ck-12 algebra 1 honors concepts answer key
TRANSCRIPT
CK-12 Algebra 1 Honors Concepts Answer Key
Chapter 1: The Real Number System
Concept: Addition of Integers
1. -9
2. -2
3. 9
4. 2
5. 4
6. -4
7. -7
8. 7
9. 4
10. -8
11. -4
12. 1
13. 13
14. -2
15. -4
16.
17.
18.
19.
20.
Concept: Addition of Fractions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18. Answers vary. Possible answer:
19.
20. Justin is correct. Amanda made the mistake of adding the denominators as well as the numerators.
Concept: Addition of Decimals
1. 23.78
2. 79.883
3. 5.897
4. 51.798
5. 103.98
6. 77.98
7. 208.747
8. 110.228
9. 301.397
10. 301.397
11. -64.56
12. 39.67
13. 13.817
14. -110.748
15. -29.64
16. $3832.86
17. $215.03
18. $824.40
19. $67.08
20. 514.65 yards
Concept: Subtraction of Integers
1. -7
2. -3
3. 9
4. 2
5. 1
6. 4
7. 5
8. -2
9. 4
10. 3
11. 6
12. -2
13. 12
14. 7
15. 10
16.
17.
18.
19.
20.
Concept: Subtraction of Fractions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16. Sally used
more cups of flour.
17. Alyssa used
cup more ingredients.
18. Possible answer:
19.
more cans
20. Sierra is correct. Clark accidentally subtracted the denominators.
Concept: Subtraction of Decimals
1. 27.05
2. 30.6083
3. 533.557
4. 3.9665
5. 8.494
6. 32.29
7. -13.932
8. -26.654
9. -929.586
10. -5.7
11. The diameter is .02374 inches larger
12. 1.132 ohms
13. 177.7°F
14. 18.84°F
15. Answers vary.
Concept: Multiplication of Real Numbers
1. 14
2. 12
3. -15
4. -8
5. -4
6. f
7. b
8. d
9. c
10. a
11. e
12. 117
13. -303.232
14.
15.
16. -127.4454
Concept: Division of Real Numbers
1. 7
2. -7
3. 3
4. 4
5. -5
6. -63
7. 64
8. -28
9. 30
10. 10
11.
12. 2.75
13. 12.05
14.
15. 72
16.
17.
18.
19. Actual size is
20.
Concept: Properties of Real Number Addition
1. c)
2. e)
3. b)
4. d)
5. a)
6. 18
7. 34
8. 4
9. 21
10. 8
11. associative property
12. identity property
13. commutative property
14. closure property
15. inverse property
Concept: Properties of Real Number Multiplication
1. c)
2. e)
3. b)
4. a)
5. d)
6. d
7. c
8. b
9. a
10. d
11. associative property of multiplication
12. identity property
13. commutative property
14. inverse property
15. closure property
Concept: PEMDAS with Positive Real Numbers
1. 40
2. 9
3. 31
4. 16
5. 20
6. wraps
7. ( )
8.
9.
10. ( )
11. 23
12. 11
13. 33
14. 42
15. 132
Concept: PEMDAS with Negative Real Numbers
1. c
2. b
3. a
4. b
5. d
6. a
7. -1
8. -17
9. -66
10. -78
11. 24
12. -29
13. -40
14. -17
15. 2
Concept: Decimal Notation
1.
.
3. 0.15
4.
5. 0.375
6.
7.
8.
9.
10.
11. 0.78125
12. 0.34375
13. 0.05
14.
15.
Concept: Real Number Line Graphs
1. The set of all real numbers greater than 8.
2. The set of all integers less than or equal to -3.
3. The set of all real numbers between -4 and 6, including -4 and 6.
4. The set of all whole numbers between 5 and 11, including 5 and 11.
5. The set of all natural numbers greater than or equal to 6.
6. { | }
7. Possible answer: { | }
8. { | }
9. { | }
10. { | }
11. { | }
12. { | }
13. { | }
14. { | }
15. { | }
16.
17.
18.
Concept: Real Number Comparisons
1. 0, 0.28, 0.33, 0.45, 0.5, 0.65, 0.75, 2
2. 0, 0.21, 0.3, 0.3, 0.31, 0.32, 0.4
3.
4.
5. √
6. Possible answer: 9
7. Possible answer: -12.5
8. Possible answer: -12.015
9. Possible answer: -7.55
10. Possible answer:
11. Possible answer:
12. Possible answer:
13. Possible answer:
14.
15. √
√
Chapter 2: Linear Equations and Inequalities
Concept: Equations with Variables on One Side
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Concept: Equations with Variables on Both Sides
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Concept: Equations with the Distributive Property
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Equations with Decimals
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Equations with Fractions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Equations with Decimals, Fractions, and Parentheses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Mathematical Symbols to Represent Words
1.
2. 34
3. 5
4. 27
5. 8
6. 26
7. 18
8. 8
9. 9
10. $125
11. $40
12. $600
13. -58
14. 17 donations
15. 17
Concept: Algebraic Equations to Represent Words
1. 79 and 80
2. 10, 11, 12
3. $714.29
4. $2400
5. 21 feet
6. 11
7. $180
8. 2
9. 17
10. $362
11. 26 hours
12. 44
13. $90
14. 20 lawns
15. 14 feet
16. 224 minutes
Concept: One Variable Inequalities
1.
2. Yes, because you did not divide or multiply by a negative number.
3. Yes
4.
5. Yes, because you did not divide or multiply by a negative number.
6. No
7.
8. Yes, because you did not divide or multiply by a negative number.
9. No
10. The other number must be greater than 348.
11. The number is less than or equal to 93.
12. The number could be 1, 2, 3, 4, 5, 6, or 7.
13. The number could be 7, 8, or 9.
14. The number could be 1, 2, or 3.
15. The number is 5.
Concept: Algebraic Solutions to One Variable Inequalities
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Graphical Solutions to One Variable Inequalities
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. They must sell at least 286 tickets.
15.
. She must get at least a 90% on the last test.
Concept: Absolute Value
1. 4.5
2. 1
3.
4.
5.
6.
7. 3
8.
9. 0.8
10. 0.6
11. 2
12. 1
13.
14. 1.4
15. 1.6
Concept: Solutions to Absolute Value Equations
1.
2.
3.
4.
5. No solution
6.
7.
8.
9. No solution
10.
11. No solution
12.
13.
14.
15.
Concept: Algebraic Solutions to Absolute Value Inequalities
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Graphical Solutions to Absolute Value Inequalities
1.
2.
3.
4.
5.
6. . Number line should have open circles at 6 and 26 with an arrow to the left from
the 6 and to the right from the 26.
7.
8.
9.
10.
11. . Number line should have open circles at -15 and 11 with an arrow to the left
from the -15 and to the right from the 11.
12.
13.
14.
15. . Number line should have open circles at -12.5 and 4.5 with an arrow to the
left from the -12.5 and to the right from the 4.5.
Chapter 3: Functions and Graphs
Concept: The Cartesian Plane
1. x-axis
2. quadrants
3. (0,0)
4. y-axis
5. abscissa
-5 -4 -3 -2 -1 1 2 3 4 5
-2
-1
1
2
3
4
5
6
7
x
y
6.
7.
8.
9.
10.
11. (2, 4)
12. (0, 5)
13. (-3,0)
14. Answers vary. Points should be on the line
15. Answers vary. Points should be on the parabola
Concept: Relations and Functions
1. Yes, function.
2. No, not a function.
3. Yes, function.
4. No, not a function.
5. No, not a function.
6. No, not a function.
7. Yes, function.
8. Yes, function.
9. Yes, function.
10. No, not a function.
11. Yes, function.
12. No, not a function.
13. Yes, function.
14. Yes, function.
15. Yes, function.
Concept: Function Notation
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6.
7.
8.
9.
10.
11. ( ) . The value of the card after 6 years is
12. After 8 years, the value of the card is
13. The original price of the card was when
14. When because then the denominator of the fraction is equal to zero.
15.
Concept: Graphs of Linear Functions from Tables
1.
2.
3.
4.
5.
6. Answers vary. Points should work with the equation
7. Answers vary. Points should work with the equation
.
8. Answers vary. Points should work with the equation
9. Answers vary. Points should work with the equation
10. Answers vary. Points should work with the equation
11.
-3 0 1 5
7 1 -1 -9
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
12.
-4 0 2 6
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
13.
-6 -2 0 4
13 7 4 -2
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
14.
-2 0 3 7
-6.75 -0.75 8.25 20.25
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
15.
0 4 6 10
18 12 9 3
-15 -10 -5 5 10 15
5
10
15
x
y
16.
17.
18.
Concept: Graphs of Linear Functions from Intercepts
1. 3
2. -7
3. -3
4. 8
5. 12
6. -6
7. 2
8. 7
9. -3
10. 8
11.
-25 -20 -15 -10 -5 5 10 15 20 25
-5
5
10
15
20
x
y
12.
-25 -20 -15 -10 -5 5 10 15 20 25
-5
5
10
15
20
x
y
13.
-20 -15 -10 -5 5 10 15
-10
-5
5
10
x
y
14.
-8 -6 -4 -2 2 4 6 8
-10
-5
5
10
x
y
15.
-6 -4 -2 2 4 6
-8
-6
-4
-2
2
4
6
8
x
y
16. d)
17. b)
18. c)
19. a)
Concept: Domain and Range
1. Continuous
2. Domain: { | } Range: { | }
3. All relations are continuous
4. The domain and range of each relation is all real numbers.
5. Discrete
6. Domain: { } Range: { }
7. Neither
8. Domain: { | }. Range: { }
9.
Number of cubes (n)
1 2 3 4 5 n 100
Number of visible faces (f)
6 10 14 18 22 4n+2 402
10. Discrete
11. Domain: { | }; Range: { | }
12.
Number of triangles (n)
1 2 3 4 5 n 100
Number of toothpicks (t)
3 5 7 9 11 2n+1 201
13. Discrete
14. Domain: { | }; Range: { | }
15.
Number of triangles (n)
1 2 3 4 5 n 100
Number of dots (d)
4 9 16 25 36 ( ) 10201
16. Discrete
17. Domain: { | }; Range: { | ( ) }
Concept: Graphs of Quadratic Functions
1. parabola
2. { | }
3.
4. downward
5. (2, 4)
6. { | }
7. 16 and -16
8. axis of symmetry
9. upward
10. vertex
11. Vertex is (1, 0)
-2 -1 1 2 3
-2
-1
1
2
x
y
12. Vertex is (-1, -4)
-4 -3 -2 -1 1 2 3
-5
-4
-3
-2
-1
1
2
x
y
13. Vertex is (2, 1)
-1 1 2 3 4
-1
1
2
3
4
5
x
y
14. Vertex is (2, 1)
-1 1 2 3 4
-1
1
2
3
x
y
15. Vertex is (-2, 4)
-5 -4 -3 -2 -1 1
-1
1
2
3
4
x
y
Concept: Transformations of Quadratic Functions
1.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
2.
-1 1 2 3 4 5 6 7 8 9 10 11 12 13
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
3.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5
-4
-3
-2
-1
1
2
3
4
5
x
y
4.
-1 1 2 3 4 5 6 7 8 9 10
-3
-2
-1
1
2
3
4
x
y
5.
-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
y
6.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-9
-8
-7
-6
-5
-4
-3
-2
-1
xy
7.
-5 -4 -3 -2 -1 1 2 3 4 5 6 7
1
2
3
4
5
6
7
8
9
x
y
8.
-15 -10 -5 5 10 15
-15
-10
-5
5
x
y
9. Vertical reflection, vertical translation=7, vertical stretch=4
10. Vertical reflection, horizontal translation=3, vertical stretch=1/2
11. Vertical translation=4, horizontal translation=-5, vertical stretch=2
12. Vertical translation=2, horizontal translation=-1, vertical stretch=3
13. Vertical reflection, horizontal translation=-3, vertical stretch=3
14. Vertical reflection, vertical translation=4, horizontal translation=-2
15. Vertical reflection, vertical translation=5, horizontal translation=1
Concept: Vertex Form of a Quadratic Function
1. Vertical stretch=4, horizontal translation=2, vertical translation=-9
2. Vertical reflection, vertical stretch=1/6, vertical translation=7
3. Vertical reflection, vertical stretch=3, horizontal translation=1, vertical translation=-6
4. Vertical stretch=1/5, horizontal translation=-4, vertical translation=3
5. Vertical stretch=5, horizontal translation=-2
6.
-10 -5 5 10 15 20
-5
5
10
15
x
y
7.
-10 -5 5 10 15
-10
-5
5
10
x
y
8.
-6 -4 -2 2 4 6
-8
-6
-4
-2
2
4
6
8
x
y
9.
-16 -14 -12 -10 -8 -6 -4 -2 2
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
10.
-6 -4 -2 2 4 6 8
-10
-8
-6
-4
-2
2
4
6
8
x
y
11.
( )
12. ( )
13.
( )
14. ( )
15.
( )
Chapter 4: Linear Functions
Concept: Slopes of Lines Functions from Graphs
1. Find two points on the line. Calculate
2. The steepness of the line and whether the line goes up or down from left to right.
3. Positive.
4. From left to right, if the line goes up then the slope is positive, if the line goes down the slope is
negative.
5. 0
6. Undefined
7. 2
8.
9.
10. -3
11.
12. -2
13. -1
14. 3
15.
16.
Concept: Slopes of Lines from Two Points
1.
2.
3.
4.
5.
6.
7.
8. undefined
9.
10.
200 400 600-20
20
40
60
80
100
120
140
160
180
x
y
11. The slope of the line is
which means that it costs $1 for each additional 7 miles driven.
12.
-4 -2 2 4 6 8 10 12 14 16 18-750
750
1500
2250
3000
3750
x
y
13. The slope of the line is , which means that each additional computer costs $180.
14.
-1 1 2 3 4
-1
1
2
3
4
x
y
15. The slope of the line is 1.3 which means that each additional quart of milk costs $1.30.
16.
-1 1 2 3 4 5 6 7 8
10
20
30
40
50
60
x
y
17. The slope of the line is 7.5, which means that each additional hour of tutoring costs $7.50.
Concept: Equations of Lines from Two Points
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. A) Two points are (320, 124) and (600, 164). The independent variable is the miles traveled and the
dependent variable is the cost. B)
.
means every 7 miles costs $1 and 78.3 is the base
cost of having the car for the month.
13. A) Two points are (10, 1950) and (15, 2850). The independent variable is the computers sold and
the dependent variable is the profit. B) $180 is the cost per computer and $150 is
the base cost before any computers are sold.
14. A) Two points are (1, 1.65) and (2, 2.95). The independent variable is the number of quarts and the
dependent variable is the cost. B) . The 1.3 means each additional quart costs $1.30 and
the $0.35 is the base cost (perhaps for packaging).
15. A) Two points are (3, 25) and (7, 55). The independent variable is the number of hours spent
tutoring and the dependent variable is the money earned. B) . This means that $7.50
was the money earned per hour and $2.50 was the base charge for tutoring.
Concept: Graphs of Lines from Equations
1. Slope is
, y-intercept is ( )
2. Slope is
y-intercept is (
)
3. Slope is
y-intercept is ( )
4. Slope is 0, y-intercept is ( )
5. Slope is
y-intercept is ( )
6.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
7.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
8.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
9.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
10.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
11.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
12. Slope is undefined.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
13. Slope is 0.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
14. Slope is 0.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
15. Slope is undefined.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
Concept: Equations of Lines from Graphs
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. You can’t if you cannot easily identify two points on the graph.
14. A vertical line will have the equation and a horizontal line will have the equation .
Where the ___ is the x or y intercept.
15.
16.
17.
Concept: Equations of Parallel and Perpendicular Lines
1. Parallel
2. Perpendicular
3. Parallel
4. Neither
5. Perpendicular
6. Parallel
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Applications of Linear Functions
1. The dependent variable is the profit and the independent variable is the number of candles sold.
2. (4, 30) and (12, 70)
3.
2 4 6 8 10 12 14
10
20
30
40
50
60
70
80
90
Number of Candles Sold
Profit
4.
5. The slope is 5. This means each candle sold creates a profit of $5.
6. The profit-intercept is 10. This means each player will have at least a $10 profit even if he/she
doesn't sell any candles.
7. The maximum profit is ( )
8. Domain: { | } Range: { | }
9. 16 candles.
10. This data is discrete because you cannot sell portions of candles.
11. The dependent variable is distance from home and the independent variable is time spent driving.
12. (5, 112) and (7, 15)
13.
1 2 3 4 5 6 7
50
100
150
200
250
300
350
Time Spent Driving (Hours)
Distance from Home (km)
14.
15. The slope is -48.5 which means his speed in kilometers per hour was 48.5.
16. The distance intercept is 354.5 kilometers which means he started 354.5 kilometers from home.
17. It took about 7.3 hours.
18. Domain: { | } Range: { | }
19. He was 160.5 miles from home
20. 3 hours
Chapter 5: Systems of Equations and Inequalities
Concept: Graphical Solutions to Systems of Equations
1. Consistent and dependent
2. Inconsistent
3. Consistent and independent
4. Consistent and independent
5. Inconsistent
6. Infinite number of solutions. Any point on the line
is a solution.
7. (
)
8. ( )
9. Infinite number of solutions . Any point on the line is a solution.
10. ( )
11. (
)
12. Infinite number of solutions. Any point on the line
is a solution.
13. No solution
14. ( )
15. ( )
Concept: Substitution Method for Systems of Equations
1. (-1, -3)
2. ( )
3. ( )
4. (
)
5. ( )
6. ( )
7. (-2, -3)
8. (-2, -4)
9. (
)
10. (
)
11. (-3, 1)
12. (3, 1)
13. (-1, 2)
14. (1, -1)
15. (4, -5)
Concept: Elimination Method for Systems of Equations
1. (11. -5)
2. (-1, -3)
3. ( )
4. (4, -1)
5. (7, 3)
6. (
)
7. ( )
8. (-39, -18)
9. (-2, -3)
10. (8, 10)
11. (4, 1)
12. (
)
13. (
)
14. ( )
15. Answers vary.
Concept: Applications of Systems of Equations
1.
2.
3.
4.
5.
6. 20 men and 52 women
7. For exactly 18 sessions, each program costs the same. Super Slim is the better deal for less than 18
sessions and Think Thin is the better deal for more than 18 sessions.
8. Jenny is 17 and Sam is 34.
9. 16 buses and 107 cars
10. 81 and 72
11. 50 large cars and 30 small cars
12. 11 pencils and 4 notebooks
13. 12 and 3
14. 3 boxes of cereal and 2 gallons of milk
15. 7 and 29
Concept: Graphs of Linear Inequalities
1. No (it is on the dotted line).
2. Yes
3. No
4. Yes
5. Yes
6.
7.
8.
9.
10.
11.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4
-3-2-1
1234
567
x
y
12.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4
-3-2-1
1234
567
x
y
13.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4
-3-2-1
1234
567
x
y
14.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4
-3-2-1
1234
567
x
y
15.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4
-3-2-1
1234
567
x
y
Concept: Graphical Solutions to Systems of Inequalities
1.
2. Answers vary
3.
4. Answers vary
5.
6. Answers vary
7.
8. Answers vary
9.
10. Answers vary
11.
12. Answers vary
13.
14. Answers vary
15.
16. Answers vary
17.
18. Answers vary
19.
20. Answers vary
Concept: Applications of Systems of Inequalities
1. Minimum at (0, 0) and maximum at (6, 0)
2. Minimum at (7, 0) and maximum at (0, 6)
3. Minimum at (-3, 2) and maximum at (1, -5)
4. Minimum at (-10, -10) and maximum at (0, 15)
5. Minimum at (-5, 5) and maximum at (6, 0)
6. Let and The constraints are:
The profit equation is
7. The feasible region is shown in dark gray.
8. The company should make 5 DVD players and 4 TVs for a profit of $1025.
9. Let and The constraints are:
The profit equation is
10. The feasible region is shown in dark gray.
11. April should make 9 hats and 2 scarves.
12. Let and The constraints are:
The profit equation is
13. The feasible region is shown in dark gray.
14. Beth should make 2 pairs of mittens and 7 pairs of gloves each day.
15. Let and The constraints are:
The cost equation is
16. The feasible region is shown in dark gray.
17. The patient should take 1 of brand X and 3 of brand Y each day.
18. Let and The constraints are:
The cost equation is
19. The feasible region is shown in dark gray.
20. The company should buy 2 carloads of ore X and 10 carloads of ore Y .
Chapter 6: Exponents and Exponential Functions
Concept: Product Rules for Exponents
1. 4096
2.
3.
4.
5.
6.
7. Cannot be simplified.
8.
9.
10.
11. Cannot be simplified.
12.
13.
14.
15.
Concept: Quotient Rules for Exponents
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Concept: Power Rules for Exponents
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. False
11. True
12.
13.
14.
15.
16.
Concept: Zero and Negative Exponents
1.
2.
3.
4.
5. 1
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Fractional Exponents
1. √
2. √
3. √ √
4.
√
5.
√
6.
7.
8.
9.
10.
11. 3
12. 36
13. 2
14. √
15. 3
Concept: Exponential Expressions
1.
2.
3.
4.
5.
6.
7.
8.
10.
11.
12.
13.
14.
15.
16. 6
17. -729
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
Concept: Scientific Notation
1.
2.
3.
4.
5.
6. 426000
7. 80000
8. 59,670,000,000
9. 0.000001482
10. 0.00764
11.
12.
13.
14.
15.
16.
Concept: Exponential Equations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Exponential Functions
1.
# of years since car was purchased
0 1 2 3 4 5
Value of car ($) 13,000 10400 8320 6656 5324.80 4259.87
2. ( )
3. Common ratio=5, y-intercept=4, growth curve
4. Common ratio=2.3, y-intercept=13, growth curve
5. Common ratio=0.16, y-intercept=0.85, decay curve
6. Common ratio=0.5, y-intercept=1.6, decay curve
7. Common ratio=2.1, y-intercept=0.4, growth curve
8. D
9. C
10. A
11. B
12. Growth
13. A
14. C
15. B
16. D
17. Decay
18. $340,730.52
Concept: Advanced Exponential Functions
1. (
)
2. ( )
3. ( )
4. ( )
( )
5. ( )
( )
6.
7. 1500 years
8. 100 grams
9. horizontal asymptote: y-intercept: ; range: { | }; growth
10. horizontal asymptote: y-intercept: ; range: { | }; growth
11. horizontal asymptote: y-intercept: ; range: { | }; decay
12. horizontal asymptote: y-intercept: ; range: { | }; decay
13. horizontal asymptote: y-intercept: ; range: { | }; growth
14. 102
15.
16. The coffee is getting 40% cooler every 12 minutes.
17.
18.
Chapter 7: Polynomials
Concept: Addition and Subtraction of Polynomials
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Multiplication of Polynomials
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Special Products of Polynomials
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Monomial Factors of Polynomials
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6. ( )
7. ( )
8. ( ) ( )
9. ( )
10. ( )
11. ( )( )
12. ( )( )
13. ( )( )
14. ( )( )
15. ( )( )
Concept: Factorization of Quadratic Expressions
1. ( )( )
2. ( )( )
3. ( )( )
4. ( )( )
5. ( )( )
6. ( )( )
7. ( )( )
8. ( )( )
9. ( )( )
10. ( )( )
11. ( )( )
12. ( )( )
13. ( )( )
14. ( )( )
15. ( )( )
16. ( )( )
17. ( )( )
18. ( )( )
19. ( )( )
20. ( )( )
21. ( )( )
22. ( )( )
23. ( )( )
24. ( )( )
25. ( )( )
26. ( )( )
27. ( )( )
28. ( )( )
29. ( )( )
30. ( )( )
Concept: Special Cases of Factoring Quadratics
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6. ( )( )
7. ( )( )
8. ( )( )
9. ( )( )
10. ( )( )
11. ( )
12. ( )( )
13. ( )
14. ( )( )
15. ( )
Concept: Zero Product Property for Quadratic Equations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Applications of Quadratic Equations
1.
2.
3.
4. 2.5 days
5. 500 units
6. 240 units
7. 30 meters; 2 seconds
8. 1 second, 4 seconds
9. 5 seconds
10. 45 meters
11. 1 second, 5 seconds
12. 6 seconds
13. 2 meters
14. 1 meter
15. 3 meters
Concept: Complete Factorization of Polynomials
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6. ( )
7. ( )( )
8. ( )
9. ( )( )
10. ( )
11. ( )
12. ( )
13. ( )
14. ( )( )
15. ( )( )
Concept: Factorization by Grouping
1. ( )( )( )
2. ( )( )( )
3. ( )( )( )
4. ( )( )
5. ( )( )
6. ( )( )( )
7. ( )( )( )
8. ( )( )
9. ( )( )
10. ( )( )( )
11. ( )( )
12. ( )( )( )
13. ( )( )( )
14. ( )( )( )
15. ( )( )
Concept: Factorization of Special Cubics
1. ( )( )
2. ( )( )
3. ( )( )
4. ( )( )
5. ( )( )
6. ( )( )
7. ( )( )
8. ( )( )
9. ( )( )
10. ( )( )
11. ( )( )
12. ( )( )
13. ( )( )
14. ( )( )
15. ( )( )
Concept: Division of a Polynomial by a Monomial
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Long Division and Synthetic Division
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Concept: The Factor Theorem
1. Yes
2. Yes
3. Yes
4. No
5. Yes
6. ( )( )
7. ( )( )
8. ( )( )
9. ( )( )
10. ( ) ( )
11. ( )( )( )
12. ( )( )( )
13. ( )( )( )
14. ( )( )( )
15. ( )( )( )( )
Concept: Graphs of Polynomial Functions
1. The real roots are -2, 2, and 3.
2. The real roots are -5, -2, and 2.
3. The real root is approximately 0.515.
4. The real root is 4.
5. The real root is 1.
6. One factor is ( ).
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-25
-20
-15
-10
-5
5
10
15
20
25
x
y
7. One factor is ( ).
-4 -3 -2 -1 1 2 3
-10
-5
5
10
x
y
8. Factors are ( ) ( ) ( ).
-12-11-10-9-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10111213
-45-40
-35-30
-25-20-15
-10-5
510
152025
x
y
9. There are no integer roots so there are no factors.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-20-15-10-5
510152025303540455055
x
y
10. Factors are ( ) and ( )
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-25-20-15-10-5
5101520253035404550556065707580859095
x
y
11. No
12. Yes
13. Yes
14. Yes
15. Yes
16. The real roots are at approximately -1.6 and 4.4.
17. The real roots are at -3 and 3.
18. The real roots are at approximately -1.5 and 1.2.
19. The real roots are at approximately -2.25, -0.85, 0.6, and 2.4.
20. The real roots are at -3, 1, and 2.
21. This graph makes a W shape and has 4 real roots.
22. This graph makes a W shape and has 2 real roots.
23. This graph makes an M shape and has 2 real roots.
24. This graph makes an M shape and has 4 real roots.
25. This graph makes an upside down U shape and has 0 real roots.
Chapter 8: Rational Expressions and Rational Functions
Concept: Rational Expression Simplification
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Concept: Rational Expression Multiplication and Division
1.
( )
2. ( )( )
3.
4.
5.
6.
7. ( )( )
8. ( )
9. ( )( )
( )( )
10.
11.
12.
( )( )
13.
14.
15.
Concept: Rational Expression Addition and Subtraction
1. 20
2.
3.
4. ( )( )( )
5. ( )( )
6.
7.
8.
9.
10.
11.
12.
13.
14.
( )( )( )
15.
( )( )
Concept: Graphs of Rational Functions
1. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
2. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
3. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
4. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
5. The red lines are the asymptotes.
-3 -2 -1 1 2 3
-1
1
x
y
6. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
7. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
8. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
9. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
10. The red lines are the asymptotes.
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
11. There is a horizontal asymptote at . There are two vertical asymptotes at
There are no x-intercepts (zeros).
12. There is a horizontal asymptote at . There is a vertical asymptote at There are no x-
intercepts (zeros).
13. There is a horizontal asymptote at There are no vertical asymptotes. There are no x-
intercepts.
14. There is a horizontal asymptote at . There are no vertical asymptotes. There are no x-
intercepts.
15. There is a horizontal asymptote at There is a vertical asymptote at . There is an x-
intercept at
Chapter 9: Quadratic Equations and Quadratic Functions
Concept: Graphs to Solve Quadratic Equations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. Graph and and look for the points of intersection. Or, graph
and and look for the points of intersection.
12. A quadratic equation has only one variable, while a quadratic function has 2 variables.
13. No, a quadratic equation could have 1 solution if there is only 1 x-intercept or no solutions if there
are no x-intercepts.
14. The graph of shows no x-intercepts.
15. Answers vary. Possible answer: The graphing method is a quick way to solve quadratic equations
that have x-intercepts, especially if you have a graphing calculator.
Concept: Completing the Square
1. 25
2. 121
3.
4.
5.
6. √
7. √
8. √
9. √
10. √
11.
12. √
13. √
14.
15. √
Concept: The Quadratic Formula
1.
2.
3.
4.
5.
6. √
7. √
8. √
9. √
10.
11. √
12. √
13. √
14. √
15. √
Concept: Applications of Quadratic Functions
1. or
2.
3. 28 and 29
4. 24.52 inches and 27.42 inches.
5. 55 and 57
6. The width is approximately 2.4 yards.
7. His time last year was 344 seconds or about 5.7 minutes.
8. The maximum height is 24.7 yards.
9. The ball reaches the maximum height at 2.2 seconds.
10. For about 2.48 seconds.
11. 25 meters below the cliff and 50 meters above the water.
12. 2 seconds
13. After about 6.4 seconds.
14. You are 4 meters above the ski jump height and you are coming down.
15. 112.85 meters below the ski jump.
Concept: Roots to Determine a Quadratic Function
1. Sum is 4, product is
.
2. Sum is -2, product is
3. Sum is
product is
4. Sum is
product is
5. Sum is -6, product is
6.
7.
8.
9.
10.
or
11. (
) ( ) ( ) ( )
12. (
) (
) ( ) ( )
13. ( ) ( )
14. (
) (
) ( ) ( )
15. (
) (
) ( ) ( )
16.
17.
18.
19.
20.
Concept: Imaginary Numbers
1. √
2. √
3. √
4. √
5. √
6.
7.
8.
9.
10.
11.
12.
13. 2
14.
15.
16.
17.
18.
Concept: Complex Roots of Quadratic Functions
1. 0, because it has 2 real roots.
2. 0, because it has 1 real root (of multiplicity 2).
3. 2, because it has 0 real roots.
4. The part under the square root: .
5. You can substitute the solutions into the original equation and make sure both sides of the equation
are equal.
6. Quadratic formula
7. √
8. √
9. √
10. √
11. √
12. √
13. √
14. √
15. √
Concept: The Discriminant
1. 2 complex solutions
2. 2 real solutions
3. 1 real solution
4. 2 complex solutions
5. 2 real solutions
6. 2 real solutions
7. 2 complex solutions
8. 2 complex solutions
9. 1 real solution
10. 2 real solutions
11.
12. or
13.
14.
15. or
Concept: Radical Equations
1. No
2. Yes
3. Yes
4. Yes
5. No
6. Yes
7. Yes
8.
9.
10.
11.
12.
13. √
14.
15.
Chapter 10: Geometric Transformations
Concept: Translations
1. 3 units to the right and 5 units down.
2. 5 units to the right and 6 units down.
3. 7 units to the right and 4 units up.
4. 9 units to the right and 2 units up.
5. 6 units left and 3 units down.
6. 5 units to the right and 3 units up.
7. 3 units to the right and 5 units down.
8. 8 units to the right.
9. 3 units to the left and 4 units up.
10. 11 units to the right and 7 units up.
11.
12.
13. 6 units up.
14.
15.
16. 3 units to the left and 2 units up.
Concept: Graphs of Translations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Concept: Rules for Translations
1. ( ) ( )
2. ( ) ( )
3. ( ) ( )
4. ( ) ( )
5. ( ) ( )
6. ( ) ( )
7. ( ) ( )
8. ( ) ( )
9. ( ) ( )
10. ( ) ( )
11. ( ) ( )
12. ( ) ( )
13. ( ) ( )
14. ( ) ( )
15. ( ) ( )
Concept: Reflections
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6. ( )
7. ( )
8. ( )
9. ( )
10. ( )
11. ( )
12. ( )
13. Reflection across the x-axis.
14. Reflection across the y-axis.
15. Reflection across the line y=x.
Concept: Graphs of Reflections
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
22.
23.
24.
Concept: Rules for Reflections
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Rotations
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6. ( )
7. ( )
8. ( )
9. ( )
10. ( )
11. about the origin.
12. about the origin.
13. about point B.
14. about point F.
15. is the same as because a full circle (one complete rotation) is
Concept: Graphs of Rotations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Concept: Rules for Rotations
rotation rotation rotation rotation
1. (1,4) (-4, 1) (-1, -4) (4, -1) (1,4)
2. (4, 2) (-2, 4) (-4, -2) (2, -4) (4, 2)
3. (2, 0) (0, 2) (-2, 0) (0, -2) (2, 0)
4. (-1, 2) (-2, -1) (1, -2) (2, 1) (-1, 2)
5. (-2, -3) (3, 2) (2, 3) (3, 2) (-2, -3)
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Concept: Dilations
1. 24 cm
2. 5 cm
3. 12 cm
4. 54 cm
5. 10 cm
6. 12 cm
7. 8 cm
8. 6 cm
9. 80 cm
10. 50 cm
11. Triangle ABC is dilated by a factor of 2 from the center point of the origin.
12. The preimage is dilated by a factor of
from the center point of the origin.
13. The preimage is dilated by a factor of
from the center point of the origin.
14. Triangle LMO is dilated by a factor of 2 from center point D.
15. Quadrilateral BCDE is dilated by a factor of 3 from center point (1, 2).
Concept: Graphs of Dilations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Concept: Rules for Dilations
1. (1,4) (2, 8) (5, 20) (
) (
)
2. (4, 2) (8, 4) (20, 10) ( ) (
)
3. (2, 0) (4, 0) (10, 0) ( ) (
)
4. (-1, 2) (-2,4 ) (-5, 10) (
) (
)
5. (-2, -3) (-4, -6) (-10, -15) (
) (
)
6. (9, 4) (18, 8) (45, 20) (
) (
)
7. (-1, 3) (-2, 6) (-5, -15) (
) (
)
8. (-5, 2) (-10, 4) (-25, 10) (
) (
)
9. (2, 6) (4, 12) (10, 30) ( ) (
)
10. (-5, 7) (-10, 14) (-30, 35) (
) (
)
11.
12.
13.
14.
15.
Concept: Composite Transformations
1. X'(1, -8) and X''(5, -2)
2. A'(-1, 2) and A''(-1, -2)
3. P'(6, -5) and P''(-5, -6)
4. J'(2,5), T'(-2,-3) and J''(8,2), T''(4,-6)
5. S'(2,-5),K'(4,5) and S''(5,2), K''(-5,-4)
6. K'(4,-1) and K''(1,4)
7. Rotation 180 degrees about point B followed by a translation to the left 4 and down 6.
8. Translation right 7 and 4 up followed by a reflection across the x-axis.
9. Rotation 90 degrees clockwise about point D followed by a translation to the right 2 and up 4.
10. Reflection across the x-axis followed by a reflection across the line
11. Translation to the right 10 and up 1 followed by a reflection across the x-axis.
12. Translation
13. Rotation
14. 180 degree rotation
15. Because it's like a reflection that has slid.
Concept: Order of Composite Transformations
1.
2.
3.
4. 180 degree rotation
5.
6. Translation 12 to the right.
7.
8. Rotation 90 degree clockwise about the origin.
9.
10.
11.
12.
13.
14.
15. The transformations were different because the order of transformations matters.
Concept: Notation for Composite Transformations
1. (1,4) (-1, -3) (-1,-4) (2,2) (1,-4)
2. (4,2) (1,0) (-4,-2) (5,4) (4,-2)
3. (2,0) (3, -2) (-2,0) (3,6) (2,0)
4. (-1,2) (1, -5) (1,-2) (0,4) (-1,-2)
5. (-2,-3) (0, -6) (2,3) (-1,9) (-2,3)
6. (4,-1) (2,0) (-4,1) (5,7) (4,1)
7. (3,-2) (5, -1) (-3,2) (4,8) (3,2)
8. (5,4) (-3,1) (-5,-4) (6,2) (5,-4)
9. (-3, 7) (-4, -7) (3, -7) (-2,-1) (-3, -7)
10. (0,0) (3,-4) (0,0) (1,6) (0,0)
11.
12.
13.
14.
15.
Concept: The Midpoint Formula
1. ( )
2. ( )
3. ( )
4. ( )
5. ( )
6. ( )
7. ( )
8. ( )
9. ( )
10. ( )
11. ( )
12. ( ) ( ) ( )
13. ( ) ( )
14. ( )
15. ( ) ( ) ( ) ( )
Concept: The Distance Formula
1. √
2. √
3. √
4. √
5. √
6. √
7. √
8. √
9.
10. √
11. √
12. √ √ √
13. √ √ √ √ √ √
14.
15. √ √