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More Lessons for SAT Preparation

Math Worksheets

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 **

**Given: **

Each angle of triangle *ABC* has the same measure as each angle in triangle *XYZ
*Length of one side of triangle

**To find: **

One possible perimeter of triangle *XYZ*

**Solution: **

*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.

**Answer: 104**

**12. Correct answer: 202 **

**Given: **

Sum of 5 consecutive integers is 5

**To find: **

The value of the greatest of these integers

**Solution:**

*Topic(s): Consecutive number problem*

Let *x* = first consecutive number

The greatest number is *x* + 4 = 198 + 4 = 202

**Answer: 202**

**13. Correct answer: 3 **

**Given:**

*y = g*(*x*)

*h*(*x*) = g(2*x*) + 2

**To find: **

The value for *h*(1)

**Solution:**

*h*(*x*) = g(2*x*) + 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

**Answer: 3**

**14. Correct answer: 24 **

**Given: **

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

**To find: **

The number of different assignments of actors possible

**Solution:**

*Topic(s): Permutations*

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

**Answer: 24**

**15. Correct answer: 40**

**Given: **

Triangle *PQR* is equilateral

intersect at point *P *

**To find**:

The value for *y *

**Solution: **

*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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