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: (D)

Given:
The sum of a list prices divided by the average of the prices = k

To find:
The value of k

Solution: Topic(s): Statistics

So, k represents the number of prices.

Answer: (D) The number of prices

12. Correct answer: (D)

Given:
The figure
Area of square = 81
Perimeter of each of the 4 triangles = 30

To find:
The perimeter of the figure outlined by the solid line

Solution: Topic(s): Area of square, perimeter of triangle

Given that the area of the square is 81, the length of any one its side would be = 9.

The side of the square is also of base of the triangle. So the length of the base of the triangle is 9.

Given that the perimeter of the triangle is 30, then the lengths of the other two sides of the triangle must be 30 – 9 = 21.

The perimeter of the figure is formed by the 4 of such triangles.
So perimeter = 4 × 21 = 84

Answer: (D) 84

13. Correct answer: (B)

Given:
The graph y = g(x) g(2) = k

To find:
The value of g(k)

Solution:
We are given g(2) = k.
From the graph, we can obtain g(2) = 5. This means that k = 5.
From the graph, we find that g(5) = 2.5

Answer: (B) 2.5

14. Correct answer: (E)

Given:
0 ≤ x ≤ 8
–1 ≤ y ≤ 3

To find:
The smallest and largest possible values for xy

Solution:
The largest value for x is 8 and the largest value for y is 3. Since both the values are positive, the largest value for xy is 8 × 3 = 24

Finding the smallest value would be trickier. The smallest value for x is 0 and the smallest value for y is – 1. Since one of the values is negative, we need to logically consider what would be the smallest negative value for xy. The smallest value would be –1 multiplied with the biggest value of x, which is 8. –1 × 8 = –8

Answer: (E) –8 ≤ xy ≤ 24

15. Correct answer: (B)

Given:
The figure

To find:
The sum of the marked angles in terms of n

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

If you know the rule that the exterior angle of a triangle is equals to the sum of the opposite interior angles then you can work out that a + b = n and c + d = n. So, a + b + c + d = 2n.

If you did not know the rule, you can deduce that n + p = 180 ⇒p =180 – n (supplementary angles) a + b + p =180 (sum of angles in a triangle) a + b + 180 – n = 180 ⇒ a + b = n

Similarly, we can deduce that c + d = n So, a + b + c + d = 2n.

Answer: (B) 2n

16. Correct answer: (C)

Given: t is the first term of a sequence t ≠ 0
After the first term, each term in the sequence is 3 greater than of the preceding term

To find:
The ratio of the 2 nd term to the 1 st term

Solution: Topic(s): Number sequence problems

The first term is t.

Answer: (C)

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