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:
10m^{2}k^{-1} = 100m where m and k are positve

To find: m^{-1} in terms of k

Solution: Topic(s): Exponents

Divide both sides with 10m^{2}

Answer: (D)

7. Correct answer: (E)

Given:
Edna and Nancy walked for 4 hours
Edna walked East at 4 km/h
Nancy walked North at 3 km/h

To find:
The distance between them at the end of 4 hours

Solution: Topic(s): 3-4-5 triangle

The above diagram shows the paths and distances taken by Edna and Nancy. (Distance = Rate × Time)

It is a 3-4-5 triangle: The ratio of the sides tells us that the hypotenuse would be 5t = 5 × 4 = 20

Answer: (E) 20

8. Correct answer: (C)

Given:
The graph with minimum point (1,1) f(b) = f(3)

To find:
The value of b

Solution:
Topic(s): Coordinate geometry

From the graph we find the f(3) = 5.
The other place where the y-coordinate of the graph is also 5 is at x = –1 i.e. f(–1) = 5

Answer: (C) –1

9. Correct answer: 7

Given:
A family of 5 planning a 4-day trip
Each person brings one bottle of water for each day
The water is sold in 3-bottle packages

To find:
The number of packages the family must buy

Solution:
The family needs 5 × 4 = 20 bottles.
The water is sold in 3-bottle packages.
The smallest multiple of 3 greater than 20 is 21.
7 × 3 = 21

Answer: 7

10. Correct answer: 13

Given:

To find:
The value of k

Solution: Topic(s): Absolute value

The equation

can be rewitten as two equations:
10 – k = 3, 10 – k = –3

We can then get two possible values for k.

10 – k = 3 ⇒ k = 10 – 3 = 7
10 – k = –3 ⇒ k = 10 + 3 = 13

We test out the two values of k for the second equation given in the question.

Answer: 13

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