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.

1. Correct answer: (B)

Given: E is a set of even integers P is a set of positive integers F is a set of integers less than 5

To find:
The integer that is in all 3 sets

Solution: Topic(s): Integers

The required integer needs to be even, positive and less than 5

Answer: (B) 4

2. Correct answer: (B)

Given:

To find:
The value of k

Solution:

Answer: (B) 49

3. Correct answer: (A)

Given:
In a poll of 35 people, 14 are against and 1 had no opinion

To find:
Fraction of those polled who are in favor

Solution: Topic(s): Fractions

Total number of people polled = 35 + 14 + 1 = 50

Fraction of people in favor =

Answer: (A)

4, Correct answer: (C)

Given:
The figure

To find:
The value of t + u

Solution: Topic(s): Vertical angles, sum of angles in a triangle

Let a be the size of the angles shown above.

The two angles are equal because they are vertical angles.

The sum of angles in a triangle is 180º.

a + 70 + 30 = 180 ⇒ a = 80 a + t + u ⇒ 80 + t + u = 180 ⇒ t + u = 100

Answer: (C) 100

5. Correct answer: (D)

Given:
The graph

To find:
The 2 consecutive years where there was the greatest change

Solution:
Calculate the change:

(A) 1981 and 1982: 3.75 – 3.5 = 0.25

(B) 1982 and 1983: 4.25 – 3.5 = 0.75

(C) 1983 and 1984: 4.75 – 4.25 = 0.5

(D) 1984 and 1985: 4.75 – 3.75 = 1

(E) 1985 and 1986: 4.5 – 3.75 = 0.75

The greatest change is (D) 1984 and 1985

Answer: (D)

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