The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the The Official SAT Study Guide Second Edition.
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: 104
Each angle of triangle ABC has the same measure as each angle in triangle XYZ
Length of one side of triangle XYZ is 24
One possible perimeter of triangle XYZ
Topic(s): AA rule, similar triangles, perimeter of triangle
You were told that the each corresponding angles of the two triangles are equal. This fulfils the AA Rule, so we know the two triangles are similar. Being similar triangles, the ratio of the corresponding sides of the two triangles would also be the same.
Lets take the ratio of the sides to be
Perimeter = sum of all three sides = 24 + 48 + 32 = 104
There are other possible measurements for triangle XYZ, but you only need to find one of them.
12. Correct answer: 202
Sum of 5 consecutive integers is 5
The value of the greatest of these integers
Topic(s): Consecutive number problem
Let x = first consecutive number
The greatest number is x + 4 = 198 + 4 = 202
13. Correct answer: 3
y = g(x)
h(x) = g(2x) + 2
The value for h(1)
h(x) = g(2x) + 2
h(1) = g(2 × 1) + 2
= g(2) + 2
The value of g(2) from the graph is 1.
h(1) = 1 + 2 = 3
14. Correct answer: 24
Exactly 4 actors try out for 4 parts in a play
Each actor can perform any one part
No one can perform more than one part
The number of different assignments of actors possible
When you select number after number from the same group, the number of possible outcomes will decrease by 1 for each choice.
The number of possible assignments is 4 × 3 × 2 × 1 = 24
15. Correct answer: 40
Triangle PQR is equilateral
intersect at point P
The value for y
Topic(s): Equilateral triangles, vertical angles
Since triangle PQR is equilateral, each of its angles is 60º.
This means that angle QPR is 60º.
Angle SPT and angle VPR are vertical angles and so are equal.
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