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: (E)**

Given:

2, 6, 14, 30, …

The 1 st term is 2

Each number after the first is obtained by adding 1 to the preceding number and then doubling the result

To find:

The 6^{th} number in the sequence

Solution:

Topic(s): Number sequence problems

We can continue by calculating the 5^{th} term from the 4^{th} term and so on

5^{th} term: 2(30 + 1) = 62

6^{th} term: 2(62 + 1) =126

**Answer: (E) 126**

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

Given:

*a*(*x* + *y*) = 45

*ax* = 15

To find:

The value of *ay *

Solution:

Topic(s): Isolate variable

*a*(*x* + *y*) = 45

*ax + ay =* 45

15 + *ay = *45

*ay* = 30

**Answer: (E) 30**

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

Given:

The figure of the speedometer

To find:

The speed in miles per hour, indicated by the needle position

Solution:

Looking at the miles per hour speedometer, we find that the values from 30 to 60 are divided into 4 segments.

This means that each segment is = 7.5 miles per hour.

The needle is at the first segment after 30. So, it is at 30 + 7.5 = 37.5

**Answer: (B) 37.5**

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

To find:

The number of different positive 3-digit integers that can be formed if the three digits 4, 5, and 6 must be used in each of the integer

Solution:

Topic(s): Permutations

We can use the permutation formula. The number of possible ways to arrange 3 digits would be 3 × 2 × 1 = 6

**Answer: (C) 6**

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

Given:

The figure

Each rectangular face has area *r
*Each triangular face has area

To find:

The total surface area in terms of *r* and *t *

Solution:

In the figure, there are 3 rectangular faces and 2 triangular faces.

The total surface area is 3*r* + 2*t*

**Answer: (B) 3 r + 2t**

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.