Algebra 1 Chapter 09 Review

Name: ________________________
Class: ___________________
Date: __________
ID: A
Algebra 1 Chapter 09 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. Between what two consecutive integers is
a. 11 and 12
b. 14 and 15
151 ?
c. 12 and 13
d.
9 and 10
2
2. If an object is dropped from a height of 38 feet, the function h(t) = −16t + 38 gives the height of the
object after t seconds. Graph the function.
a.
c.
b.
d.
1
Name: ________________________
____
ID: A
2
3. Solve x + 2 = 6 by graphing the related function.
a.
c.
There are two solutions: 2 and –2.
b.
There are two solutions: 2 and –2.
d.
There are two solutions: ±
There are no real number solutions.
8.
Solve the equation using the zero-product property.
____
____
4. (2x + 2)(5x − 5) = 0
a. x = –1 or x = –1
b. x = –1 or x = 1
5. −8n(10n − 1) = 0
1
1
a. n = − or n = −
8
10
1
b. n = 0 or n =
10
c.
d.
x = –2 or x = 5
x = 1 or x = 1
c.
n = 0 or n = −
d.
2
1
10
1
1
n = − or n =
8
10
Name: ________________________
____
____
ID: A
6. A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 Find the
2
radius of the beach ball. Use the formula A = 4 πr , where A is the surface area and r is the radius of the
sphere.
a. 24 in.
b. 48 in.
c. 75 in.
d. 576 in.
7. Find the value of x. If necessary, round to the nearest tenth.
a.
7.3 in.
b.
10.3 in.
c.
12.4 in.
c.
d.
z = 3 or z = –2
z = 3 or z = 2
c.
d.
c = 0 or c = 4
c = 1 or c = –
d.
14.6 in.
Solve the equation by factoring.
____
____
2
8. 3z + 3z − 6 = 0
a. z = 1 or z = –2
b. z = 1 or z = 2
2
9. c − 4c = 0
a. c = 0 or c = –4
b. c = 0 or c = 4
2
4
____ 10. 15 = 8x − 14x
3
2 4
5
3 5
a. −5,
b. − ,
c. −3,
d. − ,
8
5 3
8
4 2
____ 11. Tasha is planning an expansion of a square flower garden in a city park. If each side of the original
garden is increased by 7 m, the new total area of the garden will be 144 m2 . Find the length of each side
of the original garden.
a. 19 m
b. 12 m
c. 5 m
d.
5 m
2
____ 12. The area of a playground is 336 yd . The width of the playground is 5 yd longer than its length. Find the
length and width of the playground.
a. length = 26 yd, width = 21 yd
c. length = 21 yd, width = 16 yd
b. length = 21 yd, width = 26 yd
d. length = 16 yd, width = 21 yd
____ 13. Solve the cubic equation by factoring.
3
2
4x − 26x = −42x
7
7
3
7
3 7
a. 0, 3,
b. 3,
c. 0, − ,
d. − ,
2
2
2 2
2
2
3
Name: ________________________
ID: A
Solve the equation by completing the square. Round to the nearest hundredth if necessary.
2
____ 14. x + 3x = 24
a. 4.66, 5.12
b.
3.62, –6.62
c.
3.55, –6.55
d.
24.75, –27.75
b.
1.66, 2.69
c.
1.19, –4.19
d.
–8.75, 5.75
2
____ 15. x + 3x − 5 = 0
a. 1.05, –4.05
Use the quadratic formula to solve the equation. If necessary, round to the nearest
hundredth.
2
____ 16. 5y − 8y = 2
a. 1.82, –0.22
b.
11.2, –9.6
c.
3.64, –0.44
d.
0.22, –1.82
Use any method to solve the equation. If necessary, round to the nearest hundredth.
2
____ 17. 11x = 8
a. 2.83, –2.83
b.
1.17, –1.17
c.
3.32, –3.32
d.
0.85, –0.85
b.
1.15, –1.15
c.
0.87, –0.87
d.
2.83, –2.83
2
____ 18. 8x − 6 = 0
a. 2.45, –2.45
Find the number of real number solutions for the equation.
2
____ 19. x + 0x − 1 = 0
a. 0
b.
1
c.
Short Answer
20. a. Write an expression for the total area of the model below.
b. The total area is 110 m2 . Write an equation to find x.
c. Solve the equation by completing the square.
4
2
Name: ________________________
ID: A
Essay
2
2
21. Graph the quadratic functions y = −2x and y = −2x + 4. Compare the shape and position of the graphs.
22. The perimeter of a rectangular concrete slab is 114 feet and its area is 702 square feet. Find the
dimensions of the rectangle.
a. Using l for the length of the rectangle, write an expression for the width of the rectangle in terms of l.
(Hint: Solve the formula P = 2l + 2w for w.) Show your work.
b. Write a quadratic equation using l, the expression you found in part (a), and the area of the slab.
c. Solve the quadratic equation. Use the two solutions to find the dimensions of the rectangle.
5
ID: A
Algebra 1 Chapter 09 Review
Answer Section
MULTIPLE CHOICE
1. ANS:
REF:
OBJ:
TOP:
2. ANS:
OBJ:
TOP:
3. ANS:
OBJ:
TOP:
KEY:
4. ANS:
REF:
STA:
KEY:
5. ANS:
REF:
STA:
KEY:
6. ANS:
OBJ:
TOP:
KEY:
7. ANS:
OBJ:
TOP:
KEY:
8. ANS:
REF:
STA:
KEY:
9. ANS:
REF:
STA:
KEY:
10. ANS:
REF:
STA:
KEY:
C
PTS: 1
DIF: L2
9-3 Finding and Estimating Square Roots
9-3.2 Estimating and Using Square Roots
STA: CA A1 2.0 | CA A1 23.0
9-3 Example 3
KEY: estimating square roots
C
PTS: 1
DIF: L2
REF: 9-1 Exploring Quadratic Graphs
9-1.2 Graphing y = ax^2 + c
STA: CA A1 21.0 | CA A1 23.0
9-1 Example 4
KEY: graphing | quadratic function | parabola
C
PTS: 1
DIF: L2
REF: 9-4 Solving Quadratic Equations
9-4.1 Solving Quadratic Equations by Graphing
STA: CA A1 21.0 | CA A1 23.0
9-4 Example 1
solving quadratic equations | graphing | quadratic function
B
PTS: 1
DIF: L2
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 1
zero-product property | solving quadratic equations
B
PTS: 1
DIF: L2
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 1
zero-product property | solving quadratic equations
A
PTS: 1
DIF: L2
REF: 9-4 Solving Quadratic Equations
9-4.2 Solving Quadratic Equations Using Square Roots STA: CA A1 21.0 | CA A1 23.0
9-4 Example 3
solving quadratic equations | square root | word problem | problem solving
B
PTS: 1
DIF: L3
REF: 9-4 Solving Quadratic Equations
9-4.2 Solving Quadratic Equations Using Square Roots STA: CA A1 21.0 | CA A1 23.0
9-4 Example 3
solving quadratic equations | square root | word problem | problem solving
A
PTS: 1
DIF: L2
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 2
factoring | solving quadratic equations
C
PTS: 1
DIF: L2
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 2
factoring | solving quadratic equations
D
PTS: 1
DIF: L2
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 3
solving quadratic equations | factoring
1
ID: A
11. ANS:
REF:
STA:
KEY:
12. ANS:
REF:
STA:
KEY:
13. ANS:
REF:
STA:
KEY:
14. ANS:
OBJ:
TOP:
15. ANS:
OBJ:
TOP:
16. ANS:
OBJ:
STA:
KEY:
17. ANS:
OBJ:
STA:
KEY:
18. ANS:
OBJ:
STA:
KEY:
19. ANS:
OBJ:
TOP:
KEY:
C
PTS: 1
DIF: L2
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 4
factoring | solving quadratic equations | word problem | problem solving
D
PTS: 1
DIF: L3
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
TOP: 9-5 Example 4
factoring | solving quadratic equations | word problem | problem solving
A
PTS: 1
DIF: L4
9-5 Factoring to Solve Quadratic Equations
OBJ: 9-5.1 Solving Quadratic Equations
CA A1 14.0 | CA A1 23.0 | CA A1 25.1
solving quadratic equations | factoring
B
PTS: 1
DIF: L2
REF: 9-6 Completing the Square
9-6.1 Solving by Completing the Square
STA: CA A1 14.0 | CA A1 23.0
9-6 Example 2
KEY: solving quadratic equations | completing the square
C
PTS: 1
DIF: L2
REF: 9-6 Completing the Square
9-6.1 Solving by Completing the Square
STA: CA A1 14.0 | CA A1 23.0
9-6 Example 3
KEY: solving quadratic equations | completing the square
A
PTS: 1
DIF: L2
REF: 9-7 Using the Quadratic Formula
9-7.1 Using the Quadratic Formula
CA A1 19.0 | CA A1 20.0 | CA A1 23.0
TOP: 9-7 Example 2
quadratic formula | solving quadratic equations
D
PTS: 1
DIF: L3
REF: 9-7 Using the Quadratic Formula
9-7.2 Choosing an Appropriate Method for Solving
CA A1 19.0 | CA A1 20.0 | CA A1 23.0
TOP: 9-7 Example 4
solving quadratic equations
C
PTS: 1
DIF: L3
REF: 9-7 Using the Quadratic Formula
9-7.2 Choosing an Appropriate Method for Solving
CA A1 19.0 | CA A1 20.0 | CA A1 23.0
TOP: 9-7 Example 4
solving quadratic equations
C
PTS: 1
DIF: L2
REF: 9-8 Using the Discriminant
9-8.1 Number of Real Solutions and x-Intercepts
STA: CA A1 22.0 | CA A1 23.0
9-8 Example 1
solving quadratic equations | one solution | two solutions | discriminant
SHORT ANSWER
20. ANS:
a. (x + 2)(2x + 2)
2
b. 2x + 6x + 4 = 110
c. x = 5.93 m
PTS:
OBJ:
TOP:
KEY:
1
DIF: L2
REF: 9-6 Completing the Square
9-6.1 Solving by Completing the Square
STA: CA A1 14.0 | CA A1 23.0
9-6 Example 4
solving quadratic equations | completing the square | problem solving | multi-part question
2
ID: A
ESSAY
21. ANS:
[4]
2
[3]
[2]
[1]
PTS:
OBJ:
TOP:
KEY:
2
The graph for y = −2x + 4 has the same shape as y = −2x , but it is shifted up 4
units.
one error in graphs or comparison
two errors in graphs or comparison
three errors in graphs or comparison
1
DIF: L2
REF: 9-1 Exploring Quadratic Graphs
9-1.2 Graphing y = ax^2 + c
STA: CA A1 21.0 | CA A1 23.0
9-1 Example 4
graphing | quadratic function | parabola | rubric-based question
3
ID: A
22. ANS:
[4]
a. P = 2l + 2w
114 = 2l + 2w
114 − 2l = 2w
114 2l 2
−
=
2
2
w
57 − l = w
b. l(57 − l) = 702
2
57l − l = 702
2
l − 57l = −702
2
[3]
[2]
[1]
l − 57l + 702 = 0
c. Methods may vary. Check student’s work. Solutions are 18 and 39.
parts (a) and (b) correct with minor computational error in (c)
incorrect equation in (b), but appropriate method used in (c)
part (a) correct
PTS:
OBJ:
STA:
KEY:
1
DIF: L4
REF: 9-7 Using the Quadratic Formula
9-7.2 Choosing an Appropriate Method for Solving
CA A1 19.0 | CA A1 20.0 | CA A1 23.0
solving quadratic equations | rubric-based question | word problem | problem solving
4