More Lessons for SAT Math

More SAT Test Preparation

Math Worksheets

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: 875**

Given:

for all positive integers *x*, *y* and *z *

To find:

The value of

Solution:

**
= **10

= 1000 − 125

= 875

**Answer: 875**

**12. Correct answer: 2, 3**

Given:

The figure

*PQST* is a rectangle

*URST* is a square

*PU* = 5

*UT* is a positive number

Area of *PQST* must be more than 10 but less than 30

To find:

One possible value of *UT *

Solution:

Topic(s): Area of rectangle

Let *x* = *UT
*10 < area of

10 <

We need to find one integer value for *x* that will fit the range.

For example

Let *x* = 2.

*x*(*x* + 5)

= 2( 2 + 5)

=14

* x* can also be 3

Let *x* = 3.

*x*(*x* + 5)

= 3( 3 + 5)

=24

**Answer: 2 or 3**

**13. Correct answer: 36
**Given:

of the balloons are red

There are half as many green balloons, as there are red balloons

There are 18 blue balloons

To find:

The number of balloons

Solution:

Let *x* = number of balloons in the box

**Answer: 36**

**14. Correct answer: 12**

Given:

Points *P, Q* and *R* lie on a line *l
*Points

To find:

The total number of different lines that can be drawn so that each line contains exactly 2 of the 7 points

Solution:

In order to draw the line, we need one point from *P*, *Q *or *R* and another point from *S, T, U* or *V*.

The total number of possible selections would be 3 × 4 = 12

**Answer: 12**

**15. Correct answer: 5**

Given:

2* ^{x}* +
2

To find:

The value of *x*

Solution:

Topic(s): Exponents

(Be careful, we can only add the exponents when we are multiplying bases that are equal)

**Answer: 5**

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