More Lessons for SAT Preparation

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.

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

** Given:
**2

** To find:
**4

** Solution:
**

Substitute *x* = 3 into 4*x* – 3

4(3) – 3 = 12 – 3 = 9

** Answer: (B) 9 **

**2.** **Correct answer: (D) **

** Given:
**There are 8 sections of seats

Each section has at least 150 seats but not more than 200 seats

**To find: **

The total number of seats

**Solution:**

**Topic(s): Translating words to equations **

Smallest number of seats is 150 × 8 = 1200

Largest number of seats is 200 × 8 = 1600

The only given answer between 1200 and 1600 is 1,300

**Answer: (D) 1,300**

** 3. Correct answer: (A)**

**Given:**

is perpendicular to *l *

**To find: **

Line segment that has the greatest length

**Solution: **

*Topic(s): Right triangles, Pythagoras theorem*

The line segments given in the answers form the hypotenuse of right triangles.

From the Pythagoras theorem: The longer the two sides of a triangle, the longer will be the hypotenuse.

So, we choose the longest side, which is and the hypotenuse is

**Answer: (A)**

**4. Correct answer: (D)**

**Given:**

The graph showing the total number of children in the family at the end of the year

A set of twins were born

**To find: **

The year the twins were born

**Solution:**

Look at the graph and find the year where there was a change (jump) of two children. There was an increase of two children from 1996 and 1997. This indicates that the twins were born in 1997.

**Answer: (D) 1997 **

**Given:**

The average of *x* and *y* is 5. Number of terms = 2

The average of *x, y* and *z* is 8. Number of terms = 3

**To find:**

The value of *z *

**Solution:**

The formula for average (arithmetic mean) is:

The formula can also be written as

*SumofTerms = Average × Numberof Terms* .....(formula 2)

Substitute the given values into formula 2:

*x* + *y* = 5 × 2 = 10 (equation 1)

*x* + *y* + *z* = 8 × 3 = 24 (equation 2)

Subtract equation 1 from equation 2

*z* = 14

** Answer: (B) 14 **

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.