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.

1. Correct answer: (A)

Given:
3m − 1 > 10

To find:
The value of m

Solution: Topic(s): Isolate variable

3m − 1 > 10
3m > 9 m > 3

Answer: (A) 4

2. Correct answer: (D)

Given: a × k = a, , for all values of k

To find:
The value of k

Solution: Topic(s): Isolate variable

a × k = a k = 1

Answer: (D) 1

3. Correct answer: (A)

Given:
The figure

To find:
The value of z

Solution: Topic(s): Vertical angles

We can get the other two angles of the triangle because they are vertical angles of x and y.

z + 70 + 80 = 180 z + 150 = 180
z = 30

Answer: (A) 30

4. Correct answer: (C)

Given:
The scenic route is 5 km longer than the direct route
The round trip is 35 km

To find:
The distance of the direct route

Solution: Topic(s): Integer problems

Let x be the distance of the direct route x + 5 be the distance of the scenic route

x + x + 5 = 35
2x = 30 x = 15

Answer:(C) 15

5. Correct answer: (B)

Given:
A complete cycle takes 80 seconds
The light is green for 40 seconds
The light is amber for 10 seconds
The light is red for 30 seconds

To find:
The probability that the light will not be red

Solution: Topic(s): Probability

Not red means it is either green or amber

Pr(green) + Pr(amber) =

Answer: (B)

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