WORKSHEET: ANSWER KEYS - Mathconceptualized.com

Transcription

WORKSHEET: ANSWER KEYS
CONCEPT #1: LIKE TERMS, DISTRIBUTION, AND EXPRESSIONS
Algebra 1 Concept Test #1 – Integers And
Order of Operations Practice Worksheet:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
−4
24
−8
− 15
49
− 100
− 17
3
− 18
16
−1
Multiplication Message:
MATH LOVE
Multiply Message!:
BELIEVE IN YOURSELF AND
ANYTHING IS POSSIBLE.
Sum Philosophy:
TEACHER'S OPEN THE DOOR
YOU MUST CHOOSE TO ENTER.
Knock Knock Sum:
COME IN!
Algebra 1 Concept #1-Like terms, Distribution,
and Expressions Practice Worksheet:
1. 11x – 9y – 11
2
2. − 2h – 6h + 4
2
3. 13a + 3b – 5b + 11
4. 3m – 27
5. − 6x – 8
6. 6a + 17
7. 0
8. 110
9. 2
10a. − w – 34
10b. − 31
Worksheet Answer Keys
Math Crossword: Let's Add & Subtract:
DOWN:
ACROSS
1. 12
4.
−3
2. − 10
7.
21
3. 100
9.
− 40
5. 36
11.
12
6. − 9
13.
−1
8. 151
14.
69
10. − 6
16.
0
12. 205
17.
− 15
13. − 18
18.
87
15. − 8
19.
− 31
19. − 4
22.
33
20. 13
26.
231
21. − 49
27.
50
23. − 2
28.
912
24. − 117
30.
0
25. −5
31.
16
29. 11
33.
−7
32. − 7
34.
−1
33. − 82
35.
0
39. 700
36.
−7
40. 22
37.
6
41. − 309
38.
− 275
42. − 10
41.
− 74
43. − 23
42.
−2
45. 92
44.
43
47. 99
46.
28
48.
−3
49.
−9
Algebra 1 CT#1 – Exponents:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Page 1
81
16
1
343
0
121
− 64
− 125
− 64
16
11.
12.
13a.
13 b.
14a.
14b.
15a.
15b.
− 100
27
15
4
b
9
37
g5
© 2007-09 by S – Squared, Inc. All Rights Reserved.
CONCEPT #1: LIKE TERMS, DISTRIBUTION, AND EXPRESSIONS
(continued)
Guided Practice Worksheet – Distribution:
Combining Like Terms Practice Worksheet:
Example 1: 5x – 35
Example 2: − 3x + 5
1.
− 7a – 35
2.
− 8x + 12
3.
− 7a – 13
4.
b + 9
Example 3: − 5x + 30
Example 4: 6x + 2y – 22
Example 5: 3w + 6
5.
2y + 10
6.
− 12x – 3y + 27
7.
− 12x – 21
8.
13w – 10
Form A:
1.
2.
3.
4.
5.
6.
Form B:
Practice Integers Worksheet:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
12
− 17
5
− 11
7
−6
− 20
30
−1
9
11.
12.
13.
14.
15.
16.
17.
18.
63
− 48
80
12
9
5
7
− 36
Terms: 6;
Terms: 5;
Terms: 6;
4.
5.
6.
Terms: 7;
3y + 10y + 14
3
2
Terms: 9;
14n + 16n – n
Answers Vary
1.
2.
3.
4.
5.
6.
3
2
Terms: 7;
31x + 27x + 7
2
Terms: 6;
− 30x + 23x + 4
2
Terms: 7;
3m + 7m – 6
2
Terms: 9;
− 10y + 10y + 2
3
2
Terms: 10; 11n + 7n + 1
Answers Vary
Form D:
− 20
−8
0
5
2
−1
2
2x + 25x + 10
2
− 10x + 7x + 10
2
12m + m – 6
1.
2.
3.
Form C:
Algebra 1 CT# 1 - Order of Operations
Worksheet:
1.
2.
3.
4.
5.
6.
2
Terms: 7;
27x + 28x + 9
2
Terms: 6;
− 30x + 16x + 4
2
Terms: 8;
9m + 5m – 2
3
2
Terms: 9;
− 2y – 8y + 17y – 1
3
2
Terms: 10; 7n + n – 5
Answers Vary
1.
2.
3.
4.
5.
6.
Page 2
2
Terms: 6;
15x + 20x + 4
2
Terms: 7;
− 12x + 24x + 1
2
Terms: 6;
21m – 13m + 21
3
2
Terms: 7;
y – 4y + 11y
3
2
Terms: 9;
11n + 13n + 5
Answers Vary
CONCEPT #2: EQUATIONS, INEQUALITIES, & ABSOLUTE VALUE
Guided Practice Worksheet –
Solving Two - Step Equations:
Example 1:
Example 2:
1.
2.
3.
4.
Solving Numerous Equations Worksheet:
1.
2.
3.
4.
x = 13
m = 12
n = 17
Show Work
1
5. w 
2
6. x = 0
7. n = 3
8. a = 9/2 or 4 1/2
9. x = − 4
10. x = − 2 and x = 2/3
x =5
x = − 16
p = 5
m = − 33
x = 3
y = 4
Solving Equations with Distribution and
Combining Like Terms:
Example 1:
Example 2:
1. n = − 10
2. x = 1
3. w = 2
4. x = 6
x = −3
m = 3
Solving Equations with Variables on Both
Sides:
Example 1:
Example 2:
Concept #2 – Practice Worksheet Equations,
Inequalities and Absolute Value:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
x = −3
m = −3
15.
16.
Practice Worksheet – Solving Equations with
Variables on Both Sides:
1.
2.
3.
4.
x = −7
Show Work
n = 5
y = 13
− 9x + 4y + 1
35x – 21y – 28
10
38
m = 2
p = 6
a = 15
f = 2
j = 4
x = − 1 /3 , x = 2
6 terms
a) 10
b) − 7
− 4.3, − 2.1, 0, 1/5, 1, 3/2
a) <
b) >
x > 3
a) p > 3
b)
p
0
1
2
3
4
5
0
1
2
3
4
5
1
2
3
4
5
17. a) x ≤ − 1
x ≥ 3
b)
−2 −1
x
18. a) − 2 < x < 6
b)
−2 −1
Page 3
−2 −1
x
0
6
7
CONCEPT #2: EQUATIONS, INEQUALITIES, & ABSOLUTE VALUE
(continued)
Algebra 1 Concept #2 – Inequalities, Absolute
Guided Practice Worksheet Solving &
Value Practice Worksheet:
Graphing Inequalities:
1a.
1b.
2.
3a.
3b.
24
− 11
x = 2; − 1/3
m > −2
−2 −1
Example 1: x > 5
Example 2: x ≥ − 2
1.
x < 5
2.
x ≤ 3
3
4
5
−6 −5 −4 −3 −2 −1
0
1
0
1
2
m
4a. w ≤ − 3
4b.
0
Example 1: − 7 < x < 7
Example 2: x ≤ − 2; x ≥ 3
1.
−3 ≤x ≤ 5
2.
x < − 5; x > 6
w
5a. x ≤ − 1 or x ≥ 3
5b.
−3 −2 −1
Guided Practice Worksheet Solving &
Graphing Compound Inequalities:
x
1
2
3
4
5
1
2
3
4
5
6a. − 2 < x < 6
6b.
−3 −2 −1
7.
0
Algebra 1 Concept #2 – Solving and Graphing
Inequalities
x
6
1a.
1b.
x > −5
2a.
2b.
Algebra 1 Concept #2 – Inequalities, Absolute
Value More Practice Worksheet:
1a.
1b.
2.
3a.
3b.
0
1
4a.
4b.
2
3
−6 −5 −4 −3 −2 −1
4
1
2
5
7.
0
6a.
6b.
w
0
1
7a.
7b.
2 3 4
5 6
1
2 3 4
5 6
1
2 3 4
5 6
m
− 6 − 5− 4 − 3 − 2− 1 0
w ≤ −4
w
p > 4
p
3
4
5
8a.
8b.
1
2 3 4
5 6
1
2 3 4
5 6
1
2 3 4
5 6
1
2 3 4
5 6
1
2 3 4
5 6
n > −1
n
− 6 − 5− 4 − 3 − 2 − 1 0
x ≤ 3
x
− 6 − 5− 4 − 3 − 2 − 1 0
y ≤ 5
y
− 6 − 5− 4 − 3 − 2 − 1 0
x
6a. − 2 ≤ x ≤ 5
6b.
−3 −2 −1
5a.
5b.
m
5a. x < − 2 or x > 4
5b.
0
1
m ≤ 2
− 6 − 5− 4 − 3 − 2 − 1 0
4a. w < − 5
4b.
−3 −2 −1
z
− 6 − 5− 4 − 3 − 2 − 1 0
− 6 − 5− 4 − 3 − 2 − 1 0
42
− 16
x = 3; − 1/3
m > 0
−2 −1
3a.
3b.
z > −2
a ≥ 0
z
− 6 − 5− 4 − 3 − 2− 1 0
x
1
2
3
4
5
x ≤ 3
Page 4
CONCEPT #3: FRACTIONS, DECIMALS & EQUATIONS
Algebra 1 Concept # 3 – Fractions & Fraction
Equations Practice Worksheet:
Algebra 1 Concept Test #3 - Fractions,
Decimals, and Equations Practice Worksheet
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7
8.
9.
10.
11.
12.
13.
14.
3/4
1/2
1/4
2/5
12/5 or 2 2/5
7/8
23/12 of 1 11/12
16
x = − 15
x = 19
Guided Practice Worksheet – Fractional
Equations:
Example 1: x = 6
Example 2: x = 4
1.
x = 25
2.
x = − 16
Let's Do Decimals!
MADE A WEBSITE
Algebra 1 Concept #3 – Decimals Practice
Worksheet:
5.
6a.
6b.
7.
8.
15.
16.
17.
18.
19.
20.
Show work
x = − 18
7
13/20
m = 3
p = 0.2
Algebra 1 Concept #3 – Fractional Equations
Practice Worksheet:
Fraction Review:
SHOW ME THE HONEY
1.
2.
3.
4.
−1
− 10
f = − 2 /9
5 /8
1 /5
4 /5
5 /8
33/18 or 1 15/18
17/7 or 2 3/7
8.57
16.26
64.4
90
x = −9
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
x
x
x
x
x
x
x
x
x
x
=
=
=
=
=
=
=
=
=
=
10
− 7/3 or − 2 1/3
− 17
12
9
9/5 or 1 4/5
5/4 or 1 1/4
− 14/3 or 4 2/3
− 48
0
7.26
56.27
23.8
50
7
20
0.7
0.15
m = 4
p = 0.2
Page 5
CONCEPT #4: SINGLE VARIABLE WORD PROBLEMS
Algebra 1 Concept # 4 – Single Variable Word
Problems Practice Worksheet:
1a.
1b.
2a.
2b.
3a.
3b.
4a.
4b.
5a.
5b.
6.
7.
8a.
8b.
1.
2.
3.
4.
3x + 7 = 22
x = 5
2(x – 8) < 10
x < 13
2x + 1 = 87
st
1 Integer: 43
nd
2 Integer: 44
3t + 3 = 36
Carlos: 16 years old
Regina: 9 years old
Tony: 11 years old
4k + 12 = 212
Kendra:
$50.00
Juanita:
$62.00
McKenzie: $100.00
Quarters:
6
Dimes:
6
60 lbs.
52 = 10w + 2
2
Area = 105 in.
Word Problem Review Worksheet:
Page 6
x = 9
7 quarters, 7 dimes
Maggie: 65 lbs
Tony saved $1500.00
CONCEPT #5 – COORDINATE PLANE & GRAPH THEORY
Algebra 1 Concept # 5 – Coordinate Plane and
Graph Theory Practice Worksheet:
4a.
4b.
1.
y = 2x + 4
x
−1
0
1
4c.
2.
A: ( − 3, 4 ); Quadrant II
B: ( 2, 2 ); Quadrant I
C: (− 2, 0 ); x – axis
3b.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
3a.
x
−3
0
3
y
2
4
6
1 2 3 4 5 6 7
y
0
2
4
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
Page 7
CONCEPT #5 – COORDINATE PLANE & GRAPH THEORY
(continued)
Guided Practice Worksheet Graphing Linear
Equations Using A Table:
4.
Example 1:
x
−2
0
2
Graph:
y
0
1
2
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
y
7
6
5
4
3
2
1
1 2 3 4 5 6 7
x
x
y
1.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
Plotting Points on the Coordinate Plane:
y
2.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
y
7
6
5
4
3
2
1
3.
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
Page 8
CONCEPT #6 – FUNCTIONS
Algebra 1 Concept # 6 – Functions Practice
Worksheet:
1.
2a.
2b.
3a.
3b.
Example 1: f ( − 4 ) = − 7
1a.
f ( x ) = − 4x + 7
1b.
f(3) = 5
2
2a.
f ( x ) = x – 4x + 9
2b.
f(0) = 9
2
f (x)  x  8
3a.
3
3b.
f ( 12 ) = 0
2
4a.
f ( x ) = − x + 2x – 1
4b.
f ( − 4 ) = − 25
Example 2: f ( 6 ) = 1
1.
f(0) = −1
2.
f(3) = 0
3.
f(−3) = −2
4.
f(−6) = −3
f(1) = 4
f(2) = 0
f(−1) = −3
f ( x ) = 4x – 2
( − 1, − 6 ), ( 0, − 2 ), ( 1, 2 )
y
3c.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
Guided Practice Worksheet Functions:
x
C ( x ) = 5x + 20
4a.
4b.
60
Evaluating Functions:
Cost
50
40
I HEAR AND I FORGET
I SEE AND I REMEMBER
I DO AND I UNDERSTAND
30
20
10
0
5
10
15
20
25
30
# of people
4c.
4d.
4e.
4f.
4g.
$5 per person
20 people
$120.00
50 people
Number of people
Page 9
CONCEPT #7 – GRAPHING LINES
Algebra 1 Concept # 7 – Graphing Lines
Practice Worksheet:
1a.
1b.
1c.
1d.
y = − 2/5 x + 1
m = − 2/5
( 0, 1 )
Equations Using Slope – Intercept Form:
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
1 2 3 4 5 6 7
Example 1:
y
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
2c.
m = 4
3a & b.
1 2 3 4 5 6 7
1.
x
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
2.
1 2 3 4 5 6 7
x
Page 10
1 2 3 4 5 6 7
x
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
Undefined
Zero
( − 3, 5 )
1 2 3 4 5 6 7
y
x
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
(− 1, 0 ), ( 0, 4 )
7
6
5
4
3
2
1
3c.
3d.
3e.
y = −3
x = −1
m = 2/3
m = – 3/2
m = 2/3
y = 6/5 x – 7
y
7
6
5
4
3
2
1
2a.
2b.
4a.
4b.
5a.
5b.
5c.
6.
1 2 3 4 5 6 7
x
CONCEPT # 7 – GRAPHING LINES
(continued)
Graphing Linear Equations:
1.
Slope: − 1
y – intercept: ( 0, 4 )
Equation:
y = −x + 4
8.
5
3
Slope:
y
2.
3.
4.
5.
6.
7.
7
6
5
4
3
2
1
1
2
1
y x1
Equation:
2
Slope:
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1
3
y – intercept: ( 0, − 2 )
1
y x2
Equation:
3
Slope:

9.
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
Slope: 0
Equation:
y = 2
10.
Slope: Undefined
y – intercept: None
Equation:
x - −5
Slope: 5
1 2 3 4 5 6 7
x
Slope: Undefined
y – intercept: None
y
7
6
5
4
3
2
1
y
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
7
6
5
4
3
2
1
Slope: 0
y
1
2
1
y x6
Equation:
2
1 2 3 4 5 6 7
x
7
6
5
4
3
2
1
Slope:
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
1 2 3 4 5 6 7
x
x
Linear Equation Word Search:
EITHER YOU MUST MAGNIFY YOUR
SKILLS OR MODIFY YOUR DREAMS
Page 11
CONCEPT #8 – WRITING LINEAR EQUATIONS
Algebra 1 Concept #8 – Writing Linear
1a.
1b.
1c.
1d.
m = −1
( 0, 3 )
y = −x + 3
1e.
1f.
2a.
2b.
2c.
3a.
3b.
4.
1a.
1b.
1c.
1d.
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
1b.
1f.
2.
7x + 9y = 72
f( − 4 ) = − 5
1 2 3 4 5 6 7
x
(2d)
1e.
x
−1
0
5
y
1
−1
−3
1f.
The points land on the line.
The solutions of the 2 variable
equation.
2a.
2b.
2c.
2d.
3a.
3b.
y = 5/2 x + 5
− 5x + 2y = 10
( − 2, 0 ), ( 0, 5 )
see graph for 1d.
Dashed
y
10
8
6
b = 8
1e.
1d.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
7
9
7
y  x  8
9
7

9
9
7
1c.
y
x
f(x) = −x + 3
f(3) = 0
2
y x6
3
3
y x7
2
3x + 2y = − 14
12a + 5c = 300
15 adults
1
y x1
3
m
m = − 2/5
m = − 2/5
y = − 2/5 x – 1
(1d)
CT#8 Review– Writing a Linear Equation
Using Slope-Intercept Form:
1a.
Algebra 1 – Review Writing Linear Equations
& Graphing Lines:
FORM A:
4
2
−8 −6 −4 −2
−2
2
4
6
8
10
x
−4
−6
−8
− 10
3c.
3d.
3e.
3f.
Page 12
Answers vary.
see graph for 3b.
Yes
No
(continued)
& Graphing Lines:
FORM B:
1a.
1b.
1c.
1d.
m = − 5/6
m = − 5/6
y = − 5/6 x – 1
& Graphing Lines:
FORM C:
1a.
m = − 5/7
1b.
m = − 5/7
1c.
y = − 5/7 x – 2
y
1d.
y
(1d)
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
(1d)
1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
2a.
2b.
2c.
2d.
3a.
3b.
x
−7
0
7
y
4
−1
−6
The solutions of the 2 variable
equation.
y = 6/5 x + 6
− 6x + 5y = 30
( − 5, 0 ), ( 0, 6 )
see graph for 1d.
Dashed
y
1 2 3 4 5 6 7
The solutions of the 2 variable equation.
2a.
2b.
2c.
2d.
3a.
3b.
y = 7/5 x + 7
− 7x + 5y = 35
( − 5, 0 ), ( 0, 7 )
see graph for 1d.
Dashed
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
3c.
3d.
3e.
3f.
Answers vary.
see graph for 3b.
Yes
No
y
3
−2
−7
1f.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
3c.
3d.
3e.
3f.
x
1e.
1e.
1f.
1 2 3 4 5 6 7
(2d)
(2d)
x
−6
0
6
7
6
5
4
3
2
1
Page 13
1 2 3 4 5 6 7
x
Answers vary.
see graph for 3b.
Yes
No
(continued)
& Graphing Lines:
FORM D:
1a.
m = − 3/5
1b.
m = − 3/5
1c.
y = − 3/5 x – 4
y
1d.
(1d)
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
(2d)
1e.
x
−5
0
6
y
−1
−4
−7
1f.
The solutions of the 2 variable equation.
2a.
2b.
2c.
2d.
3a.
3b.
y = 5/3 x + 5
− 5x + 3y = 15
( − 3, 0 ), ( 0, 5 )
see graph for 1d.
Dashed
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
3c.
3d.
3e.
3f.
1 2 3 4 5 6 7
x
Answers vary.
See graph for 3b.
Yes
No
Page 14
CONCEPT #9 – TWO VARIABLE INEQUALITIES
Algebra 1 Concept # 9 – Review Writing Linear
Equations Review Worksheet:
1a.
1b.
1c.
1d.
1e.
1f.
2.
y
3.
m = − 5/6
( 0, 2 )
y = − 5/6 x + 2
m = − 5/6
m = 6/5
5x – 6y = 12
f ( − 5 ) = 31
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
Inequalities Using Slope – Intercept Form:
y
4.
Example 1:
7
6
5
4
3
2
1
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
1 2 3 4 5 6 7
x
y
7
6
5
4
3
2
1
1.
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
y
2.
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
x
Page 15
CONCEPT #9 – TWO VARIABLE INEQUALITIES
(continued)
Concept #9 – Writing Linear Equations
Practice Review
1a.
1b.
1c.
1d.
1e.
1f.
m = − 3/8
b = 3
y = − 3/8 x + 3
− 3/8
Algebra 1 Concept # 9 – Two Variable
Inequalities Practice Worksheet:
1.
2.
3a.
3b.
No
y ≤ 4/3 x – 4
Solid
y
7
6
5
4
3
2
1
8/3
3x + 8y = 24
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
4a.
4b.
1 2 3 4 5 6 7
x
Dashed
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
5a.
5b.
1 2 3 4 5 6 7
x
Solid
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
Page 16
1 2 3 4 5 6 7
x
CONCEPT #10 – SYSTEM OF LINEAR EQUATIONS
Algebra 1 Concept # 10 – System of Linear
1.
2a.
( 2, − 2 )
2b.
3.
4.
5.
6.
7.
1.
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
2.
1 2 3 4 5 6 7
3.
4.
x
1.
2.
No
( 1, 1 )
( 1, − 1 )
No Solution
st
1 Number: 8
nd
2 Number: 12
Dimes: 9
Quarters: 7
3.
4.
5.
Example 1: ( − 1, 1 )
1.
( − 2, − 1 )
2.
( 3, 2 )
5 seconds
Length: 28 cm
Width: 11 cm
80% solution: 128 Liters
30% solution: 72 Liters
Page 17
Dimes: 20
Quarters: 8
Length: 5 cm
Width: 12 cm
Nickels: 5
Dimes: 9
Amount: $2250.00
Items: 450
4 months
Algebra 1 Concept #10 – System of Linear
Equations Practice Worksheet 2:
1.
2.
3.
4.
5.
6.
7.
System of Equations – Word Problem:
1.
3.
Example 1: ( − 1, 1 )
1.
( − 1, 2 )
2.
( 1, − 2 )
Infinite
No point of intersection
 9 15 
 , 
 4 2 
Equations Word Problems Practice Worksheet:
2.
Guided Practice Worksheet – Solving System of
Equations Using The Combination Method:
3.
1st number: 5
2nd number: 1
Nickels: 20
Dimes: 15
( − 3, 0 )
( − 4, 7 )
Systems of Linear Equations – Special Cases &
Word Problems:
Guided Practice Worksheet – Solving System of
Equations Using The Substitution Method:
1.
2.
Equations Review Worksheet:
( 4, − 1 )
( 7, 1 )
Show work
( − 3, ½ )
No Solution
1st:
20
2nd:
Dimes:
12
Nickels:
9
7
CONCEPT #11 – EXPONENTS
Algebra 1 Concept #11 Growth & Decay
Practice Worksheet:
1a.
1b.
1c.
2a.
2b.
2c.
t
Graphing Exponential Functions Practice
Worksheet:
1a.
1b.
1c.
1d.
y = 1000(1.08)
$1,259.71
4 years
t
y = 10000( 0.98 )
$9,411.92
5 years
2.
3.
4.
5.
6.
y
4
2
1
½
¼
1
v8
1f.
1g.
1h.
w4
1
3x 7
b8
− 10
12b 5
a
1a.
2.
3.
4.
5.
6.
t
y = 1000( 1.05 )
$1215.51
3 years
t
y = 10,000( 1.03 )
$11,592.74
1 year
t
y = 100( 1.07 )
$122.50
$245.00
t
y = 10,000( 0.94 )
$8043.57
5 years
t
y = 1000( 0.99 )
$294.03
$288.18
( 0, ½ )
None
y ≥ 0
Exponents Practice Worksheet:
 64a 7
Algebra 1 Concept #11 – Exponential Growth
& Decay More Practice Worksheet:
1a.
1b.
1c.
2a.
2b.
2c.
3a.
3b.
3c.
4a.
4b.
4c.
5a.
5b.
6c.
1e.
x
3
2
1
0
−1
Exponents Practice Worksheet:
1.
1
2
All real numbers
7a.
7b.
7c.
8a.
x
2
1
0
−1
−2
8c.
8d.
8e.
8f.
9.
Page 18
0.563
1.48 x 10
1b.
4.3 x 104
81
y6
32x9y29
1
− 36
m3n5
y = 10,000( 0.93 )t
$8043.57
y
5 years
7
8b.
6
f(x)
5
4
0
3
2
−2
1
−3
-7 -6 -5 -4 -3 -2 -1
1
-1
-2
− 7/2
-3
-4
− 15/4
( 0, − 3 )
( 2, 0 )
All real numbers
y > −4
38 bacteria
2 3 4 5 6 7
x
-5
-6
-7
CONCEPT #12 – SQUARE ROOTS
Algebra 1 Concept # 12 – Square Roots Practice Radical Riddle:
Worksheet:
TAKE AWAY THE S!
1.
0.000532
2.
3.
4
5.
6.
7.
8.
9.
10.
11a.
11b.
12.
13.
14.
15.
16.
17.
18.
19a.
x
4
1
¼
0
19c.
19d.
19e.
19f.
19g.
144n 8
m6
Graphing Square Root Functions Practice
Worksheet:
15
−t
250 items
3 10
a.
b.
x ≥ 0
c
x
0
¼
1
4
6
3x
2
6/7
x2y3 15
−6 2
4.1
10.9
10
10 – 11 5
11a4b
x = 49
x = 256
Show work
x = 0
b.
y
1
0
−½
−1
d.
e.
f.
g.
( 0, 1 )
( 0, 1 )
None
y ≥ 1
Simplifying Square Roots Practice Worksheet:
y
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7
1.
5
5
2.
4
6
3.
2
11
4.
9
3
2
6
x
5.
6.
( 0, − 1 )
( 0, − 1 )
( 1, 0 )
x ≥ 0
y ≥ −1
y
1
2
3
5
7.
8.
Page 19
9
6
2
7
4
2
11
3
2
CONCEPT #12 – SQUARE ROOTS
(continued)
Algebra 1 Concept Test #12 – Square Roots
Introduction:
2
x
x
0
0
1
2
Algebra 1 Concept #12 – Review Graphing
Square Roots Practice Worksheet:
1a.
1b.
x
x
0
7
49
7
1
1
8
64
8
2
4
2
9
81
9
3
9
3
10 100
10
x
x
0
1
4
9
16
Y
0
5
10
15
20
1c.
4
16
4
11 121
y
18
11
16
5
25
5
12 144
12
14
12
6
36
6
13 169
13
10
8
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
9
5
4
1
13
3
10
7
2
3
5
9
1
7
6
4
2
−4
−2
2
4
6
8
10
12
14
16
x
−2
4
6
10
2
8
1d.
1e.
1f.
1g.
3.2
5.9
9.5
1.7
7.5
Page 20
( 0, 0 )
( 0, 0 )
x ≥ 0
y ≥ 0
CONCEPT #13 – SOLVING & GRAPHING QUADRATIC EQUATIONS
Guided Practice Worksheet – Solving
Quadratic Equations Using the Quadratic
Formula:
3
Example 1: x =  , x = 3
4
Example 2: x = 2
3
1.
x =  , x = 2
5
2.
x = 3
11e.
11f.
11g.
( 0, − 12 )
( 2, 0 ), ( − 6, 0 )
y
4
2
− 10 − 8
−6
−4
−2
−2
x
2
4
6
8
10
−4
−6
−8
− 10
Algebra 1 Concept Test #13 – Solving &
Graphing Quadratic Equations Practice
Worksheet:
5
3b
2.
8m5
n3
−4 5
3.
9
4.
5a.
5b.
6a.
6b.
6c.
6d.
6e.
7a.
7b.
7c.
7d.
7e.
8.
9.
10.
11a.
11.b.
11c.
11d.
x
2
0
−2
−4
−6
4.398 x 105
x = 64
x = 9/64
x2 – 2x + 8 = 0
a = 1, b = − 2, c = 8
− 28
zero
No solution
4x2 + 4x + 1 = 0
a = 4, b = 4, c = 1
0
1 real solution
−½
x = ±1
x =± 2 3
x = 2/5, x = 2
x = −2
( − 2, 16 )
Up
1a.
2
1b.
− 12
− 14
− 16
11h.
11i.
11j.
– 10
( − 2, − 16 )
x is any real number
y ≥ − 16
y
0
− 12
− 16
− 12
0
Page 21
CONCEPT # 14 – POLYNOMIALS
Algebra 1 Concept # 14 – Adding, Subtracting
& Identifying Polynomials Practice Worksheet:
1a.
1b.
1c.
1d.
2.
3.
4.
5.
IT'S NOT THAT I'M SO SMART
IT'S JUST THAT I STAY WITH PROBLEMS
LONGER.
2
− 5x + 6x + 3
2
Quadratic
Trinomials
2
2x – 5x – 3
3
2
2x – 2x – 3x – 20
2
− 4b + 12b + 7
2
− b – 3b – 15
Algebra 1 Concept # 14 – Review of Graphing
Quadratics Practice Worksheet:
Algebra 1 Concept # 14 – Multiplying
Polynomials & the Zero Product Property
Practice Worksheet:
1.
2.
3.
4.
5.
6.
7.
Adding & Subtracting Polynomials:
1a.
1b.
1c.
1d.
x = −2
( − 2, 9)
Down
x
−5
−4
−3
−2
−1
0
1
2
m – 6m – 27
2
− 8a + 22a – 15
2
y – 9
2
16x + 8x + 1
3
2
6x + 10x – 18x
p = 7, p = − 3
s = 0, s = 9, s = − 3
Guided Practice Worksheet Multiplying
Polynomials:
y
0
5
8
9
8
5
0
1e.
1f.
1g.
( 0, 5 )
( 1, 0 ), ( − 5, 0 )
1h.
1i.
1j.
Maximum ( − 2, 9 )
All real numbers
y ≤ 9
2
Example 1: x + 2x – 35
2
1.
x – 7x – 44
2
2.
3a + 26a + 16
2
3.
m – 12m + 35
2
2
4.
16r – s
2
Example 2: 2x + 2xy + 15x + 3y + 18
2
5.
x + 2xy + 10x + 14y + 21
3
2
6.
6w – 24w 18w
3
2
7.
2b + 5b + 15b – 9
2
2
8.
8m – 18n
Guided Practice Worksheet Solving Quadratic
Equations with the Zero Product Property:
Example 1: x = − 3, x = 8
1.
x = 4, x = 11
2.
x = − 12, x = 3
Page 22
CONCEPT # 15 – SOLVING & GRAPHING QUADRATIC EQUATIONS BY FACTORING
Algebra 1 Concept #15 – Factoring Diamonds:
1.
2.
24
6
3.
32
4
16
18
2
10
6
1a.
1b.
3
18
Guided Practice Factoring Quadratics
(Diamond Method):
9
a = 1, b = 7, c = 10
10
5
2
7
4.
5.
− 36
−9
− 10
4
−5
7.
− 15
2
−5
8.
−2
9.
− 20
−3
− 15
−4
5
9
1c.
x
5
1d.
1e.
2a.
2b.
( x + 5)( x + 2 )
Show work
a = 1, b = 7, c = − 18
3
−8
− 36
12
6.
− 20
2
− 18
−1
15
1
, x
−2
9
14
7
10.
11.
12.
12
6
−6
−4
−3
−7
−1
2
0
−8
1
0
3c.
18.
− 12
45
−2
− 14
3d.
3e.
4a.
4b.
− 55
6
− 11
5
−6
4
3
−5
−1
2
17.
−5
( x + 9)( x – 2 )
Show work
a = 1, b = − 5, c = − 24
−1
4
16.
2d.
2e.
3a.
3b.
−2
− 24
4
−6
−4
, x
15.
− 36
−9
−4
−8
14.
6
x
9
16
−7
13.
2c.
x
−8
, x
3
( x – 8)( x + 3 )
Show work
a = 1, b = 8, c = 16
16
4
19.
20.
21.
− 32
25
−4
8
4
−5
− 10
7
−5
4
8
7
1
4c.
x
4
4d.
4e.
( x + 4)( x + 4 )
Show work
8
Page 23
, x
4
(continued)
Algebra 1 Concept Test #15 – Factoring
Quadratics ( a ≠ 1 ):
Guided Practice Worksheet – Factoring
Quadratic Expressions with a = 1:
1a.
1b.
Example 1:
Example 2:
1.
2.
3.
4.
a = 2, b = 13, c = 21
42
6
7
13
1c.
2x
7
, x
1d.
1e.
2a.
2b.
( 2x + 7)( x + 3 )
Show work
a = 2, b = 11, c = − 6
3
+ 8 )( x + 2 )
– 9 )( x + 3 )
+ 9 )( x + 2 )
– 11 )( x + 2 )
– 7 )( x – 3 )
– 4 )( x + 7 )
Guided Practice Worksheet – Factoring
Quadratic Expressions with a ≠ 1:
Example 1:
Example 2:
1.
2.
− 12
−1
12
(x
(x
(x
(x
(x
(x
( 2x + 3 )( 3x + 1 )
( x – 2 )( 4x – 5 )
( 3x + 2 )( x + 6 )
( 3x + 8 )( 2x – 1 )
11
2c.
2d.
2e.
3a.
3b.
2x
−1
, x
Guided Practice Worksheet – Factoring The
Difference of Two Perfect Squares:
6
( 2x – 1)( x + 6 )
Show work
a = 3, b = − 17, c = 20
Example 1:
Example 2:
1.
2.
3.
4.
60
−5
− 12
− 17
3c.
3d.
3e.
4a.
4b.
3x
−5
( x – 3 )( x + 3 )
( 2x – 5 )( 2x + 5 )
( x – 10 )( x + 10 )
( x – 1 )( x + 1 )
( 3x – 4 )(3 x + 4 )
( 4x – 7 )( 4x + 7 )
, x
−4
Factoring Fun!
NACHO CHEESE
( 3x – 5)( x – 4 )
Show work
a = 6, b = 5, c = − 4
− 24
−3
8
5
4c.
4d.
4e.
2x
−1
, 3x
4
( 2x − 1)( 3x + 4 )
Show work
Page 24
(continued)
Guided Practice Worksheet Graphing
Quadratic Functions With Intercepts:
Algebra 1 Concept # 15 – Graphing Quadratics
Using Intercepts Practice Worksheet:
Example 1:
1a.
1b.
1c.
1d.
1e.
1f.
1g.
a = 1, b = − 4, c = − 5
Up
( 2, − 9 )
( 0, − 5 )
x = − 1, x = 5
( − 1, 0 ), ( 5, 0 )
1h.
1i.
1j.
Minimum at ( 2, −9 )
x is any real number
y ≥ −9
1.
a = 1, b = 8, c = 7; Up
Vertex: ( −4, − 9 )
x – intercepts: ( − 7, 0 ), ( − 1, 0 )
Algebra 1 Concept # 15 - Vertical Motion
Model Practice Worksheet:
2.
a = − 1, b = − 1, c = 6; Down
Vertex: ( − ½ , − 6 ¼ )
x – intercepts: ( 2, 0 ), ( − 3, 0 )
1.
2.
9 seconds
3 seconds
Algebra 1 Concept # 15 – Factoring Quadratics
Practice Worksheet:
1a.
1b.
2a.
2b.
3a.
3b.
4a.
4b.
5.
Page 25
( x + 1 )( x + 8 )
2
x + 9x + 8
( x + 1 )( x – 12 )
2
x – 11x – 12
( p – 4 )( p + 4 )
2
p – 16
( 3x – 5 )( x + 2 )
2
3x + x – 10
2
4w( 2w + 3w + 1 )
(continued)
Guided Practice Worksheet Solving Quadratic
Equations by Factoring:
1.
2.
3.
4a.
4b.
4c.
4d.
4e.
5a.
5b.
6a.
6b.
7a.
7b.
8a.
8b.
8c.
8d.
9a.
9b.
9c.
Example 1: x = 2, x = − 9
Example 2: x = 4, x = 6
1.
x = 2, x = − 8
2.
x = − 6, x = − 1
Algebra 1 Concept # 15 – Solving Quadratic
1a.
1b.
1c.
2a.
2b.
2c.
3a.
3b.
3c.
4a.
4b.
4c.
5a.
6a.
6b.
6c.
6d.
6e.
( x + 1 )( x + 3 ) = 0
x = − 3, x = − 1
Show Work
( 2x + 3 )( x – 5 ) = 0
x = 5, x = − 3/2
Show work
( x – 10 )( x + 10 ) = 0
x = 10, x = − 10
Show work
2
2( 3x + 16x + 21 ) = 0
2( 3x + 7 )( x + 3 ) = 0
x = − 7/3, x = − 3
8 seconds
( −1, − 9 )
( 0, − 8 )
x = − 4, x = 2
( −4, 0 ), ( 2, 0 )
10
8
6
4
2
−8
−6
−4
−2
2
3
2
6a – a – 4a + 3
2
49x – 28x + 4
3
2
m + 4m – 12m
3
2
14t – 14t + 5t
3
trinomial
cubic
14
( x + 1 )( x + 13 )
( w – 6 )( w – 4 )
( x – 11 )( x + 2 )
( n + 10 )( n – 4 )
( p + 6 )( p – 6 )
( 2b + 3 )( 2b – 3 )
( 2a – 7 )( a – 3 )
( 3x – 1 )( x + 4 )
( 5x – 1 )( x + 2 )
( 7x – 2 )( x + 3 )
( v + 7 )( v + 3 )
( x + 6 )( x – 4 )
( 2x – 9 )( x – 2 )
Algebra 1 Concept Test #15 – Quadratic Area
Problems:
y
− 10
CT #15 – Factoring Quadratics More Practice:
4
6
8
10
−2
−4
−6
−8
x
1.
2a.
2b.
2c.
3a.
3b.
3c.
4.
5a.
5b.
5c.
6a.
6b.
6c.
27 units squared
A(x) = 7x – 14
21 units squared
x > 2
A(x) = x2 + 9x + 20
42 units squared
x > −4
42 units squared
A(x) = 9x – 27
45 units squared
x > 3
A(x) = x2 + 5x + 4
88 units squared
x > −1
− 10
Page 26
CONCEPT #16 – STATISTICS
Algebra 1 Concept Test #16 - Statistics Practice
Worksheet:
1a.
Stem
1
2
3
4
5
1b.
4c.
4d.
4e.
4f.
11 students
16 students
6 students
51 – 73 inches
Leaf
2 5 7
0 0 2 4
2 7
0
Mean:
Median:
Mode:
Range:
24.9
21
20
38
1c.
12 17
2.
3a.
3b.
3c.
3d.
4a.
32
20
50
x = 85
Positive
W(h) = 4h – 144
96 lbs.
56"
Height
(in inches)
Tally
Frequency
Cumulative
Frequency
50-53"
54-57"
58-61"
62-65"
66-69"
70-73"
||
|||
||||
|||
|
||
2
3
5
3
1
2
2
3
5
3
1
2
# of Students
4b.
Height of Students in Math Class
8
7
6
5
4
3
2
1
0
50 - 53
54 - 57
58 - 61
62 - 65
66 - 69
70 - 73
Height (in inches)
Page 27
CONCEPT #17 – PROBABILITY
Algebra 1 Concept Test #17 – Probability
Practice Worksheet:
1a.
1b.
1c.
1d.
1e.
2.
3a.
3b.
4a.
4b.
4c.
4d.
5a.
5b.
2/5
4/5
1/30
2/25
Dependent
1/26
36 outfits
1/3
{ 1, 2, 3, 4, 5, 6 }
1/6
¼
1/3
1/16
5/8 ≈ .625
Page 28
CONCEPT #18 – RATIONAL EXPRESSIONS & PROPORTIONS
Algebra 1 Concept #18 – Simplifying Rational
Expressions Practice Worksheet:
1.
2.
3.
4.
5x
3
r( r  4 )
3
3( y – 3 )
2
(x – 4)
Algebra 1 Concept # 18 - Adding & Subtracting
Rational Expressions with Unlike
Denominators Practice Worksheet:
1.
2.
3.
Algebra 1 Concept # 18 – Proportions Practice
Worksheet:
4.
1.
2.
3.
4.
5.
9
2
j = −6
Show work
m = − 2, m = 2
a = 3, a = − 6
x =
6x 2
1
x2
x( x  4 )
3( x  2 )
x( x  13 )
( x  2 )( x  8 )
Simplifying Rational Expressions:
A SQUARE MEAL
Solving Rational Equations:
Algebra 1 Concept # 18 – Solving Rational
1.
2.
3.
4.
2  5x
NINE CENTS
m = − 2, m = 8
x = −2
x = −6
x = 8, x = − 1
Algebra 1 Concept # 18 – Adding &
Subtracting Rational Expressions with Like
Denominators Practice Worksheet:
1.
2.
3.
4.
1
4
3
1
h  3
x 5
4
Page 29
CONCEPT #19 – RATIOS, RATES, AND PERCENTS
Algebra 1 Concept #6 – Ratios, Rates, and
Percents Practice Worksheet:
1a.
1b.
2.
3.
4.
5.
6.
7.
8.
9a.
9b.
10.
11.
12.
7:2
2:9
60 mph
420 minutes
1
2 feet
2
$1.69
$1.17
19.5
130
32%
68%
25%
$85.00
30%
CONCEPT #20 – GEOMETRY
Algebra 1 Concept # 22 – Geometry Practice
Worksheet:
1.
2.
3.
4.
5.
6.
7.
d = 6 2 ,
Perimeter:
Area:
Width:
Midpoint: ( − 1, 0 )
34 cm
2
60 cm
10 cm
15 feet, 17 feet
7
2
3
3
Volume:
yds OR 1 yds
5
5
Circumference:
50.24 m
2
Area:
200.96 m
Perimeter: 56 in
2
Area:
192 in
Page 30
BENCHMARK
Cumulative Review Crossword – CT # 1 – 3:
DOWN:
ACROSS:
DOWN:
ACROSS:
1.
4.
−1
7.
49
1.
2.
12
m < 3
4.
7.
3.
5.
6.
8.
54
2
3
100
12
.6
9.2
9.
11.
14.
16.
3.
540
9.
10.
−3
17.
− 60
21
3x
0
7
4
5.
6.
8.
10.
11.
12.
14.
20.
38
2
84
12
$402
x ≥ 5
NO
−1
13.
15.
16.
17.
18.
19.
22.
23.
21.
−6
24.
25.
26.
29.
32.
50
$65.45
1 < x < 4
28.5
27.
28.
30.
31.
33.
2.
23.
24.
28.
29.
36.
1
4
1
5
27
64
2
3
−4
−2
.1
−1
YES
37.
− 13
12.
13.
15.
20.
21.
18.
53
22.
25.
5
6
49
400
26.
25
27.
30.
31.
32.
33.
3.6
−2
−5
21
4
3
4
5
ADD
19.
34.
35.
DOWN:
1.
2.
3.
−3
28
1
4
24
0
100
53
NO
15
121
60
25
7
48
−8
LINE
125
YES
Page 31
2

3
1
4
7
5
ACROSS:
4.
−6
6.

7.
0
5.
( 0, 3 )
8.
9.
10.
12.
15.
16.
18.
21.
22.
24.
26.
57
351
4
12
−4
NO
YES
0
16
9
11.
13.
14.
17.
19.
20.
23.
25.
27.
3
5
3
5
9
100
0
25
SLOPE
−3
UNDEFINED
( − 2, 2 )
( 9, 2 )
BENCHMARK (continued)
DOWN:
ACROSS:
1.
2.
3.
5.
7.
8.
4.
6.
10.
12.
13.
15.
−9
4
− 8x
11
2
3 5
4
17.
64
11.
14.
16.
18.
RADICAL
8
4x
3
7x
YES
81
14
1
3
10
16
0
6  21
21.
23.
24.
25.
x = ±3
DASHED
PARABOLA
x = 1
19.
8x
27.
20.
22.
26.
3
( 2, 5 )
15
28.
29.
9.
2
7
2
1
Page 32

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