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.

6. Correct answer: (D)

Given:
The number line

To find:
The point that is closest to |u + v|

Solution: Topic(s): Absolute value

|u + v| is an absolute value, so it will always be positive.

We can eliminate points t and w.

To decide between x, y and z, we have to approximate the values of u and v.

u is approximately –0.75 and v is approximately –0.5.

|u + v| is approximately |–0.75 +(–0.5)| = |–1.25| = 1.25

The point closest to 1.25 is point y.

Answer: (D) y

7. Correct answer: (B)

Given:

To find:

Solution: Topic(s): Fractions

Substitute into the equation

Answer: (B) 0

8. Correct answer: (A)

Given:
The figure RS = ST S is (k, 3)

To find:
The value of k

Solution: Topic(s): Coordinate geometry

SR is perpendicular to the x-axis and parallel to the y-axis.

The y-coordinate of S is 3, which means the length of SR is 3

ST is perpendicular to y-axis and parallel to the x-axis.

We are given that ST = SR. So ST = 3

S is then 3 units to the left of the y-axis.

This means that its x-coordinate (which is k) = – 3

Answer: (A) – 3

9. Correct answer: (A)

Given:
The table

To find:
The function f

Solution:
We can substitute in the values for x and eliminate the answers that do not get the required values for f(x).

We are left with only (A)

Answer: (A) f(x) = x 2 + 1

10. Correct answer: (E)

Given: x years ago, the person was y years old

To find:
The age of the person 1 year ago

Solution: Topic(s): Age problems

Let a be the person’s age now.

x years ago the person’s age was y

a – x = y ⇒ a = y + x

1 year ago, the person’s age would have been:

a – 1 = y + x – 1

Answer: (E) y + x –1

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