

20 + x + b = 180 (supplementary angles)

⇒ 20 + x + 25 = 180 ⇒ x = 135

Answer: 135

12. Correct answer: 46

Given:
The median of a set of 9 consecutive integers is 42

To find:
The greatest of these 9 integers

Solution: Topic(s): Statistics

Median is the middle value of a list when the numbers are in order.

The middle value of the 9 numbers would be the fifth number.

The greatest number will be the 9^{th} number, which is 42 + 4 = 46

Answer: 46

13. Correct answer: 28

Given: f(x) = x + 1
2f(p) = 20

To find: f(3p)

Solution:
Given the function f(x) = x + 1

2f(p) = 2(p +1) = 20 ⇒ p + 1 = 10 ⇒ p = 9

f(3p) = f(3 × 9) = f(27) = 27 + 1 = 28

Answer: 28

14. Correct answer: 70

Given:
The figure

To find:
The value of x

Solution: Topic(s): Types of triangles, pairs of angles

means that LMN is an isosceles triangle.

The base angles of an isosceles triangle are equal.

Let a = angle LNM = angle LMN

125 + a = 180 (supplementary angles)

⇒ a = 55

a + x = 125 (corresponding angles)

⇒ 55 + x = 125 ⇒ x = 70

Answer: 70

15. Correct answer: 7/15

Given:

cup of orange juice

Filled to 1 cup with a mixture that contains equal amounts of orange, grapefruit and pineapple juices

To find:
The fraction of the final mixture that is orange juice

Solution:

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