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.

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

Given:

A floor that is 12 feet by 18 feet

To find:

The number of square yards of carpet needed to cover the floor

Solution:

Since there is no waste we can just find the area of the carpet and then convert to square yards.

Area of floor = 12 × 18 = 216 square feet = 216 ÷ 9 = 24 square yard

**Answer: (C) 24**

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

Given:

Kitten and bunny weighs 7 pounds

Kitten and puppy weighs 8 pounds

Bunny and puppy weighs 9 pounds

To find:

The weight of the puppy

Solution:

Topic(s): Integer word problem

Let *k* = weight of kitten

*b* = weight of bunny

*p* = weight of puppy

Substitute equation 1 into equation 2

7 − *b* + *p* = 8 (equation 4)

Substitute equation 3 into equation 4

7 − (9 - *p*) + *p* = 8

7 − 9 + *p* + *p* = 8

2*p* = 10 *
p* = 5

**Answer: (D) 5 pounds**

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

Given:

On a blueprint, inch represents 16 feet

A driveway is 40 feet

To find:

The length of the driveway on the map

Solution:

Topic(s): Proportional word problem

If 16 feet then inch, if 40 feet then how many?

16 →

40 →

**Answer: (B) **

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

Given:

The graphs *y* = *x*^{2} + 9 and *y* = *x*^{2} − 9 intersects at (*p*, 0)

*p* is positive

To find:

The value of *p *

Solution:

Since (*p*, 0) is the point of intersection, we can equate the two graphs.

−*x*^{2} + 9 = *x*^{2} − 9

2*x*^{2} = 18

*x*^{2} = 9

*x* = ±3

*p* is positive, so it would have the value 3

**Answer: (A) 3**

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

Given:

The old machine makes 300 bolts per hour

The new machine makes 450 bolts per hour

To find:

The number of minutes it will take the two machines to make a total of 900 bolts

Solution:

Topic(s): Proportional word problem

Let *t* be the time taken by the machines in hours.

300*t* + 450*t* = 900*t*

750*t* = 900

*t* = 1.3

The time in minutes would be 1.2 × 60 = 72

**Answer: (B) 72**

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.