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: (B)

Given:
The rectangle ABCD is made up of 7 non-overlapping rectangles
The 2 smallest rectangles have the same area
Each of the other rectangles has twice the area of the next smaller rectangle

To find:
The area of the shaded rectangle is what fraction of the area of the rectangle ABCD

Solution: Topic(s): Area of rectangle

Fill up the rectangle, each time reducing the area by half.

Answer: (B)

12. Correct answer: (B)

Given:
2x < y < 0

To find:
The answer that is the greatest value

Solution: Topic(s): Signed operations

We can choose any values for x and y that is true for the inequality.
2x < y < 0

Choose y = – 1 and x = – 2.

Test each of the answers. Be careful about the signed operations.

Given:
He delivers n packages on Monday
4 times as many on Tuesday as on Monday
3 more packages on Wednesday than on Monday

To find:
The average number of packages delivered per day over the 3 days

Solution: Topic(s): Statistics

Given n = Mon

Then, 4n = Tues

n + 3 = Wed

Answer: (C) 2n + 1

14. Correct answer: (E)

Given:

To find:
The answers that must be true

Solution: Topic(s): Exponents, difference of two squares, distributive rule

Square both sides of the equation.

Recognize that it is a difference of two squares or use the distributive rule.

Answer: (E)

15. Correct answer: (E)

Given:
The graphs: y = x^{2} y = a – x^{2} PQ = 6

To find:
The value of a

Solution: Topic(s): Coordinate geometry

The two graphs are symmetrical about the y-axis.

If PQ = 6,then the point Q is units from the y-axis.

This means that the x-coordinate of point Q is 3.

The y-coordinate of Q can be obtained by substituting x = 3 into the equation y = x 2. y = x^{2} = 3^{2} = 9

Point Q is (3, 9).
Point Q also belongs to the graph y = a – x 2.

Substituting x = 3 and y = 9 into y = a – x 2.
9 = a – 3^{2
}a = 9 + 9 = 18

Answer: (E) 18

16. Correct answer: (D)

Given:
Set X has x members
Set Y has y members
Set Z has all members that are either in set X or set Y with the exception of k common members

To find:
The expression that represents the number of members in set Z

Solution: Topic(s): Sets

Number of members in set X excluding k is x – k.
Number of members in set Y excluding k is y – k.
Number of members in set Z = x – k + y – k = x + y – 2k

Answer: (D) x + y – 2k

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