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Chapter 1 59 Glencoe Algebra 2

1

1. Evaluate x3 - y3

− -1(x2 + 2y2)

if x = 4 and y = -2. 1.

2. Evaluate (n - v) 2 + 3v 3 if n = 5 and v = -2. 2.

3. Determine whether the statement is sometimes, always, ornever true. Explain your reasoning.If a and b are real numbers, then - a + 2b is negative. 3.

4. The formula for the volume of a cylinder is V = π r 2 h, where r 4. is the radius of the base and h is the height of the cylinder. Find the volume of a cylinder with a radius of 1.2 inches and a height of 3 inches. Use 3.14 for π.

5. Name the sets of numbers to which each number belongs. 5.

a. -4 b. √ �� 15 c. 0 d. 3 − 4 e. 2

6. Simplify 3 − 8 (16 x - 8) + 2 −

3 (15 y + 12). 6.

7. Write a verbal expression to represent the algebraic expression 4( n 2 + 2n). 7.

For Questions 8–11, solve each equation.

8. -6 (n - 8) = 4 (12 - 5 n) + 14 n 8.

9. 2 3x - 5 = 14 9.

10. A = 1 − 2 h(a + b), for a 10.

11. y - 8 + 7 = 3 11.

12. Define a variable, write an equation, and solve the problem. The width of a rectangle is 3 meters more than one-fourth its length. The perimeter is 10 meters more than twice its length. Find the length and width. 12.

Chapter 1 Test, Form 3

-3

� = length;

2 [� + ( 1 − 4 � + 3) ] =

2� + 10;length: 8 meters width: 5 meters

four times the sum of the square of a number and twice the same number

a = 2A − h - b

Sometimes; if a = -2b, the value of the expression is 0.

25

13.5648 in 3

6x + 10y + 5

all real numbers

{- 2 − 3 , 4}

Ø

a. Z, Q, R

b. I, R

c. W, Z, Q, R

d. Q, R

e. N, W, Z, Q, R

053_064_ALG2_A_CRM_C01_AS_661313.indd 59 12/11/12 2:37 PM

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Chapter 1 60 Glencoe Algebra 2

1

13. The formula for the area of a triangle is A = 1−2

bh,13. where b represents the base length, and h

represents the height. The perimeter of the triangle shown is 28 inches. Write an equation for the area A of this triangle in terms of its base length b.

For Questions 14 –19, solve each inequality. Graph the solution set on a number line.

14. 14 − 5 < 4 x-3 −

5 14.

15. -3(5 y - 4) ≥ 17 15.

16. 5 x + 2 ≤ -18 or 2 x + 1 > 21 16.

17. 33 − 4 ≤ 3w + 9 < 12 17.

18. x - 3 > 5 18.

19. 3w - 7 ≤ 2 19.

20. Define a variable and write an inequality. Then solve the resulting inequality. Mr. Brooks plans to invest part of $5000 in a stock that pays 8% interest annually. The rest will be invested in a savings account that pays 6% interest annually. Mr. Brooks wants to make at least $350 on the investment for the first year. What is the least amount that should be invested in the stock? 20.

Bonus A jet is flying from Hawaii to San Francisco, a distance of 2400 miles. In still air, the jet flies at 600 mph, but there is now a 40-mph tailwind. In case of emergency, how many hours after takeoff will it be faster for the jet to go on to San Francisco rather than to return to Hawaii? B:

b inches

10 inchesh

Chapter 1 Test, Form 3 (continued)

more than 1.75h

{x x ≤ -4 or x > 10}

{x x < -2 or x > 8}

a = amount invested in stock; 0.08a + 0.06 (5000 - a) ≥ 350; at least $2500

A = 1 − 2 b(18 - b)

{x x > 17 − 4 }

{y y ≤ - 1 − 3 }

{w - 1 − 4 ≤ w < 1}

{w 5 − 3 ≤ w ≤ 3}

134

72

154

174

92

194

3 4

43

53

73

103

113

83

2 3

-6-4-2 0 2 6 8 104

-24-1

414

24

34

54

0 1

-4-2 0 62 4 8 10 12

-23

43-1

313

23

-1 0 1

053_064_ALG2_A_CRM_C01_AS_661313.indd 60 12/11/12 2:37 PM