Chapter 1 Test Form K

Name

Chapter 1 Test

Class

Date

Form K

Do you know HOW?

Identify a pattern and find the next three numbers in the pattern.

1. 25, 21, 3, 7, c

Each term is 4 more than the previous term; 11, 15, 19

2. 64, 32, 16, 8, c

Each term is half of the previous term; 4, 2, 1

3. What properties of real numbers are illustrated by each equation below?

a. 28 1 3 5 3 1 (28) Commutative Property of Addition

b. 4 1 (24) 5 0 Inverse Property of Addition

c. 2(8 1 t) 5 2 ? 8 1 2 ? t Distributive Property

d.

7 8

?

8 7

5

1

Inverse Property of Multiplication

Evaluate the expression for the given value of the variable.

4. a2 2 2(a 1 1); a 5 3 1

5. 5(2s 2 1) 2 3(s 1 2); s 5 4 17

6. The expression 15 1 5x models the daily cost in dollars of renting scuba gear from the water sports store. In the expression, x represents the number of hours the scuba gear is used. What is the cost of renting scuba gear for a day when the gear is used for 3 hours? $30

Solve each equation. 7. 2r 1 2 5 3r 2 5 7

8. 8(t 1 1) 5 64 7

Solve each equation for x. State any restrictions on the variables.

9.

xt

2 8

1

1

3

5

a

x

5

8a

2 t

23 ;

t

u

0

10.

6x

2 5

1

5

y

x

5

5y

1 6

1

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Name

Class

Date

Chapter 1 Test (continued)

Form K

Write an equation and solve the problem.

11. Two buses leave Columbus, Ohio at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 48 mi/h. When will they be 618 mi apart? 6 h

Solve each inequality. Graph the solution. 12. 2n 1 1 $ 7 n L 3

13. 2a 1 5 , 6a 1 1 a S 1

0 12 345 6

0 12 345 6

Solve each compound inequality. Graph the solutions.

14. 3x # 26 or 2x 1 1 $ 3 x K 22 or x L 115. 22t 1 2 , 4 and 2t , 6 21 R t R 3

3 2 1 0 1 2 3

3 2 1 0 1 2 3

Solve each equation. Check for extraneous solutions.

16. u 3x 1 3 u 5 18 x 5 5 or x 5 27

17. u b 1 2 u 5 2b b 5 2

18. The weatherman announced that the temperature T over the next few weeks will be at least 648F and at most 788F. Write an absolute value inequality for the temperature over the next few weeks. ?T 2 71... K 7

Do you UNDERSTAND? 19. What is another name for the multiplicative inverse? reciprocal

20. Reasoning Explain in words why 2 u x u , 24 has no solution.

Answers may vary. Sample: Dividing both sides by 2 gives |x| R 22. The absolute value of any number must be nonnegative, so the inequality has no solution.

21. Open-Ended What is the difference between simplifying an expression and evaluating an expression?

Answers may vary. Sample: Simplifying an expression is rewriting it using the properties of real numbers and combining like terms, resulting in a simpler expression. Evaluating an expression is substituting values for the variables, resulting in a numerical value.

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Name

Chapter 2 Test

Class

Date

Form K

Do you know HOW?

Determine whether each relation is a function.

1. 5(0, 2), (4, 3), (5, 5), (4, 7)6 no

2. 5(21, 0), (25, 2), (0, 4), (2, 28)6 yes

Evaluate each function for the given value of x, and write the input x and output

f(x) as an ordered pair.

3. f (x) 5 7x 1 5 for x 5 22 (22, 29)

4.

f (x) 5

1 4

x

2

6

for x 5 8

(8, 24)

For each function, determine whether y varies directly with x. If so, find the constant of variation, and write the function rule.

5. x y yes; k 5 4; y 5 4x 3 12 5 20 8 32

6. x y no 6 11 9 14 15 20

Graph each equation.

7. 4x 2 3y 5 22

y 2

2 2

2x

8. 3 1 x 1 y 5 0

y x

O2

4

Write in point-slope form an equation of the line through each pair of points.

9. (5, 8) and (0, 22)

y 2 8 5 2(x 2 5) or y 1 2 5 2(x 2 0)

10. (1, 3) and (6, 22)

y 2 3 5 2(x 2 1) or y 1 2 5 2(x 2 6)

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Name

Class

Date

Chapter 2 Test (continued)

Form K

Write the function rule g(x) for the given transformations applied to the graph of f (x) 5 x2.

11. 4 units down, 1 unit left g( x) 5 (x 1 1)2 2 4

12. 7 units up, 3 units right g( x) 5 (x 2 3)2 1 7

Graph each equation. Then describe the transformation from the parent function f (x) 5 |x|.

13. y 5 |x 2 2|

y 4

2

translation 2 units right

14. y 5 2|x|

y

4 2 O 2

reflection in the x-axis

x

24

2 O

2 4x

4

Graph each absolute-value inequality.

15. y , u 3x u 1 1

y

4

2

2 O 2 x

16. y 2 3 $ u x 1 5 u

y 6

4

2 x

6 4 2 O

Do you UNDERSTAND?

17. If y varies directly with x and y 5 18 when x 5 6, what is the constant of variation? Find the value of y when x 5 10. k 5 3; y 5 30

18. Open-Ended Graph a line that has a slope that is undefined. Answers may vary. Sample: a graph of any vertical line

19. Suppose you manufacture and sell tarps. The table at the right displays your current sizes and prices. a. Draw a scatter plot showing the relationship between the area of a tarp and its price. Use area as the independent variable. b. Draw a trend line and write the equation. c. Reasoning Is this an accurate model? Explain. d. Using your model, predict the price of a 250 ft2 tarp. b. Equations should be close to y 5 0.04x 1 0.02 c. Yes; all the points are very close to the line, so the linear model is accurate. d. about $10.02

Size (ft2)

35 48 80 120 192 200 320

Price

$1.39 $1.99 $3.19 $4.79 $7.69 $7.99 $12.79

y 14

12

8

4

x

100 200 300

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Name

Chapter 3 Test

Class

Date

Form K

Do you know HOW?

Solve each system by substitution or elimination.

1. e 2x 2 y 5 7 6x 2 3y 5 14

2. e 5x 1 2y 5 12 26x 2 2y 5 214

no solution

(2, 1)

3. e 5x 1 2y 5 28 4x 1 3y 5 2

(24, 6)

Graph the solution of each system.

4. e y $ 22x 1 3 y,x

y

2 x

4 2

4

2

4

5. e y 2 1 # 3x y11#x

y

2 4 2

x 24

4

6. e y . 2x 1 4 y # 2x 1 1

y 6

4

2 x

2

24

7. You have 13 bills in your wallet in $1, $5, and $10 bills. There are twice as many $1 bills as $5 bills. The number of $10 bills is one more than the number of $5 bills. How many of each bill do you have? How much money do you have? six $1 bills, three $5 bills, four $10 bills; $61

Graph the system of constraints. Identify all vertices. Find the values of x and y

that maximize or minimize the objective function. Then find the maximum or

minimum value.

y # 2x 1 7 8. ? 4y # x 1 8

x $ 0, y $ 0

y 6

4 B(0, 2)

C(4, 3) x

Maximize for P 5 5x 1 2y max P at (7, 0) 5 35

A(0, 0) 2 4 6 D(7, 0)

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