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: (A)**

Given:

Set *X* = {30, 31, 32, 33}

Set *Y* = {32, 33, 34, 35, 36}

To find:

The number of numbers that are in set *X* and are also in set *Y *

Solution:

The numbers that belong to both sets are 32, 33

**Answer: (A) Two**

**2. Correct answer: (C)**

Given:

Peg traveled 10 miles in 2 hours

Linda traveled twice as far in half the time

To find:

Linda’s average speed

Solution:

Peg traveled 10 miles in 2 hours

Linda travels twice as far (which is 20 miles) at half the time (which is 1 hour)

Linda’s speed would be 20 mph

**Answer: (C) 20**

**3. Correct answer: (C)**

Given:

*x* = *k*(*k* − 2)

To find:

*x* + 1

Solution:

*x* = *k*(*k* − 2)

*x* + 1 = *k*(*k* − 2) + 1

*x* + 1*= k*^{2} − 2*k* + 1

**Answer: (C) k^{2} − 2k + 1 **

**4. Correct answer: (B)**

Given:

The figure with the graph, *y* = *ax + b*, where *a* and *b* are constants.

To find:

The graph of the line *y = *2*ax + b *

Solution:

Topic(s): Coordinate geometry

Comparing the lines:

Line 1: *y* = *ax + b
*Line 2:

Slope of line 1 is *a* and the slope of line 2 is 2*a*.

So, the slope of line 2 is twice that of line 1.

*y*-intercept of line 1 = *y*-intercept of line 2 = *b*

The line where the slope has increased and the intercept is the same as line 1 is shown in graph (B)

**Answer: (B)**

**5. Correct answer: (A)**

Given:

The figure of a triangle

The perimeter of the triangle is 4 + 2

To find:

The value of *x*

Solution:

Topic(s): 45-45-90 special triangle

The triangle is a right triangle with 2 equal sides and so it must be a 45-45-90 special triangle.

**Answer: (A) 2**

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