**This is for SAT in Jan 2016 or before.**

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.

**16. Correct answer (B) **

Given:

The figure

Diane travels from *A to B,*from *B* to *C* and from *C* to *D*

*AB* = 16

*BC* = 15

*CD* = 4

To find:

How much shorter is the trip if she travels directly from *A* to *D*

Solution:

Topic(s): Pythagoras theorem

The direct path from *A* to *D* is the hypotenuse of the right triangle *ADE*.

We can use Pythagoras theorem to get the length of *AD*.

Length of *AE* = 16 + 4 = 20

Given:

One circle has a radius of

Another circle has a radius of 1

To find:

Ratio of the area of the larger circle to the area of the smaller circle

Solution:

Topic(s): Area of circle

Area of larger circle = π(1)^{2} = π

Area of smaller circle =

Ratio of area of larger circle to the area of smaller circle =

**Answer: (D) 4:1 **

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

Given:

The sum of consecutive integers from –22 to *x, *inclusive is 72

To find:

The value of *x*

Solution:

Topic(s): Consecutive integer problems

The consecutive integers for –22 to *x* inclusive are

-22, -21, -20, …, -1, 0, 1, …,22, 23,.., *x*

Sum of consecutive numbers from –22 to 22 is 0

We can then add from 23 until we get the sum of 72

23 + 24 + 25 = 72

**Answer: (B) 25**

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

Given:

*k, n, x* and *y* are positive numbers

To find:

The value of in terms of *n* and *k *

Solution:

Topic(s): Exponents

**Answer: (A)**

**20. Correct answer: (E)**

Given:

*f*(*x*) = *x*^{2} – 4*x*

*g*(*x*) = *f*(*x* + *h*) + *k*

To find:

The value of *hk *

Solution:

This is a graph translation question.

From the graph, we see that the function *g*(*x*) is the function *f*(*x*) moved 3 units to the right and 2 units down.

Moving 3 units to the right means *h* = – 3 and moving 2 units down means k = – 2 i.e. *g*(*x*) = *f*(*x* – 3) – 2

So, *hk* = (-3)(-2) = 6

**Answer: (E) 6**

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