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# the standard deviation

Exponents and Polynomials]

1. Simplify each expression.

a. = b. =

a. (3×2 + 1)(4×2 + 7) =

b. (a + 2)(a3 – 3a2 + 7) =

3. Write a polynomial that describes the area of the shaded region.

[Chapter 5. Factoring Polynomials and Solving Quadratic Equations]

a. 15×3 + 5×2 -6x -2 =

b. -40x8y6 – 16x9y5 =

5. Write an expression for the area of the shaded region. Then write the expression as a factored polynomial.

6. Factor each polynomial completely.

a. 2x3y + 2x2y – 12xy =

b. (x + 2)2 – y2 =

c. X2n – 100 =

7. Find solutions for each equation.

a. x2 – 4x = 32

b. 24×2 + 44x =8

8. Use the quadratic formula to solve the following quadratic equation. Find the exact solutions; then approximate the solution to the nearest tenth (such as -0.6).

x2 + 6x +1 = 0

[Chapter 6 Geometry and Measurement]

9. Find the measures of angles x, y, and z in the figure.

10. Find the perimeter and the area of the figure.

11. Perform each indicated operation. Remember to insert units when writing your answers.

a. 15 km – 2360 m =

b. 5 lb 3 oz x 6 =

c. 6 tons 1500 lb ÷ 5 =

d. 9 g – 7150 mg =

e. 3 gal 1 qt – 1 qt 1 pt =

f. 26º F = º C

[Chapter 7 Introduction to Counting and Probability]

12. You are unsure of 3 questions on a multiple-choice exam. If each question has choices A, B, C, or D, how many different ways can you answer these questions?

13. In how many different ways can we arrange the letters in the word “second”?

14. Find the number of distinct arrangements of 4 of the letters of the word “flower.” No letter may be used more than once.

15. A club with 30 members is selecting a committee of 3 members. How many outcomes are possible for this committee?

[Chapter 8 Introduction to Statistics]

16. For the following set of numbers, find the mean, median, and mode.

7.6, 8.2, 8.2, 9.6, 5.7, 9.1

17. Find the standard deviation of the following data set.

16, 21, 26, 31, 36

18. A brand of standard batteries has an average life span of 2500 hours with a standard deviation of 300 hours.

a. Find the life span for 1 Standard Deviation above the mean.

b. What percent of these batteries should last than 2500 hours?

c. What percent of these batteries should last more than 2800 hours?