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: 110

Given:
A triangle has two equal angles
The lengths of two sides are 50 and 30

To find:
The least possible value of the perimeter of the triangle

Solution: Topic(s): Types of triangles

If a triangle has two equal angles then it would also have two equal sides.

Given that two sides of the triangle are 50 and 30, then the third side can either be 50 or 30.

For the perimeter to be the least possible value, the third side would have to be 30.

The perimeter is then 50 + 30 + 30 =110.

Answer: 110

12. Correct answer: 9

Given: x^{2} – y^{2} = 77
(x + y) = 11

To find:
The value of
x

Solution: Topic(s): Difference of two squares, Addition Method

Use the Difference of two squares to factorize.

Now, we have the two equations:

x + y = 11 (equation 1) x – y = 7 (equation 2)

Use the Addition Method. Add equation 1 to equation 2.

2x = 18 x = 9

Answer: 9

13. Any of the following answers is acceptable: 13, 14, 15, 16, 17

Given:
A circle is sliced into wedge-shaped pieces
The angle of each tip is greater than 20 but less than 30

To find:
One possible value for the number of pieces that can be cut

Solution:

The most number of pieces =

The least number of pieces =

The number of pieces is between 12 and 18 (not including 12 or 18).

Any of the following answers is acceptable: 13, 14, 15, 16, 17

14. Correct answer: 5

Given:
The first term in a sequence is a Each term after the first is 3 times the preceding term
Sum of the first 5 terms is 605

To find:
The value of a

Solution: Topic(s): Number sequence problems

Answer: 5

15. Correct answer:

Given:

To find:

Solution: Topic(s): Area of triangle

Given

Let QS = x and QV = 3x then from the diagram, SV = 2x

Given

Let PT = 3y and PR = 4y

Area of triangle

Answer:

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