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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.

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

**Given:**

The line *l* that has a positive slope

Line *l* passes through (0, 0)

Line *k* is perpendicular to *l *

**To find: **

The statement that is true for line *k *

**Solution: **

Topic(s): Coordinate geometry

If *k *is perpendicular to *l *then the product of their slopes is –1.

Since *l *has a positive slope, it means that *k* must have a negative slope.

**Answer: (C) line k has a negative slope.**

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

** Given: **

**To find:**

The value of *x*

**Solution: **

Topic(s): Symbol problems

**Answer: (A) 4**

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

**Given: **

One shirt costs *x* dollars

Each additional shirt costs *z* dollars less than the first shirt

**To find: **

The expression that represents the cost for *n* shirts

**Solution:**

Try to detect the pattern:

1 shirt → *x
*2 shirts →

3 shirts →

.

.

.

**Answer: (A) x + (n – 1) (x – z)**

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

**Given:**

*QR* is the arc of a circle with center *P
*Length of arc

To find:

Area of sector *PQR *

**Solution: **

Topic(s): Circles, angles

Formula of circumference of circle:

Angle *QPR* is 30º. The sum of angles around a point is 360º.

This means that the arc *QR* is of the circumference of the circle =

Given Arc *QR* =

Area of sector PQR is of the area of the circle.

Formula of area of circle:

Substitute *r* = 36

**Answer: (A)**

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

**Given: **

75 more women than men enrolled

*n *men enrolled

**To find: **

In terms of *n*, the percent of those enrolled are men

**Solution: **

Topic(s): Percent

Let *n* = men

*n* + 75 = women

Total = *n* + *n* + 75

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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