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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: (E)**

Given:

A table with the values of the linear function *g* for selected values of *t*

To find:

The function that defines *g *

Solution:

Topic(s): Coordinate geometry

The *y*-intercept occurs at *t* = 0.

From the table, when *t* = 0, *g*(*t*) = 2.

So the *y*-intercept is at 2. We can eliminate (A), (B) and (C)

The slope is

The slope is –2. So, the answer is (E) *g*(*t*) = – 2*t* + 2

**Answer: (E) g(t) = – 2t + 2**

**12. Correct answer: (C)**

Given:

A scatter plot that shows the distance that the students at various grade levels travel to school.

To find:

The statement that is true

Solution:

For questions involving scatter plots, we need to check the answers with the grid to find the one that is true.

(A) There is only one student who travels 2 miles to school. *(From the grid, there are 2 students who travel 2 miles to school)*

(B) Half of the students travel less than 4 miles to school. *(From the grid, 5 students travel less than 4 miles from school and 5 is not half of the students)*

(C) More 12 th graders than 11 th graders travel 6 or more miles to school. *(From the grid, three 12 th graders and two 11 th graders travel 6 or more miles to school)*

(D) The students who travel less than 3 miles to school are all 12 th graders. *(From the grid, the students who travel less than 3 miles to school are not 12 th graders)*

(E) Of the students who travel 7 or more miles to school, half are 9 th graders. *(From the grid, two 9 th graders and three non-9 th grader travel 7 or more miles to school and 2 is not half of 5)*

**Answer: (C)**

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

To find:

The number of positive 3-digit integers that have hundreds digit equal to 3 and the unit digit equal to 4

Solution:

Hundreds digit = 3 and units digit =4

The possible integers are 3*x*4 where *x* is from 0 to 9 inclusive. So, there are 10 integers.

**Answer: (A) 10**

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

Given:

The graph of the line *y = mx+ b *, where *m* and *b *are constants

To find:

The graph that represents *y* = –3*m* + *b*

Solution:

Topic(s): Coordinate geometry

From the figure given, the slope *m* is negative and *b* is negative.

So, for the line *y* = –3*m* + *b*. The slope –3*m* is positive because *m* is negative and the *y*-intercept is negative because *b* is negative.

From the graphs shown only (D) has a positive slope and a negative *y*-intercept.

**Answer: (D) **

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

Given:

Volume of cube = 8

To find:

Shortest distance from the center of the cube to the base of the cube

Solution:

Let *s* be the length of the side of the cube.

The shortest distance from the center of the cube to the base of the cube = half of the length of the height (side) of the cube =

**Answer: (A) 1**

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