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.

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

Given:

The graph of a quadratic function *h* whose maximum value is *h*(2)

*h*(*a*) = 0

To find:

The value of *a *

Solution:

If *h*(*a*) = 0, then *x* = *a* is where the graph intersects the *x*-axis.

The maximum value at *h*(2) means that the graph is symmetrical along the line *x* = 2

We can** eliminate (C)**. If *a* = 2, then the graph must intersect the *x*-axis at *x = *2. The given graph does not intersect the *x*-axis at *x = *2.

We can **eliminate (D)**.If *a* = 3, then the graph must intersect the *x*-axis at *x = *3.In order for the graph to intersect the *x*-axis at *x = *3, the other intersection must be at *x* = 1 (to maintain the symmetry of the graph) and the graph would like that:

We can

The only answer left is (A). If the graph intersects the *x*-axis at *x = *-1, the other intersection must be at *x* = 5 (to maintain the symmetry of the graph). A sketch the graph (as shown below) will indicate that it could be the given figure.

**Answer: (A)**

**17. Correct answer: (D)**

Given:

*x*^{2} + *kx* + 7 = (*x* +1)(*x* + *h*)

*k* and *h* are constants

To find:

The value of *k *

Solution:

(*x* +1)(*x* + *h*)

= *x*^{2} + *hx + x + h
= x*

Equating the 2 equations:

*x*^{2} + (*h +*1)*x + h * = *x*^{2} + *kx* + 7

We find that

*h* = 7

and *k* = *h* + 1 = 7 + 1 = 8

**Answer: (D) 8**

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

Given:

The figure

The legs of triangle *ABC* are parallel to the axes

To find:

Which of the following could be the length of the sides of triangle *ABC *

Solution:

Topic(s): Coordinate geometry, Pythagoras theorem

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

Given:

*f*(*x*) = 2*x* − 1

To find:

The value of *t*

Solution:

Topic(s): Isolate variable

**Answer: (E)**

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

Given:

*k* is a positive integer

To find:

Which of the following represent an even integer that is twice the value of an odd integer

Solution:

Topic(s): Odd and even numbers

If *k* is an integer then 2*k* would be an even integer and

2*k* + 1 would be an odd integer.

Twice 2*k* + 1 = 2(2*k* + 1)= 4*k* + 2 would be an even integer

**Answer: (E) 4 k + 2**

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