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Math Worksheets

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

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: (A)**

Given:

A “simple square” is any integer > 1 that has only three positive integer factors – itself, its square root, and 1.

To find:

The answer that is a simple square

Solution:

Topic(s): Square root of integers

** Answer: (A) 121**

**7. Correct answer: (B)**

Given:

In the triangle *XYZ*, *XZ* is , which is the length of the altitude

To find:

Area of triangle *XYZ *in terms of* h *

Solution:

Topic(s): Area of triangle

From the diagram, we can see that *XZ* is the base (*b*) and *h* is the height of the triangle.

Area of triangle *XYZ* =

**Answer: (B) **

**8. Correct answer: (B)**

Given:

= 432 (where *a* and *b* are positive integers)

To find:

The value of *ab*.

Solution:

Topic(s): Exponents, factors

First, multiply the exponents

Next, find the prime factors of 432.

432 = 3 × 3 × 3 × 2 × 2 × 2 × 2 = 3 3 × 2 4

Then, we change the base to get the exponents of 3 and 2 in order to match with the exponents of *a* and *b*.

3^{3} × 2^{4} = 3^{3} × 4^{2} = *a*^{3}*b*^{2} ⇒ *a* = 3, *b* = 4

*ab* = *a* × *b* = 3 × 4 = 12

** Answer: (B) 12**

**9. Correct answer: 990**

To find:

The greatest three-digit integer that has a factor of 10

Solution:

Topic(s): Factors

Having a factor of 10, means the integer must end with a 0.

In order for it to be the greatest, the other two digits must be 9s.

So, the 3-digit integer must be 990.

**Answer: 990**

**10. Correct answer: 30**

Given:

A recipe for chili for 20 people requires 4 pounds of beans

To find:

Pounds of beans required to make chili for 150 people

Solution:

Topic(s): Proportional word problem

Rewrite the problem as:

If 20 people then 4 pounds, if 150 people then how many pounds?

20 → 4

150 →

**Answer: 30**

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