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.

6. Correct answer: (D)

Given: AC = 24 AB = BC Point D is on the line between A and B such that AD = DB

To find:
The value of DC

Solution:

AC = 24

If B bisects AC, then AB = BC = 12
If D bisects AB, then AD = DB = 6 DC = DB + BC = 6 + 12 = 18

Answer: (D) 18

7. Correct answer: (B)

Given: n is a positive integer

To find:

Solution: Topic(s): Exponents

Answer: (B)

8. Correct answer: (B)

To find:
How many more degrees of arc are there in of a circle than in of a circle

Solution: Topic(s): Arc of circle

The difference in arc sizes is

The difference in degrees is

Answer: (B) 18º

9. Correct answer: (B)

Given:
The graph of function f

To find:
The values of x for which f(x) is negative

Solution: f(x) is negative when the graph is below the x-axis

The values of x for which f(x) is negative (below the x-axis) is 0 < x < 6

Answer: (B) 0 < x < 6

10. Correct answer: (C)

Given:
The figure of a pedestal constructed of 4 layers of marble
Each layer is a rectangular solid that is 1 foot high and has a square base

To find:
The number of cubic feet of marble that make up the pedestal

Solution:
Starting from the highest block:

Volume of 1^{st} block = 1 × 1 × 1 = 1

Volume of 2^{nd} block = 2 × 2 × 1 = 4

Volume of 3^{rd} block = 3 × 3 × 1 = 9

Volume of 4^{th} block = 4 × 4 × 1 = 16

Sum of all the volumes = 1 + 4 + 9 + 16 = 30

Answer: (C) 30

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