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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.

**16. Correct answer: 10**

Given:

The figure

2 circles with same center

Shaded area = 64π

The smaller circle has a radius of 6

To find:

The radius of the larger circle

Solution:

Topic(s): Area of circle

Let *r* be the radius of the bigger circle

Shaded area = Area of bigger circle – area of smaller circle

**Answer: 10**

**17. Correct answer: 8**

Given:

*p*, *r* and *s* are 3 different prime numbers greater than 2

*n* = *p* × *r* × *s *

To find:

The number of positive factors of *n*, including 1 and *n*

Solution:

Topic(s): Factors

The positive factors of *n* are

1, *n*, *p, r, s, pr, ps, *and *sr*

There are 8 factors

**Answer: 8**

**18. Correct answer: 70**

Given:

*h*(*t*)= *c* – (*d* – 4*t*)^{2}

At *t* = 0, the height = 6

At *t* = 2.5, the height = 106

To find:

The height of the ball at time *t*

Solution:

Substitute *t* = 0 and *h*(*t*) = 6

6 = *c* – *d*^{2} (equation 1)

Substitute *t* = 2.5 and *h*(*t*) = 106

Replace *c* – *d* 2 by 6 (from equation 1)

(equation 2)

To find height at *t* =1.

(equation 3)

Substitute equation 1 and equation 2 into equation 3

*h*(1) = 6 + 8(10) – 16 = 70

**Answer 70**

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