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: (C)

Given:
A circle with center O and diameter AB Circumference of the circle is
Two semicircles with diameters OA and OB

To find:
Length of the curved path from A to B through O

Solution: Topic(s): Circumference of circle

Formula for circumference of circle is

The circumference is given as

So, AB, which is the diameter of the circle, is 36.

The curved path from A to B through O joins together to form a circle with diameter of AO.

From the diagram, we can see

The circumference of the circle with diameter AO is

Answer: (C)

12. Correct answer: (C)

Given:
The table

x

f(x)

0

a

1

24

2

b

f is a linear function

To find:
The value of a + b

Solution: Topic(s): Equation of a line

Since f is a linear function, this means that the slope of f is constant.

Answer: (C) 48

13. Correct answer: (A)

Given:
The sequence 3, 5, –5, …
Each even term is 2 more than previous term
Each odd term, after the first, is –1 times the previous

To find:
The 55 th term of the sequence

Solution: Topic(s): Number sequence problems

From the question, the formula to generate the sequence of numbers is
+2, × –1
Continue writing out the sequence of numbers until you find a repeating pattern.
3, 5, –5, –3, 3, 5, …

Notice that the sequence repeats after four terms.
To find the 55th term, get the remainder for 55 ÷ 4, which is 3.
The 55th term is the same as the 3rd term, which is –5.

Answer: (A) –5

14. Correct answer: (A)

Given:
Line l is y = 2x + 5
Line m is the reflection of line l in the x-axis

To find:
The equation of the line m

Solution: Topic(s): Coordinate geometry

Line l is y = 2x + 5
Line m is the reflection of line l on the x-axis.

A reflection on the x-axis would mean that all the values of y are changed to their negative equivalents: y → – y – y = – (2x + 5) = –2x – 5

Answer: (A) y = –2x – 5

15. Correct answer: (C)

Given:
The graph that shows Elina’s height from the age of 6 to the age of 12

To find:
Elina’s height at age 12 was at what percent greater than her height at age 6

Solution:
From the graph:
Elina’s height at age 12 is 60 inches.
Elina’s height at age 6 is 45 inches.
Difference in height is 60 – 45 = 15

Percentage of difference in height compared with height at age 6 is

Answer: (C)

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