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
Prentice Hall Foundations Algebra 2 ? Teaching Resources
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67
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.
Prentice Hall Foundations Algebra 2 ? Teaching Resources
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68
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)
Prentice Hall Foundations Algebra 2 ? Teaching Resources
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87
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
Prentice Hall Foundations Algebra 2 ? Teaching Resources
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88
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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