The Practice SSAT Middle Level Test Takers Need to Prepare ...
Transcript of The Practice SSAT Middle Level Test Takers Need to Prepare ...
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 1
The Practice SSAT Middle Level Test
Takers Need to Prepare for the SSAT
Middle Level Math Test
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 2
SSAT Middle Level Math Concepts
1. Simplifying Fractions ........................................................................................................................ 5
2. Adding and Subtracting Fractions .................................................................................................... 7
3. Multiplying and Dividing Fractions .................................................................................................. 9
4. Adding and Subtracting Mixed Numbers ....................................................................................... 11
5. Multiplying and Dividing Mixed Numbers ..................................................................................... 13
6. Adding and Subtracting Decimals .................................................................................................. 15
7. Multiplying and Dividing Decimals ................................................................................................. 17
8. Comparing Decimals ...................................................................................................................... 19
9. Rounding Decimals ........................................................................................................................ 21
10. Factoring Numbers ........................................................................................................................ 23
11. Greatest Common Factor............................................................................................................... 25
12. Least Common Multiple ................................................................................................................. 27
13. Adding and Subtracting Integers ................................................................................................... 29
14. Multiplying and Dividing Integers .................................................................................................. 31
15. Order of Operations ....................................................................................................................... 33
16. Ordering Integers and Numbers .................................................................................................... 35
17. Integers and Absolute Value .......................................................................................................... 37
18. Simplifying Ratios ........................................................................................................................... 39
19. Proportional Ratios ........................................................................................................................ 41
20. Similarity and Ratios ...................................................................................................................... 43
21. Ratio and Rates Word Problems .................................................................................................... 45
22. Percentage Calculations ................................................................................................................. 47
23. Percent Problems ........................................................................................................................... 49
24. Discount, Tax and Tip ..................................................................................................................... 51
25. Percent of Change .......................................................................................................................... 53
26. Simple Interest ............................................................................................................................... 55
27. Simplifying Variable Expressions.................................................................................................... 57
28. Simplifying Polynomial Expressions ............................................................................................... 59
29. Translate Phrases into an Algebraic Statement ............................................................................. 61
30. The Distributive Property ............................................................................................................... 63
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 3
31. Evaluating One Variable Expressions ............................................................................................. 65
32. Evaluating Two Variables Expressions ........................................................................................... 67
33. Combining like Terms..................................................................................................................... 69
34. OneβStep Equations ...................................................................................................................... 71
35. MultiβStep Equations ..................................................................................................................... 73
36. Graphing SingleβVariable Inequalities ........................................................................................... 75
37. OneβStep Inequalities .................................................................................................................... 77
38. Multi-Step Inequalities ................................................................................................................... 79
39. Finding Slope .................................................................................................................................. 81
40. Graphing Lines Using Line Equation............................................................................................... 83
41. Writing Linear Equations................................................................................................................ 85
42. Graphing Linear Inequalities .......................................................................................................... 87
43. Multiplication Property of Exponents ............................................................................................ 90
44. Zero and Negative Exponents ........................................................................................................ 92
45. Division Property of Exponents...................................................................................................... 94
46. Powers of Products and Quotients ................................................................................................ 96
47. Negative Exponents and Negative Bases ....................................................................................... 98
48. Scientific Notation ........................................................................................................................ 100
49. Square Roots ................................................................................................................................ 102
50. Angles ........................................................................................................................................... 104
51. Pythagorean Relationship ............................................................................................................ 106
52. Triangles ....................................................................................................................................... 108
53. Polygons ....................................................................................................................................... 110
54. Trapezoids .................................................................................................................................... 112
55. Circles ........................................................................................................................................... 114
56. Cubes............................................................................................................................................ 116
57. Rectangular Prism ........................................................................................................................ 118
58. Cylinder ........................................................................................................................................ 120
59. Pyramids and Cone ...................................................................................................................... 122
60. Mean and Median ........................................................................................................................ 124
61. Mode and Range .......................................................................................................................... 126
62. Histograms ................................................................................................................................... 128
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 4
63. StemβandβLeaf Plot ..................................................................................................................... 130
64. Pie Graph...................................................................................................................................... 132
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 5
Simplifying Fractions
Simplify each fraction to its lowest terms.
1) 9
18=
2) 8
10=
3) 6
8=
4) 5
20=
5) 18
24=
6) 6
9=
7) 12
15=
8) 4
16=
9) 18
36=
10) 6
42=
11) 13
39=
12) 21
28=
13) 63
77=
14) 36
40=
15) 21
63=
16) 30
84=
17) 50
125=
18) 72
108=
19) 49
112=
20) 240
320=
21) 120
150=
Solve each problem.
22) Which of the following fractions equal to 4
5? ____
A. 64
75 B.
92
115 C.
60
85 D.
160
220
23) Which of the following fractions equal to 3
7? ____
A. 63
147 B.
75
182 C.
54
140 D.
39
98
24) Which of the following fractions equal to 2
9? ____
A. 84
386 B.
52
234 C.
96
450 D.
112
522
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 6
Answers
Simplifying Fractions
1) 1
2
2) 4
5
3) 3
4
4) 1
4
5) 3
4
6) 2
3
7) 4
5
8) 1
4
9) 1
2
10) 1
7
11) 1
3
12) 3
4
13) 9
11
14) 9
10
15) 1
3
16) 5
14
17) 2
5
18) 2
3
19) 7
16
20) 3
4
21) 4
5
22) B
23) A
24) B
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 7
Adding and Subtracting Fractions
Find the sum.
1) 1
3+
2
3=
2) 1
2+
1
3=
3) 2
5+
1
2=
4) 3
7+
2
3=
5) 3
4+
2
5=
6) 3
5+
1
5=
7) 5
9+
1
2=
8) 3
5+
3
8=
9) 5
9+
3
7=
10) 5
11+
1
4=
11) 3
7+
1
6=
12) 3
14+
3
4=
Find the difference.
13) 1
2β
1
3=
14) 4
5β
2
3=
15) 2
3β
1
6=
16) 3
5β
1
2=
17) 8
9β
2
5=
18) 4
7β
1
9=
19) 2
5β
1
4=
20) 5
8β
2
6=
21) 4
15β
1
10=
22) 7
20β
1
5=
23) 3
18β
1
12=
24) 9
24β
3
16=
25) 3
7β
2
5=
26) 5
9β
1
6=
27) 2
5β
1
10=
28) 5
12β
2
9=
29) 2
13β
3
7=
30) 4
11β
5
8=
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 8
Answers
Adding and Subtracting Fractions
1) 3
3= 1
2) 5
6
3) 9
10
4) 23
21
5) 23
20
6) 4
5
7) 19
18
8) 39
40
9) 62
63
10) 31
44
11) 25
42
12) 27
28
13) 1
6
14) 2
15
15) 1
2
16) 1
10
17) 22
45
18) 29
63
19) 3
20
20) 7
24
21) 1
6
22) 3
20
23) 1
12
24) 3
16
25) 1
35
26) 7
18
27) 3
10
28) 7
36
29) β25
91
30) β15
88
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 9
Multiplying and Dividing Fractions
Find the value of each expression in lowest terms.
1) 1
2Γ
3
4=
2) 3
5Γ
2
3=
3) 1
4Γ
2
5=
4) 1
6Γ
4
5=
5) 1
5Γ
1
4=
6) 2
5Γ
1
2=
7) 7
9Γ
1
3=
8) 5
7Γ
3
8=
9) 8
9Γ
6
7=
10) 5
6Γ
3
5=
11) 3
8Γ
1
9=
12) 1
12Γ
3
7=
Find the value of each expression in lowest terms.
13) 1
2Γ·
1
4=
14) 1
3Γ·
1
2=
15) 2
5Γ·
1
3=
16) 1
4Γ·
2
3=
17) 1
5Γ·
3
10=
18) 2
7Γ·
1
3=
19) 3
5Γ·
5
9=
20) 2
23Γ·
2
9=
21) 4
13Γ·
1
4=
22) 9
14Γ·
3
7=
23) 8
15Γ·
2
5=
24) 2
9Γ·
7
11=
25) 2
5Γ·
3
4=
26) 4
11Γ·
2
5=
27) 2
15Γ·
5
8=
28) 3
10Γ·
2
5=
29) 4
5Γ·
3
7=
30) 2
11Γ·
3
5=
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 10
Answers
Multiplying and Dividing Fractions
1) 3
8
2) 2
5
3) 1
10
4) 2
15
5) 1
20
6) 1
5
7) 7
27
8) 15
56
9) 16
21
10) 1
2
11) 1
24
12) 1
28
13) 2
14) 2
3
15) 6
5
16) 3
8
17) 2
3
18) 6
7
19) 27
25
20) 9
23
21) 16
13
22) 21
14
23) 4
3
24) 22
63
25) 8
15
26) 10
11
27) 16
75
28) 3
4
29) 28
15
30) 10
33
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 11
Adding and Subtracting Mixed Numbers
Find the sum.
1) 21
2+ 1
1
3=
2) 61
2+ 3
1
2=
3) 23
8+ 3
1
8=
4) 41
2+ 1
1
4=
5) 13
7+ 1
5
14=
6) 65
12+ 3
3
4=
7) 51
2+ 8
3
4=
8) 37
8+ 3
1
3=
9) 33
9+ 7
6
11=
10) 75
12+ 4
3
10=
Find the difference.
11) 31
3β 1
1
3=
12) 41
2β 3
1
2=
13) 51
2β 2
1
4=
14) 61
6β 5
1
3=
15) 81
2β 1
1
10=
16) 91
2β 2
1
4=
17) 91
5β 5
1
6=
18) 143
10β 13
1
3=
19) 192
3β 11
5
8=
20) 203
4β 14
2
3=
21) 21
2β 1
1
5=
22) 31
6β 1
1
10=
23) 162
7β 11
2
3=
24) 151
7β 10
1
8=
25) 123
4β 7
1
3=
26) 152
5β 5
2
3=
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 12
Answers
Adding and Subtracting Mixed Numbers
1) 356
2) 10
3) 51
2
4) 53
4
5) 211
14
6) 101
6
7) 141
4
8) 75
24
9) 1029
33
10) 1143
60
11) 2
12) 1
13) 31
4
14) 5
6
15) 72
5
16) 71
4
17) 41
30
18) 29
30
19) 81
24
20) 61
12
21) 13
10
22) 21
15
23) 413
21
24) 51
56
25) 55
12
26) 911
15
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 13
Multiplying and Dividing Mixed Numbers
Find the product.
1) 41
3Γ 2
1
5=
2) 31
2Γ 3
1
4=
3) 52
5Γ 2
1
3=
4) 21
2Γ 1
2
9=
5) 34
7Γ 2
3
5=
6) 72
3Γ 2
2
3=
7) 98
9Γ 8
3
4=
8) 24
7Γ 5
2
9=
9) 52
5Γ 2
3
5=
10) 35
7Γ 3
5
6=
Find the quotient.
11) 12
3Γ· 3
1
3=
12) 21
4Γ· 1
1
2=
13) 101
2Γ· 1
2
3=
14) 31
6Γ· 4
2
3=
15) 41
8Γ· 2
1
2=
16) 21
10Γ· 2
3
5=
17) 14
11Γ· 1
1
4=
18) 91
2Γ· 9
2
3=
19) 83
4Γ· 2
2
5=
20) 121
2Γ· 9
1
3=
21) 21
8Γ· 1
1
2=
22) 11
10Γ· 1
3
5=
23) 52
5Γ· 1
3
4=
24) 51
2Γ· 2
2
3=
25) 33
4Γ· 1
1
5=
26) 31
2Γ· 1
1
3=
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 14
Answers
Multiplying and Dividing Mixed Numbers
1) 98
15
2) 113
8
3) 123
5
4) 31
18
5) 92
7
6) 204
9
7) 8619
36
8) 133
7
9) 141
25
10) 145
21
11) 1
2
12) 11
2
13) 63
10
14) 19
28
15) 113
20
16) 21
26
17) 11
11
18) 57
58
19) 331
48
20) 119
56
21) 15
12
22) 11
16
23) 33
35
24) 21
16
25) 31
8
26) 25
8
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 15
Adding and Subtracting Decimals
Add and subtract decimals.
1)
31.13β 11.45
_______
2)
35.25+ 24.47
_______
3)
73.50+ 22.78
_______
4)
56.67β 44.39
_______
5)
71.47+ 16.25
_______
6)
68.99β 53.61
_______
7)
66.24β 23.11
_______
8)
39.75+ 12.85
_______
9)
229.25β 84.67
_______
Find the missing number.
10) ____ + 2.5 = 3.9
11) 1.7 + ____ = 4.98
12) 5.25 + ____ = 7
13) 6.55 β ____ = 2.45
14) ____ β 3.98 = 5.32
15) ____ β 11.67 = 14.48
16) 12.35 + ____ = 14.78
17) ____ β 23.89 = 13.90
18) ____ + 17.28 = 19.56
19) 77.90 + ____ = 102.60
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 16
Answers
Adding and Subtracting Decimals
1) 19.68
2) 59.72
3) 96.28
4) 12.28
5) 87.72
6) 15.38
7) 43.13
8) 52.60
9) 144.58
10) 1.4
11) 3.28
12) 1.75
13) 4.1
14) 9.3
15) 26.15
16) 2.43
17) 37.79
18) 2.28
19) 24.7
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 17
Multiplying and Dividing Decimals
Find the product.
1) 0.5 Γ 0.4 =
2) 2.5 Γ 0.2 =
3) 1.25 Γ 0.5 =
4) 0.75 Γ 0.2 =
5) 1.92 Γ 0.8 =
6) 0.55 Γ 0.4 =
7) 3.24 Γ 1.2 =
8) 12.5 Γ 4.2 =
9) 22.6 Γ 8.2 =
10) 17.2 Γ 4.5 =
11) 25.1 Γ 12.5 =
12) 33.2 Γ 2.2 =
Find the quotient.
13) 1.67 Γ· 100 =
14) 52.2 Γ· 1,000 =
15) 4.2 Γ· 2 =
16) 8.6 Γ· 0.5 =
17) 12.6 Γ· 0.2 =
18) 16.5 Γ· 5 =
19) 13.25 Γ· 100 =
20) 25.6 Γ· 0.4 =
21) 28.24 Γ· 0.1 =
22) 34.16 Γ· 0.25 =
23) 44.28 Γ· 0.5 =
24) 38.78 Γ· 0.02 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 18
Answers
Multiplying and Dividing Decimals
1) 0.2 2) 0.5 3) 0.625 4) 0.15 5) 1.536 6) 0.22 7) 3.888 8) 52.5
9) 185.32 10) 77.4 11) 313.75 12) 73.04 13) 0.0167 14) 0.0522 15) 2.1 16) 4.3
17) 63 18) 3.3 19) 0.1325 20) 64 21) 282.4 22) 136.64 23) 88.56 24) 1,939
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 19
Comparing Decimals
Write the correct comparison symbol (>, < or =).
1) 0.50 β 0.050
2) 0.025 β 0.25
3) 2.060 β 2.07
4) 1.75 β 1.07
5) 4.04 β 0.440
6) 3.05 β 3.5
7) 5.05 β 5.050
8) 1.02 β 1.1
9) 2.45 β 2.125
10) 0.932 β 0.0932
11) 3.15 β 3.150
12) 0.718 β 0.89
13) 7.060 β 7.60
14) 3.59 β 3.129
15) 4.33 β 4.319
16) 2.25 β 2.250
17) 1.95 β 1.095
18) 8.051 β 8.50
19) 1.022 β 1.020
20) 3.77 β 3.770
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 20
Answers
Comparing Decimals
1) > 2) <
3) <
4) >
5) >
6) <
7) =
8) <
9) >
10) >
11) =
12) <
13) <
14) >
15) >
16) =
17) >
18) <
19) >
20) =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 21
Rounding Decimals
Round each decimal to the nearest whole number.
1) 23.18
2) 8.6
3) 14.45
4) 7.5
5) 3.95
6) 56.7
Round each decimal to the nearest tenth.
7) 22.652
8) 30.342
9) 47.847
10) 82.88
11) 16.184
12) 71.79
Round each decimal to the nearest hundredth.
13) 5.439
14) 12.907
15) 26.1855
16) 48.623
17) 91.448
18) 29.354
Round each decimal to the nearest thousandth.
19) 14.67374
20) 7.54647
21) 78.7191
22) 70.2732
23) 10.0678
24) 46.54765
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 22
Answers
Rounding Decimals
1) 23 2) 9 3) 14 4) 8 5) 4 6) 57 7) 22.7 8) 30.3
9) 47.8 10) 82.9 11) 16.2 12) 71.8 13) 5.44 14) 12.91 15) 26.19 16) 48.62
17) 91.45 18) 29.35 19) 14.674 20) 7.546 21) 78.719 22) 70.273 23) 10.068 24) 46.548
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 23
Factoring Numbers
List all positive factors of each number.
1) 8
2) 9
3) 15
4) 16
5) 25
6) 28
7) 26
8) 35
9) 42
10) 48
11) 50
12) 36
13) 55
14) 40
15) 62
16) 84
17) 75
18) 68
19) 96
20) 78
21) 94
22) 82
23) 81
24) 72
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 24
Answers
Factoring Numbers
1) 1, 2, 4, 8
2) 1, 3, 9
3) 1, 3, 5, 15
4) 1, 2, 4, 8, 16
5) 1, 5, 25
6) 1, 2, 4, 7, 14, 28
7) 1, 2, 13, 26
8) 1, 5, 7, 35
9) 1, 2, 3, 6, 7, 14, 21, 42
10) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
11) 1, 2, 5, 10, 25, 50
12) 1, 2, 3, 4, 6, 9, 12, 18, 36
13) 1, 5, 11, 55
14) 1, 2, 4, 5, 8, 10, 20, 40
15) 1, 2, 31, 62
16) 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
17) 1, 3, 5, 15, 25, 75
18) 1, 2, 4, 17, 34, 68
19) 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
20) 1, 2, 3, 6, 13, 26, 39, 78
21) 1, 2, 47, 94
22) 1, 2, 41, 82
23) 1, 3, 9, 27, 81
24) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 25
Greatest Common Factor
Find the GCF for each number pair.
1) 4, 2
2) 3, 5
3) 2, 6
4) 4, 7
5) 5, 10
6) 6, 12
7) 7, 14
8) 6, 14
9) 5, 12
10) 4, 14
11) 15, 18
12) 12, 20
13) 12, 16
14) 15, 27
15) 8, 24
16) 28, 16
17) 32, 24
18) 18, 36
19) 26, 20
20) 30, 14
21) 24, 20
22) 14, 22
23) 25, 15
24) 28, 32
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 26
Answers
Greatest Common Factor
1) 2 2) 1 3) 2 4) 1 5) 5 6) 6 7) 7 8) 2
9) 1 10) 2 11) 3 12) 4 13) 4 14) 3 15) 8 16) 4
17) 8 18) 18 19) 2 20) 2 21) 4 22) 2 23) 5 24) 4
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 27
Least Common Multiple
Find the LCM for each number pair.
1) 3, 6
2) 5, 10
3) 6, 14
4) 8, 9
5) 6, 18
6) 10, 12
7) 4, 12
8) 5, 15
9) 4, 18
10) 9, 12
11) 12, 16
12) 15, 18
13) 8, 24
14) 9, 28
15) 12, 24
16) 15, 20
17) 25, 18
18) 27, 24
19) 28, 18
20) 16, 30
21) 14, 28
22) 20, 35
23) 25, 30
24) 32, 27
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 28
Answers
Least Common Multiple
1) 6 2) 10 3) 42 4) 72 5) 18 6) 60 7) 12 8) 15
9) 36 10) 36 11) 48 12) 90 13) 24 14) 252 15) 24 16) 60
17) 450 18) 216 19) 252 20) 240 21) 28 22) 140 23) 150 24) 864
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 29
Adding and Subtracting Integers
Find each sum.
1) 12 + (β5) =
2) (β14) + (β18) =
3) 8 + (β28) =
4) 43 + (β12) =
5) (β 7) + (β11) + 4 =
6) 37 + (β16) + 12 =
7) 29 + (β21) + (β12) + 20 =
8) (β15) + (β25) + 18 + 25 =
9) 30 + (β28) + (35 β 32) =
10) 25 + (β15) + (44 β 17) =
Find each difference.
11) (β12) β (β8) =
12) 15 β (β20) =
13) (β11) β 25 =
14) 30 β (β16) =
15) 56 β (45 β 23) =
16) 15 β (β4) β (β34) =
17) (24 + 14) β (β55) =
18) 23 β 15 β (β3) =
19) 49 β (15 + 12) β (β4) =
20) 29 β (β17) β (β25) =
21) 12 β (β8) β (β18) =
22) (15 β 28) β (β22) =
23) 19 β 44 β (β14) =
24) 67 β (57 + 19) β (β8) =
25) 56 β (β12) + (β19) =
26) 22 β (β44) + (β55) =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 30
Answers
Adding and Subtracting Integers
1) 7
2) β32
3) β20
4) 31
5) β14
6) 33
7) 16
8) 3
9) 5
10) 37
11) β4
12) 35
13) β36
14) 46
15) 34
16) 53
17) 93
18) 11
19) 26
20) 71
21) 38
22) 9
23) β11
24) β1
25) 49
26) 11
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 31
Multiplying and Dividing Integers
Find each product.
1) (β7) Γ (β8) =
2) (β4) Γ 5 =
3) 5 Γ (β11) =
4) (β 5) Γ (β20) =
5) β(2) Γ (β8) Γ 3 =
6) (12 β 4) Γ (β10) =
7) 14 Γ (β10) Γ (β5) =
8) (18 + 12) Γ (β8) =
9) 9 Γ (β15 + 6) Γ 3 =
10) (β5) Γ (β8) Γ (β12) =
Find each quotient.
11) 16 Γ· (β4) =
12) (β25) Γ· (β5) =
13) (β40) Γ· (β8) =
14) 64 Γ· (β8) =
15) (β49) Γ· 7 =
16) (β112) Γ· (β4) =
17) 168 Γ· (β12) =
18) (β121) Γ· (β11) =
19) 216 Γ· (β12) =
20) β(152) Γ· (8) =
21) (β152) Γ· (β8) =
22) β216 Γ· (β12) =
23) (β198) Γ· (β9) =
24) 195 Γ· (β13) =
25) β(182) Γ· (β7) =
26) (126) Γ· (β14) =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 32
Answers
Multiplying and Dividing Integers
1) 56
2) β20
3) β55
4) 100
5) 48
6) β80
7) 700
8) β240
9) β243
10) β480
11) β4
12) 5
13) 5
14) β8
15) β7
16) 28
17) β14
18) 11
19) β18
20) β19
21) 19
22) 18
23) 22
24) β15
25) 26
26) β9
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 33
Order of Operations
Evaluate each expression.
1) 5 + (4 Γ 2) =
2) 13 β (2 Γ 5) =
3) (16 Γ 2) + 18 =
4) (12 β 5) β (4 Γ 3) =
5) 25 + (14 Γ· 2) =
6) (18 Γ 5) Γ· 5 =
7) (48 Γ· 2) Γ (β4) =
8) (7 Γ 5) + (25 β 12) =
9) 64 + (3 Γ 2) + 8 =
10) (20 Γ 5) Γ· (4 + 1) =
11) (β9) + (12 Γ 6) + 15 =
12) (7 Γ 8) β (56 Γ· 4) =
13) (4 Γ 8 Γ· 2) β (17 + 11) =
14) (18 + 8 β 15) Γ 5 β 3 =
15) (25 β 12 + 45) Γ (95 Γ· 5) =
16) 28 + (15 β (32 Γ· 2)) =
17) (6 + 7 β 4 β 9) + (18 Γ· 2) =
18) (95 β 17) + (10 β 25 + 9) =
19) (18 Γ 2) + (15 Γ 5) β 12 =
20) 12 + 8 β (42 Γ 4) + 50 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 34
Answers
Order of Operations
1) 13
2) 3
3) 50
4) β5
5) 32
6) 18
7) β96
8) 48
9) 78
10) 20
11) 78
12) 42
13) β12
14) 52
15) 1,102
16) 27
17) 9
18) 72
19) 99
20) β98
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 35
Ordering Integers and Numbers
Order each set of integers from least to greatest.
1) 7, β9, β6, β1, 3 ___, ___, ___, ___, ___, ___
2) β4, β11, 5, 12, 9 ___, ___, ___, ___, ___, ___
3) 18, β12, β19, 21, β20 ___, ___, ___, ___, ___, ___
4) β15, β25, 18, β 7, 32 ___, ___, ___, ___, ___, ___
5) 37, β42, 28, β11, 34 ___, ___, ___, ___, ___, ___
6) 78, 46, β19, 77, β24 ___, ___, ___, ___, ___, ___
Order each set of integers from greatest to least.
7) 11, 16, β9, β12, β4 ___, ___, ___, ___, ___, ___
8) 23, 31, β14, β20, 39 ___, ___, ___, ___, ___, ___
9) 45, β21, β18, 55, β5 ___, ___, ___, ___, ___, ___
10) 68, 81, β14, β10, 94 ___, ___, ___, ___, ___, ___
11) β5, 69, β12, β43, 34 ___, ___, ___, ___, ___, ___
12) β56, β25, β30, 18, 29 ___, ___, ___, ___, ___, ___
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 36
Answers
Ordering Integers and Numbers
1) β9, β6, β1, 3, 7
2) β11, β4, 5, 9, 12
3) β20, β19, β12, 18, 21
4) β25, β15, β7, 18, 32
5) β42, β11, 28, 34, 37
6) β24, β19, 46, 77, 78
7) 16, 11, β4, β9, β12
8) 39,31,23, β14, β20
9) 55, 45, β5, β18, β21
10) 94, 81, 68, β10, β14
11) 69, 34, β5, β12, β43
12) 29, 18, β25, β30, β56
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 37
Integers and Absolute Value
Write absolute value of each number.
1) |β7| =
2) |β11| =
3) |β9| =
4) |8| =
5) |4| =
6) |β18| =
7) |6| =
8) |0| =
9) |16| =
10) |β2| =
11) |β12|
12) |10| =
13) |3| =
14) |7| =
15) |β15| =
16) |β13| =
17) |19| =
18) |β12| =
19) |4| =
20) |β25| =
Evaluate the value.
21) |β2| β |β10|
2=
22) 8 β |2 β 14| β |β2| =
23) |β36|
6Γ |β6| =
24) |5 Γ β3|
5Γ
|β20|
4=
25) |2 Γ β4| + |β40|
5=
26) |β28|
4Γ
|β55|
11=
27) | β 12 + 4| Γ |β4Γ5|
2
28) |β10 Γ3|
2Γ |β12| =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 38
Answers
Integers and Absolute Value
1) 7
2) 11
3) 9
4) 8
5) 4
6) 18
7) 6
8) 0
9) 16
10) 2
11) 12
12) 10
13) 3
14) 7
15) 15
16) 13
17) 19
18) 12
19) 4
20) 25
21) β3
22) β6
23) 36
24) 15
25) 16
26) 35
27) 80
28) 180
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 39
Simplifying Ratios
Reduce each ratio.
1) 12: 8 = ____: ____
2) 2: 20 = ____: ____
3) 3: 36 = ____: ____
4) 8: 16 = ____: ____
5) 6: 100 = ____: ____
6) 10: 60 = ____: ____
7) 21: 49 = ____: ____
8) 20: 40 = ____: ____
9) 10: 50 = ____: ____
10) 14: 18 = ____: ____
11) 45: 27 = ____: ____
12) 49: 21 = ____: ____
13) 100: 10 = ____: ____
14) 35: 45 = ____: ____
15) 8: 20 = ____: ____
16) 25: 35 = ____: ____
17) 21: 27 = ____: ____
18) 52: 82 = ____: ____
19) 12: 36 = ____: ____
20) 24: 3 = ____: ____
21) 15: 30 = ____: ____
22) 14: 63 = ____: ____
23) 68: 80 = ____: ____
24) 8: 80 = ____: ____
Write each ratio as a fraction in simplest form.
25) 2: 4 =
26) 6: 20 =
27) 5: 35 =
28) 10: 55 =
29) 8: 24 =
30) 9: 42 =
31) 12: 48 =
32) 6: 40 =
33) 15: 36 =
34) 18: 82 =
35) 22: 26 =
36) 8: 36 =
37) 16: 128 =
38) 14: 77 =
39) 12: 180 =
40) 36: 108 =
41) 24: 42 =
42) 18: 120 =
43) 44: 82 =
44) 60: 240 =
45) 36: 180 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 40
Answers
Simplifying Ratios
1) 3 βΆ 2
2) 1 βΆ 10
3) 1 βΆ 12
4) 1 βΆ 2
5) 3 βΆ 50
6) 1 βΆ 6
7) 3 βΆ 7
8) 1 βΆ 2
9) 1 βΆ 5
10) 7 βΆ 9
11) 5 βΆ 3
12) 7 βΆ 3
13) 10 βΆ 1
14) 7 βΆ 9
15) 2 βΆ 5
16) 5 βΆ 7
17) 7 βΆ 9
18) 26 βΆ 41
19) 1 βΆ 3
20) 8 βΆ 1
21) 1 βΆ 2
22) 2 βΆ 9
23) 17 βΆ 20
24) 1 βΆ 10
25) 1
2
26) 3
10
27) 1
7
28) 2
11
29) 1
3
30) 3
14
31) 1
4
32) 3
20
33) 5
12
34) 9
41
35) 11
13
36) 2
9
37) 1
8
38) 2
11
39) 1
15
40) 1
3
41) 4
7
42) 3
20
43) 22
41
44) 1
4
45) 1
5
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 41
Proportional Ratios
Fill in the blanks; solve each proportion.
1) 3 βΆ 7 = ___ βΆ 49
2) 1 βΆ 2 = 20 βΆ ___
3) 1 βΆ 5 = ___ βΆ 50
4) 7 βΆ 9 = 14 βΆ ___
5) 5 βΆ 3 = 45 βΆ ___
6) 7 βΆ 3 = ___ βΆ 18
7) 10 βΆ 1 = ___ βΆ 10
8) 1 βΆ 3 = ___ βΆ 27
9) 8 βΆ 1 = ___ βΆ 8
10) 9 βΆ 2 = ___ βΆ 14
11) 3 βΆ 12 = 12 βΆ ___
12) 6 βΆ 4 = 24 βΆ ___
State if each pair of ratios form a proportion.
13) 3
10πππ
9
30
14) 1
2πππ
16
32
15) 5
6πππ
35
42
16) 3
7πππ
27
72
17) 2
5πππ
16
45
18) 4
9πππ
40
81
19) 6
11πππ
42
77
20) 1
6πππ
8
48
21) 6
17πππ
36
85
22) 2
7πππ
24
86
23) 12
19πππ
156
247
24) 13
21πππ
182
294
Solve each proportion.
25) 2
5=
14
π₯, π₯ = _____
26) 1
6=
7
π₯, π₯ = _____
27) 3
5=
27
π₯, π₯ = _____
28) 1
5=
π₯
80, π₯ = _____
29) 3
7=
π₯
63, π₯ = _____
30) 1
4=
13
π₯, π₯ = _____
31) 7
9=
56
π₯, π₯ = _____
32) 6
11=
42
π₯, π₯ = _____
33) 4
7=
π₯
77, π₯ = _____
34) 5
13=
π₯
143, π₯ = _____
35) 7
19=
π₯
209, π₯ = _____
36) 3
13=
π₯
195, π₯ = _____
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 42
Answers
Proportional Ratios
1) 21
2) 40
3) 10
4) 18
5) 27
6) 42
7) 100
8) 9
9) 64
10) 63
11) 48
12) 16
13) Yes
14) Yes
15) Yes
16) No
17) No
18) No
19) Yes
20) Yes
21) No
22) No
23) Yes
24) Yes
25) 35
26) 42
27) 45
28) 16
29) 27
30) 52
31) 72
32) 77
33) 44
34) 55
35) 77
36) 45
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 43
Similarity and Ratios
Each pair of figures is similar. Find the missing side.
1) 2)
3) 4)
Solve.
5) Two rectangles are similar. The first is 6 feet wide and 20 feet long. The second is 15
feet wide. What is the length of the second rectangle? ________________
6) Two rectangles are similar. One is 2.5 meters by 9 meters. The longer side of the second
rectangle is 22.5 meters. What is the other side of the second rectangle?
__________________
7) A building casts a shadow 24 ft long. At the same time a girl 5 ft tall casts a shadow 2 ft
long. How tall is the building? ______________________
8) The scale of a map of Texas is 2 inches: 45 miles. If you measure the distance from Dallas
to Martin County as 14.4 inches, approximately how far is Martin County from Dallas?
_________
9
6
9
?
9
15 3
4
5
3
?
3
12
15
4
?
?
8
60
32
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 44
Answers
Similarity and ratios
1) 12
2) 2
3) 5
4) 15
5) 50 feet
6) 6.25 meters
7) 60 feet
8) 324 miles
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 45
Ratio and Rates Word Problems
Solve each word problem.
1) Bob has 12 red cards and 20 green cards. What is the ratio of Bob's red cards
to his green cards? _______________
2) In a party, 10 soft drinks are required for every 12 guests. If there are 252
guests, how many soft drinks is required? _______________
3) In Jackβs class, 18 of the students are tall and 10 are short. In Michaelβs class
54 students are tall and 30 students are short. Which class has a higher ratio
of tall to short students? _______________
4) The price of 3 apples at the Quick Market is $1.44. The price of 5 of the same
apples at Walmart is $2.50. Which place is the better buy? _______________
5) The bakers at a Bakery can make 160 bagels in 4 hours. How many bagels can
they bake in 16 hours? What is that rate per hour? _______________
6) You can buy 5 cans of green beans at a supermarket for $3.40. How much does
it cost to buy 35 cans of green beans? _______________
7) The ratio of boys to girls in a class is 2:3. If there are 18 boys in the class, how
many girls are in that class? _______________
8) The ratio of red marbles to blue marbles in a bag is 3:4. If there are 42 marbles
in the bag, how many of the marbles are red? _______________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 46
Answers
Ratio and Rates Word Problems
1) 3: 5
2) 210
3) The ratio for both classes is 9 to 5.
4) Quick Market is a better buy.
5) 640, the rate is 40 per hour.
6) $23.80
7) 27
8) 18
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 47
Percentage Calculations
Calculate the given percent of each value.
1) 2% of 50 = _____
2) 10% of 30 = _____
3) 20% of 25 = _____
4) 50% of 80 = _____
5) 40% of 200 = _____
6) 20% of 45 = _____
7) 35% of 20 = _____
8) 12% of 400 = _____
9) 40% of 90 = _____
10) 25% of 812 = _____
11) 32% of 600 = _____
12) 87% of 500 = _____
13) 77% of 300 = _____
14) 29% of 86 = _____
15) 33% of 54 = _____
16) 71% of 112 = _____
17) 44% of 165 = _____
18) 17% of 232 = _____
Calculate the percent of each given value.
19) _____% of 7 = 3.5
20) _____% of 15 = 9
21) _____% of 80 = 4
22) _____% of 50 = 12.5
23) _____% of 64 = 8
24) _____% of 72 = 18
25) _____% of 250 = 12.5
26) _____% of 400 = 12
27) _____% of 190 = 9.5
28) ____% of 900 = 126
Solve each percent problem.
29) A Cinema has 240 seats. 144 seats were sold for the current movie. What percent of
seats are empty? _____ %
30) There are 18 boys and 46 girls in a class. 87.5% of the students in the class take the
bus to school. How many students do not take the bus to school? _____
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 48
Answers
Percentage Calculations
1) 1
2) 3
3) 5
4) 40
5) 80
6) 9
7) 7
8) 48
9) 36
10) 203
11) 192
12) 435
13) 231
14) 24.94
15) 17.82
16) 79.52
17) 72.6
18) 39.44
19) 50%
20) 60%
21) 5%
22) 25%
23) 12.5%
24) 25%
25) 5%
26) 3%
27) 5%
28) 14%
29) 40%
30) 8
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 49
Percent Problems
Solve each problem.
1) 20 is what percent of 50? _____%
2) 18 is what percent of 90? _____%
3) 12 is what percent of 15? _____%
4) 16 is what percent of 200? _____%
5) 24 is what percent of 800? _____%
6) 48 is what percent of 4,00? _____%
7) 90 is what percent of 750? _____%
8) 24 is what percent of 300? _____%
9) 60 is what percent of 400? _____%
10) 42 ππ π€βππ‘ πππππππ‘ ππ 350? ____%
11) 11 ππ π€βππ‘ πππππππ‘ ππ 44? ____%
12) 8 ππ π€βππ‘ πππππππ‘ ππ 64? ____%
13) 210 ππ π€βππ‘ πππππππ‘ ππ 875? ____%
14) 80 ππ π€βππ‘ πππππππ‘ ππ 64? ____%
15) 15 ππ π€βππ‘ πππππππ‘ ππ 12? ____%
16) 56 ππ π€βππ‘ πππππππ‘ ππ 40? ____%
17) 36 ππ π€βππ‘ πππππππ‘ ππ 240? ____%
18) 32 ππ π€βππ‘ πππππππ‘ ππ 20? ____%
Solve each percent word problem.
19) There are 48 employees in a company. On a certain day, 36 were present. What percent
showed up for work? _____%
20) A metal bar weighs 24 ounces. 15% of the bar is gold. How many ounces of gold are in the
bar? ____________
21) A crew is made up of 12 women; the rest are men. If 20% of the crew are women, how many
people are in the crew? ____________
22) There are 48 students in a class and 6 of them are girls. What percent are boys? _____%
23) The Royals softball team played 75 games and won 60 of them. What percent of the games
did they lose? _____%
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 50
Answers
Percent Problems
1) 40%
2) 20%
3) 80%
4) 8%
5) 3%
6) 12%
7) 12%
8) 8%
9) 15%
10) 12%
11) 25%
12) 12.5%
13) 24%
14) 125%
15) 125%
16) 140%
17) 15%
18) 160%
19) 75%
20) 3.6 ounces
21) 60
22) 87.5%
23) 20%
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 51
Discount, Tax and Tip
Find the selling price of each item.
1) Original price of a computer: $500
Tax: 6% Selling price: $_______
2) Original price of a laptop: $350
Tax: 8% Selling price: $_______
3) Original price of a sofa: $800
Tax: 7% Selling price: $_______
4) Original price of a car: $18,500
Tax: 8.5% Selling price: $_______
5) Original price of a Table: $250
Tax: 5% Selling price: $_______
6) Original price of a house: $250,000
Tax: 6.5% Selling price: $_______
7) Original price of a tablet: $400
Discount: 20% Selling price: $_______
8) Original price of a chair: $150
Discount: 15% Selling price: $_______
9) Original price of a book: $50
Discount: 25% Selling price: $_______
10) Original price of a cellphone: $500
Discount: 10% Selling price: $_______
11) Food bill: $24
Tip: 20% Price: $_______
12) Food bill: $60
Tipp: 15% Price: $_______
13) Food bill: $32
Tip: 20% Price: $_______
14) Food bill: $18
Tipp: 25% Price: $_______
Solve each word problem.
15) Nicolas hired a moving company. The company charged $400 for its services, and Nicolas
gives the movers a 15% tip. How much does Nicolas tip the movers? $_________
16) Mason has lunch at a restaurant and the cost of his meal is $30. Mason wants to leave a
20% tip. What is Masonβs total bill including tip? $_________
17) The sales tax in Texas is 8.25% and an item costs $400. How much is the tax?
$_________
18) The price of a table at Best Buy is $220. If the sales tax is 6%, what is the final price
of the table including tax? $_________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 52
Answers
Discount, Tax and Tip
1) $530.00
2) $378.00
3) $856.00
4) $20,072.50
5) $262.50
6) $266,250
7) $320.00
8) $127.50
9) $37.50
10) $450.00
11) $28.80
12) $69.00
13) $38.40
14) $22.50
15) $60.00
16) $36.00
17) $33.00
18) $233.20
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 53
Percent of Change
Find each percent of change.
1) From 200 to 500. ___ %
2) From 50 ft to 75 ft. ___ %
3) From $250 to $350. ___ %
4) From 60 cm to 90 cm. ___ %
5) From 30 to 90. ___ %
6) From 30 to 6. ___ %
7) From 80 to 120. ___ %
8) From 800 to 200. ___ %
9) From 25 to 15. ___ %
10) From 32 to 8. ___ %
Solve each percent of change word problem.
11) Bob got a raise, and his hourly wage increased from $12 to $15. What is the percent
increase? _____ %
12) The price of a pair of shoes increases from $20 to $32. What is the percent increase?
___ %
13) At a coffeeshop, the price of a cup of coffee increased from $1.20 to $1.44. What is
the percent increase in the cost of the coffee? _____ %
14) 6 cm are cut from a 24 cm board. What is the percent decrease in length? _____ %
15) In a class, the number of students has been increased from 18 to 27. What is the percent
increase? _____ %
16) The price of gasoline rose from $2.40 to $2.76 in one month. By what percent did the
gas price rise? _____ %
17) A shirt was originally priced at $48. It went on sale for $38.40. What was the percent
that the shirt was discounted? _____ %
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 54
Answers
Percent of Change
1) 150%
2) 50%
3) 40%
4) 50%
5) 200%
6) 80%
7) 50%
8) 75%
9) 40%
10) 75%
11) 25%
12) 60%
13) 20%
14) 25%
15) 50%
16) 15%
17) 20%
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 55
Simple Interest
Determine the simple interest for these loans.
1) $450 at 7% for 2 years. $ ________
2) $5,200 at 4% for 3 years. $ ________
3) $1,300 at 5% for 6 years. $ ________
4) $5,400 at 3.5% for 6 months. $ ________
5) $600 at 4% for 9 months. $ _______
6) $24,000 at 5.5% for 5 years. $ ________
7) $15,600 at 3% for 2 years. $ _______
8) $1,200 at 5.5% for 4 years. $ ________
9) $1,600 at 4.5 % for 9 months. $ _______
10) $12,000 at 2.2% for 5 years. $ ________
Solve each simple interest word problem.
11) A new car, valued at $28,000, depreciates at 9% per year. What is the value of the
car one year after purchase? $_____________
12) Sara puts $4,000 into an investment yielding 5% annual simple interest; she left the
money in for five years. How much interest does Sara get at the end of those five years?
$_____________
13) A bank is offering 3.5% simple interest on a savings account. If you deposit $7,500,
how much interest will you earn in two years? $_____________
14) $400 interest is earned on a principal of $2,000 at a simple interest rate of 5%
interest per year. For how many years was the principal invested? _____
15) In how many years will $1,200 yield an interest of $180 at 3% simple interest? _____
16) Jim invested $4,000 in a bond at a yearly rate of 4.5%. He earned $540 in interest.
How long was the money invested? _____
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 56
Answers
Simple Interest
1) $63.00
2) $624.00
3) $390.00
4) $94.50
5) $18.00
6) $6,600.00
7) $936.00
8) $264.00
9) $54
10) $1,320.00
11) $25,480.00
12) $1,000.00
13) $525.00
14) 4 years
15) 5 years
16) 3 years
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 57
Simplifying Variable Expressions
Simplify each expression.
1) 3(π₯ + 9) =
2) (β6)(8π₯ β 4) =
3) 7π₯ + 3 β 3π₯ =
4) β2 β π₯2 β 6π₯2 =
5) 3 + 10π₯2 + 2 =
6) 8π₯2 + 6π₯ + 7π₯2 =
7) 5π₯2 β 12π₯2 + 8π₯ =
8) 2π₯2 β 2π₯ β π₯ =
9) 4π₯ + 6(2 β 5π₯) =
10) 10π₯ + 8(10π₯ β 6) =
11) 9 (β2π₯ β 6) β 5 =
12) 2π₯2 + (β 8π₯) =
13) π₯ β 3 + 5 β 3π₯ =
14) 2 β 3π₯ + 12 β 2π₯ =
15) 32π₯ β 4 + 23 + 2π₯ =
16) (β6)(8π₯ β 4) + 10π₯ =
17) 14π₯ β 5(5 β 8π₯) =
18) 23π₯ + 4(9π₯ + 3) + 12 =
19) 3(β7π₯ + 5) + 20π₯ =
20) 12π₯ β 3π₯(π₯ + 9) =
21) 7π₯ + 5π₯(3 β 3π₯) =
22) 5π₯(β8π₯ + 12) + 14π₯ =
23) 40π₯ + 12 + 2π₯2 =
24) 5π₯(π₯ β 3) β 10 =
25) 8π₯ β 7 + 8π₯ + 2π₯2 =
26) 2π₯2 β 5π₯ β 7π₯ =
27) 7π₯ β 3π₯2 β 5π₯2 β 3 =
28) 4 + π₯2 β 6π₯2 β 12π₯ =
29) 12π₯ + 8π₯2 + 2π₯ + 20 =
30) 2π₯2 + 6π₯ + 3π₯2 =
31) 23 + 15π₯2 + 8π₯ β 4π₯2 =
32) 8π₯ β 12π₯ β π₯2 + 13 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 58
Answers
Simplifying Variable Expressions
1) 3π₯ + 27
2) β48π₯ + 24
3) 4π₯ + 3
4) β 7π₯2 β 2
5) 10π₯2 + 5
6) 15π₯2 + 6π₯
7) β7π₯2 + 8π₯
8) 2π₯2 β 3π₯
9) β24π₯ + 12
10) 90π₯ β 48
11) β18π₯ β 59
12) 2π₯2 β 8π₯ 13) β2π₯ + 2 14) β5π₯ + 14 15) 34π₯ + 19 16) β38π₯ + 24 17) 54π₯ β 25 18) 59π₯ + 24 19) βπ₯ + 15 20) β3π₯2 β 15π₯
21) β15π₯2 + 22π₯
22) β40π₯2 + 74π₯
23) 2π₯2 + 40π₯ + 12
24) 5π₯2 β 15π₯ β 10
25) 2π₯2 + 16π₯ β 7
26) 2π₯2 β 12π₯
27) β8π₯2 + 7π₯ β 3
28) β5π₯2 β 12π₯ + 4
29) 8π₯2 + 14π₯ + 20
30) 5π₯2 + 6π₯
31) 11π₯2 + 8π₯ + 23
32) βπ₯2 β 4π₯ + 13
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 59
Simplifying Polynomial Expressions
Simplify each polynomial.
1) (2π₯3 + 5π₯2) β (12π₯ + 2π₯2) = ______________________________________________
2) (2π₯5 + 2π₯3) β (7π₯3 + 6π₯2) = _______________________________________________
3) (12π₯4 + 4π₯2) β (2π₯2 β 6π₯4) = ______________________________________________
4) 14π₯ β 3π₯2 β 2(6π₯2 + 6π₯3) = ________________________________________________
5) (5π₯3 β 3) + 5(2π₯2 β 3π₯3) = _______________________________________________
6) (4π₯3 β 2π₯) β 2(4π₯3 β 2π₯4) = ______________________________________________
7) 2(4π₯ β 3π₯3) β 3(3π₯3 + 4π₯2) = ______________________________________________
8) (2π₯2 β 2π₯) β (2π₯3 + 5π₯2) = ________________________________________________
9) 2π₯3 β (4π₯4 + 2π₯) + π₯2 = ____________________________________________________
10) π₯4 β 2(π₯2 + π₯) + 3π₯ = _____________________________________________________
11) (2π₯2 β π₯4) β (4π₯4 β π₯2) = ________________________________________________
12) 4π₯2 β 5π₯3 + 15π₯4 β 12π₯3 = _______________________________________________
13) 2π₯2 β 5π₯4 + 14π₯4 β 11π₯3 = ______________________________________________
14) 2π₯2 + 5π₯3 β 7π₯2 + 12π₯ = ________________________________________________
15) 2π₯4 β 5π₯5 + 8π₯ 4 β 8π₯2 = _________________________________________________
16) 5π₯3 + 15π₯ β π₯2 β 2π₯3 = ___________________________________________________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 60
Answers
Simplifying Polynomial Expressions
1) 2π₯3 + 3π₯2 β 12π₯ 2) 2π₯5 β 5π₯3 β 6π₯2 3) 18π₯4 + 2π₯2 4) β12π₯3 β 15π₯2 + 14π₯ 5) β10π₯3 + 10π₯2 β 3 6) 4π₯4 β 4π₯3 β 2π₯ 7) β15π₯3 β 12π₯2 + 8π₯ 8) β2π₯3 β 3π₯2 β 2π₯
9) β4π₯4 + 2π₯3 + π₯2 β 2π₯ 10) π₯4 β 2π₯2 + π₯ 11) β5π₯4 + 3π₯2 12) 15π₯4 β 17π₯3 + 4π₯2 13) 9π₯4 β 11π₯3 + 2π₯2 14) 5π₯3 β 5π₯2 + 12π₯ 15) β5π₯5 + 10π₯ 4 β 8π₯2 16) 3π₯3 β π₯2 + 15π₯
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 61
Translate Phrases into an Algebraic Statement
Write an algebraic expression for each phrase.
1) 4 multiplied by π₯. _________________
2) Subtract 8 from π¦. _________________
3) 6 divided by π₯. _________________
4) 12 decreased by π¦. _________________
5) Add π¦ to 9. _________________
6) The square of 5. _________________
7) π₯ raised to the fourth power. _________________
8) The sum of nine and a number. _________________
9) The difference between sixtyβfour and π¦. _________________
10) The quotient of twelve and a number. _________________
11) The quotient of the square of π₯ and 7. _________________
12) The difference between π₯ and 8 is 22. _________________
13) 2 times π reduced by the square of π. _________________
14) Subtract the product of π and π from 12. _________________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 62
Answers
Translate Phrases into an Algebraic Statement
1) 4π₯ 2) π¦ β 8
3) 6
x
4) 12 β π¦ 5) π¦ + 9
6) 52 7) π₯4 8) 9 + π₯ 9) 64 β π¦
10) 12
π₯
11) π₯2
7
12) π₯ β 8 = 22 13) 2π β π2 14) 12 β ππ
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 63
The Distributive Property
Use the distributive property to simply each expression.
1) 2(2 + 3π₯) =
2) 3(5 + 5π₯) =
3) 4(3π₯ β 8) =
4) (6π₯ β 2)(β 2) =
5) (β 3)(π₯ + 2) =
6) (2 + 2π₯)5 =
7) (β4)(4 β 2π₯) =
8) β(β2 β 5π₯) =
9) (β6π₯ + 2)(β1) =
10) (β5)(π₯ β 2) =
11) β(7 β 3π₯) =
12) 8(8 + 2π₯) =
13) 2(12 + 2π₯) =
14) (β6π₯ + 8)4 =
15) (3 β 6π₯)(β7) =
16) (β12)(2π₯ + 1) =
17) (8 β 2π₯)9 =
18) 5(7 + 9π₯) =
19) 11(5π₯ + 2) =
20) (β4π₯ + 6)6 =
21) (3 β 6π₯)(β8) =
22) (β12)(2π₯ β 3) =
23) (10 β 2π₯)9 =
24) (β5)(11π₯ β 2) =
25) (1 β 9π₯)(β10) =
26) (β6)(π₯ + 8) =
27) (β4 + 3π₯)(β8) =
28) (β5)(1 β 11π₯) =
29) 11(3π₯ β 12) =
30) (β12π₯ + 14)(β5) =
31) (β5)(4π₯ β 1) + 4(π₯ + 2) =
32) (β3)(π₯ + 4) β (2 + 3π₯) =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 64
Answers
The Distributive Property
1) 6π₯ + 4
2) 15π₯ + 15
3) 12π₯ β 32
4) β12π₯ + 4
5) β3π₯ β 6
6) 10π₯ + 10
7) 8π₯ β 16
8) 5π₯ + 2
9) 6π₯ β 2
10) β5π₯ + 10
11) 3π₯ β 7
12) 16π₯ + 64
13) 4π₯ + 24
14) β24π₯ + 32
15) 42π₯ β 21
16) β24π₯ β 12
17) β18π₯ + 72
18) 45π₯ + 35
19) 55π₯ + 22
20) β24π₯ + 36
21) 48π₯ β 24
22) β24π₯ + 36
23) β18π₯ + 90
24) β55π₯ + 10
25) 90π₯ β 10
26) β6π₯ β 48
27) β24π₯ + 32
28) 55π₯ β 5
29) 33π₯ β 132
30) 60π₯ β 70
31) β16π₯ + 13
32) β6π₯ β 14
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 65
Evaluating One Variable Expressions
Evaluate each expression using the value given.
1) 5 + π₯ , π₯ = 2
2) π₯ β 2, π₯ = 4
3) 8π₯ + 1, π₯ = 9
4) π₯ β 12, π₯ = β1
5) 9 β π₯ , π₯ = 3
6) π₯ + 2, π₯ = 5
7) 3π₯ + 7, π₯ = 6
8) π₯ + (β5), π₯ = β2
9) 3π₯ + 6, π₯ = 4
10) 4π₯ + 6, π₯ = β1
11) 10 + 2π₯ β 6, π₯ = 3
12) 10 β 3π₯, π₯ = 8
13) 2π₯ β 5, π₯ = 4
14) 5π₯ + 6, π₯ = β3
15) 12π₯ + 6, π₯ = 2
16) 10 β 3π₯, π₯ = β2
17) 5(6π₯ + 2), π₯ = 8
18) 2(β7π₯ β 2), π₯ = 3
19) 9π₯ β 3π₯ + 12, π₯ = 6
20) (6π₯ + 3) Γ· 5, π₯ = 2
21) (π₯ + 16) Γ· 3, π₯ = 8
22) 4π₯ β 12 + 8π₯, π₯ = β6
23) (16 β 12π₯)(β2), π₯ = β3
24) 12π₯2 + 5π₯ β 3, π₯ = 2
25) π₯ 2 β 11π₯, π₯ = β4
26) 2π₯(6 β 4π₯), π₯ = 5
27) 14π₯ + 7 β 3π₯2, π₯ = β3
28) (β5)(10π₯ β 20 + 2π₯), π₯ = 2
29) (β3) +π₯
4+ 2π₯, π₯ = 16
30) (β2) +π₯
7, π₯ = 21
31) (β14
π₯) β 9 + 4π₯, π₯ = 2
32) (β6
π₯) β 9 + 2π₯, π₯ = 3
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 66
Answers
Evaluating One Variables
1) 7 2) 2 3) 73 4) β13 5) 6
6) 7
7) 25
8) β 7
9) 18
10) 2
11) 10
12) β14
13) 3 14) β9 15) 30 16) 16 17) 250 18) β46 19) 48 20) 3 21) 8 22) β84
23) β104 24) 55 25) 60 26) β140 27) β62 28) β20 29) 33
30) 1
31) β8
32) β5
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 67
Evaluating Two Variables Expressions
Evaluate each expression using the values given.
1) 2π₯ + 4π¦,
π₯ = 3, π¦ = 2
2) 8π₯ + 5π¦,
π₯ = 1, π¦ = 5
3) β2π + 4π,
π = 6, π = 3
4) 4π₯ + 7 β 2π¦,
π₯ = 7, π¦ = 6
5) 5π§ + 12 β 4π,
π§ = 5 , π = 2
6) 2 (βπ₯ β 2π¦),
π₯ = 6, π¦ = 9
7) 18π + 2π,
π = 2, π = 8
8) 4π₯ Γ· 3π¦,
π₯ = 3, π¦ = 2
9) 2π₯ + 15 + 4π¦,
π₯ = β2, π¦ = 4
10) 4π β (15 β π),
π = 4, π = 6
11) 5π§ + 19 + 8π,
π§ = β5, π = 4
12) π₯π¦ + 12 + 5π₯,
π₯ = 7, π¦ = 2
13) 2π₯ + 4π¦ β 3 + 2,
π₯ = 5, π¦ = 3
14) (β12
π₯) + 1 + 5y,
π₯ = 6, π¦ = 8
15) (β4) (β 2π β 2π),
π = 5, π = 3
16) 10 + 3π₯ + 7 β 2π¦,
π₯ = 7, π¦ = 6
17) 9π₯ + 2 β 4π¦ + 5,
π₯ = 7, π¦ = 5
18) 6 + 3(β2π₯ β 3π¦),
π₯ = 9, π¦ = 7
19) 2π₯ + 14 + 4π¦,
π₯ = 6, π¦ = 8
20) 4π β (5π β π) + 5,
π = 4, π = 6
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 68
Answers
Evaluating Two Variables
1) 14 2) 33 3) 0 4) 23 5) 29 6) β48 7) 52 8) 2
9) 27 10) 7 11) 26 12) 61 13) 21
14) 39
15) 64
16) 26
17) 50
18) β111
19) 58
20) 7
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 69
Combining like Terms
Simplify each expression.
1) 2π₯ + π₯ + 2 =
2) 2(5π₯ β 3) =
3) 7π₯ β 2π₯ + 8 =
4) (β4)(3π₯ β 5) =
5) 9π₯ β 7π₯ β 5 =
6) 16π₯ β 5 + 8π₯ =
7) 5 β (5π₯ + 6) =
8) β12π₯ + 7 β 10π₯ =
9) 7π₯ β 11 β 2π₯ + 2 =
10) 12π₯ + 4π₯ β 21 =
11) 5 + 2π₯ β 8 =
12) (β2π₯ + 6)2 =
13) 7 + 3π₯ + 6π₯ β 4 =
14) 9(π₯ β 7π₯) β 5 =
15) 7(3π₯ + 6) + 2π₯ =
16) 3π₯ β 12 β 5π₯ =
17) 2(4 + 3π₯) β 7π₯ =
18) 22π₯ + 6 + 2π₯ =
19) (β5π₯) + 12 + 7π₯ =
20) (β3π₯) β 9 + 15π₯ =
21) 2(5π₯ + 7) + 8π₯ =
22) 2(9 β 3π₯) β 17π₯ =
23) β4π₯ β (6 β 14π₯) =
24) (β4) β (3)(5π₯ + 8) =
25) (β2)(9π₯ β 3) β 12π₯ =
26) β22π₯ + 6 + 4π₯ β 3π₯ =
27) 4(β13π₯ + 2) β 14π₯ =
28) β6π₯ β 19 + 15π₯ =
29) 21π₯ β 12π₯ + 6 β 7π₯ =
30) 5(6π₯ + 2π₯) β 15 =
31) 18 β 12π₯ β 25 β 15π₯ =
32) β3(β4π₯ β 2π₯) + 8π₯ =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 70
Answers
Combining like Terms
1) 3π₯ + 2 2) 10π₯ β 6 3) 5π₯ + 8 4) β12π₯ + 20 5) 2π₯ β 5 6) 24π₯ β 5 7) β5π₯ β 1 8) β22π₯ + 7 9) 5π₯ β 9 10) 16π₯ β 21 11) 2π₯ β 3
12) β4π₯ + 12
13) 9π₯ + 3
14) β54π₯ β 5
15) 23π₯ + 42
16) β2π₯ β 12
17) βπ₯ + 8
18) 24π₯ + 6
19) 2π₯ + 12
20) 12π₯ β 9
21) 18π₯ + 14
22) β23π₯ + 18 23) 10π₯ β 6 24) β15π₯ β 28
25) β30π₯ + 6 26) β21π₯ + 6 27) β66π₯ + 8 28) 9π₯ β 19 29) 2π₯ + 6 30) 40π₯ β 15 31) β27π₯ β 7 32) 26π₯
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 71
OneβStep Equations
Solve each equation.
1) 2π₯ = 20, π₯ = _____
2) 4π₯ = 16, π₯ = _____
3) 8π₯ = 24, π₯ = _____
4) 6π₯ = 30, π₯ = _____
5) π₯ + 5 = 8, π₯ = _____
6) π₯ β 1 = 5, π₯ = _____
7) π₯ β 8 = 3, π₯ = _____
8) π₯ + 6 = 12, π₯ = _____
9) π₯ β 2 = 17, π₯ = _____
10) 8 = 12 + π₯, π₯ = _____
11) π₯ β 5 = 4, π₯ = _____
12) 2 β π₯ = β12, π₯ = _____
13) 16 = β4 + π₯, π₯ = _____
14) π₯ β 4 = β25, π₯ = _____
15) π₯ + 12 = β9, π₯ = _____
16) 14 = 18 β π₯, π₯ = _____
17) 2 + π₯ = β14, π₯ = _____
18) π₯ β 5 = 15, π₯ = _____
19) 25 = π₯ β 5, π₯ = _____
20) π₯ β 3 = β12, π₯ = _____
21) π₯ β 12 = 12, π₯ = _____
22) π₯ β 12 = β25, π₯ = _____
23) π₯ β 13 = 32, π₯ = _____
24) β55 = π₯ β 18, π₯ = _____
25) π₯ β 12 = 18, π₯ = _____
26) 20 = 5π₯, π₯ = _____
27) π₯ β 30 = 20, π₯ = _____
28) π₯ β 12 = 32, π₯ = _____
29) 36 β π₯ = 3, π₯ = _____
30) π₯ β 14 = 14, π₯ = _____
31) 19 β π₯ = β15, π₯ = _____
32) π₯ β 19 = β35, π₯ = _____
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 72
Answers
OneβStep Equations
1) 10
2) 4
3) 3
4) 5
5) 3
6) 6
7) 11
8) 6
9) 19
10) β4
11) 9
12) 14
13) 20
14) β21
15) β21
16) 4
17) β16
18) 20
19) 30
20) β9
21) 24
22) β13
23) 45
24) β37
25) 30
26) 4
27) 50
28) 42
29) 33
30) 28
31) 34
32) β16
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 73
MultiβStep Equations
Solve each equation.
1) 2π₯ + 3 = 5
2) βπ₯ + 8 = 5
3) 3π₯ β 4 = 5
4) β(2 β π₯) = 5
5) 2π₯ β 18 = 12
6) 4π₯ β 2 = 6
7) 2π₯ β 14 = 4
8) 5π₯ + 10 = 25
9) 8π₯ + 9 = 25
10) β3(2 + π₯) = 3
11) β2(4 + π₯) = 4
12) 20 = β (π₯ β 8)
13) 2(2 β 2π₯) = 20
14) β12 = β(2π₯ + 8)
15) 5(2 + π₯) = 5
16) 2(π₯ β 14) = 4
17) β28 = 2π₯ + 12π₯
18) 3π₯ + 15 = βπ₯ β 5
19) 2(3 + 2π₯) = β18
20) 12 β 2π₯ = β8 β π₯
21) 10 β 3π₯ = 14 + π₯
22) 10 + 10π₯ = β2 + 4π₯
23) 24 = (β4π₯) β 8 + 8
24) 12 = 2π₯ β 12 + 6π₯
25) β12 = β4π₯ β 6 + 2π₯
26) 4π₯ β 12 = β18 + 5π₯
27) 5π₯ β 10 = 2π₯ + 5
28) β7 β 3π₯ = 2(3 β 2π₯)
29) π₯ β 2 = β3(6 β 3π₯)
30) 10π₯ β 56 = 12π₯ β 114
31) 4π₯ β 8 = β4(11 + 2π₯)
32) β5π₯ β 14 = 6π₯ + 52
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 74
Answers
MultiβStep Equations
1) 1
2) 3
3) 3
4) 7
5) 15
6) 2
7) 9
8) 3
9) 2
10) β3
11) β6
12) β12
13) β4
14) 2
15) β1
16) 16
17) β2
18) β5
19) β6
20) 20
21) β1
22) β2
23) β6
24) 3
25) 3
26) 6
27) 5
28) 13
29) 2
30) 29
31) β3
32) β6
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 75
Graphing SingleβVariable Inequalities
Draw a graph for each inequality.
1) π₯ > 2
2) π₯ < 5
3) π₯ > β1
4) π₯ > 3
5) π₯ < β5
6) π₯ > β2
7) π₯ < 0
8) π₯ > 4
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 76
Answers
Graphing SingleβVariable Inequalities
1)
2)
3)
4)
5)
6)
7)
8)
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 77
OneβStep Inequalities
Solve each inequality and graph it.
1) π₯ + 2 β₯ 3
2) π₯ β 1 β€ 2
3) 2π₯ β₯ 12
4) 4 + π₯ β€ 5
5) π₯ + 3 β€ β3
6) 4π₯ β₯ 16
7) 9π₯ β€ 18
8) π₯ + 2 β₯ 7
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 78
Answers
OneβStep Inequalities
1)
2)
3)
4)
5)
6)
7)
8)
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 79
Multi-Step Inequalities
Solve each inequality.
1) π₯ β 2 β€ 6
2) 3 β π₯ β€ 3
3) 2π₯ β 4 β€ 8
4) 3π₯ β 5 β₯ 16
5) π₯ β 5 β₯ 10
6) 2π₯ β 8 β€ 6
7) 8π₯ β 2 β€ 14
8) β5 + 3π₯ β€ 10
9) 2(π₯ β 3) β€ 6
10) 7π₯ β 5 β€ 9
11) 4π₯ β 21 < 19
12) 2π₯ β 3 < 21
13) 17 β 3π₯ β₯ β13
14) 9 + 4π₯ < 21
15) 3 + 2π₯ β₯ 19
16) 6 + 2π₯ < 32
17) 4π₯ β 1 < 7
18) 3(3 β 2π₯) β₯ β15
19) β(3 + 4π₯) < 13
20) 20 β 8π₯ β₯ β28
21) β3(π₯ β 7) > 21
22) 2π₯ + 6
4β€ 10
23) 4π₯ + 8
2β€ 12
24) 3π₯ β 8
7> 1
25) 4 + π₯3
< 7
26) 9π₯
7β 7 < 2
27) 4π₯+ 12
4> 1
28) 15 + π₯5
< 12
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 80
Answers
Multi-Step Inequalities
1) π₯ β€ 8 2) π₯ β₯ 0 3) π₯ β€ 6 4) π₯ β₯ 7 5) π₯ β₯ 15 6) π₯ β€ 7 7) π₯ β€ 2 8) π₯ β€ 5 9) π₯ β€ 6 10) π₯ β€ 2
11) π₯ < 10 12) π₯ < 12 13) π₯ β€ 10 14) π₯ < 3 15) π₯ β₯ 8 16) π₯ < 13 17) π₯ < 2 18) π₯ β€ 4 19) π₯ > β4 20) π₯ β€ 6
21) π₯ < 0 22) π₯ β€ 17 23) π₯ β€ 4 24) π₯ > 5 25) π₯ < 9 26) π₯ < 7 27) π₯ > β2 28) π₯ < β15
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 81
Finding Slope
Find the slope of each line.
1) π¦ = π₯ β 1
2) π¦ = β2π₯ + 5
3) π¦ = 2π₯ β 1
4) π¦ = βπ₯ β 8
5) π¦ = 6 + 5π₯
6) π¦ = 2 β 3π₯
7) π¦ = 4π₯ + 12
8) π¦ = β6π₯ + 2
9) π¦ = βπ₯ + 8
10) π¦ = 7π₯ β 5
11) π¦ =1
2π₯ + 3
12) π¦ = β2
3π₯ + 1
13) βπ₯ + 2π¦ = 5
14) 2π₯ + 2π¦ = 6
15) 8π¦ β 2π₯ = 10
16) 5π¦ β π₯ = 2
Find the slope of the line through each pair of points.
17) (1, 1), (2, 3)
18) (β1, 2), (0, 3)
19) (3, β1), (2, 3)
20) (β2, β1), (0, 5)
21) (5, 1), (2, 4)
22) (β3,1), (β2, 4)
23) (6, 2), (7, 4)
24) (6, β5), (3, 4)
25) (12, β9), (11, β8)
26) (7, 4), (5, β2)
27) (1, 1), (3, 5)
28) (7, β12), (5, 10)
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 82
Answers
Finding Slope
1) 1 2) β2 3) 2 4) β1 5) 5 6) β3 7) 4 8) β6 9) β1 10) 7
11) 1
2
12) β2
3
13) 1
2
14) β1
15) 1
4
16) 1
5
17) 2 18) 1
19) β4 20) 3 21) β1 22) 3 23) 2 24) β3 25) β1 26) 3 27) 2 28) β11
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 83
Graphing Lines Using Line Equation
Sketch the graph of each line.
1) π¦ = 3π₯ β 2 2) π¦ = βπ₯ + 1 3) π₯ + π¦ = 4
4) π₯ β π¦ = β5
5) 2π₯ β π¦ = β4
6) 3π₯ β 2π¦ = β6
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 84
Answers
Graphing Lines Using Line Equation
1) π¦ = 3π₯ β 2 2) π¦ = βπ₯ + 1 3) π₯ + π¦ = 4
4) π₯ β π¦ = β5 5) 2π₯ β π¦ = β4 6) 3π₯ β 2π¦ = β6
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 85
Writing Linear Equations
Write the equation of the line through the given points.
1) through: (1, β2), (2, 3)
2) through: (β2, 1), (1, 4)
3) through: (β2, 1), (0, 5)
4) through: (5, 4), (2, 1)
5) through: (β4, 9), (3, 2)
6) through: (8, 3), (7, 2)
7) through: (7, β2), (5, 2)
8) through: (β3, 9), (5, β7)
9) through: (6, 8), (4, 14)
10) through: (5, 9), (7, β3)
11) through: (β2, 8), (β6, β4)
12) through: (3, 3), (1, β5)
13) through: (8, β5), (β5, 8)
14) through: (2, β6), (β1, 3)
15) through: (5, 5), (2, β4)
16) through: (β1, 8), (2, β7)
Solve each problem.
17) What is the equation of a line with slope 2 and intercept 4? _______________
18) What is the equation of a line with slope 4 and intercept 12? _______________
19) What is the equation of a line with slope 4 and passes through point (4, 2)?
_______________
20) What is the equation of a line with slope β2 and passes through point (β2, 4)?
_______________
21) The slope of a line is β3 and it passes through point (β1, 5). What is the equation of
the line? _______________
22) The slope of a line is 3 and it passes through point (β1, 4). What is the equation of the
line? _______________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 86
Answers
Writing Linear Equations
1) π¦ = 5π₯ β 7
2) π¦ = π₯ + 3
3) π¦ = 2π₯ + 5
4) π¦ = π₯ β 1
5) π¦ = βπ₯ + 5
6) π¦ = π₯ β 5
7) π¦ = β2π₯ + 12
8) π¦ = β2π₯ + 3
9) π¦ = β3π₯ + 26
10) π¦ = β6π₯ + 39
11) π¦ = 3π₯ + 14
12) π¦ = 4π₯ β 9
13) π¦ = βπ₯ + 3
14) π¦ = β3π₯
15) π¦ = 3π₯ β 10
16) π¦ = β5π₯ + 3
17) π¦ = 2π₯ + 4
18) π¦ = 4π₯ + 12
19) π¦ = 4π₯ β 14
20) π¦ = β 2π₯ + 8
21) π¦ = β3π₯ + 2
22) π¦ = 3π₯ + 7
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 87
Graphing Linear Inequalities
Sketch the graph of each linear inequality.
1) π¦ > 3π₯ β 1 2) π¦ < βπ₯ + 4 3) π¦ β€ β5π₯ + 8
4) 2π¦ β₯ 8 + 6π₯
5) π¦ < 2π₯ β 3
6) 4π¦ β€ β6π₯ + 2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 88
Answers
Graphing Linear Inequalities
1) π¦ > 3π₯ β 1 2) π¦ < βπ₯ + 4 3) π¦ β€ β5π₯ + 8
4) 2π¦ β₯ 8 + 6π₯ 5) π¦ < 2π₯ β 3 6) 4π¦ β€ β6π₯ + 2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 89
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 90
Multiplication Property of Exponents
Simplify and write the answer in exponential form.
1) 2 Γ 22 =
2) 53 Γ 5 =
3) 32 Γ 32 =
4) 42 Γ 42 =
5) 73 Γ 72 Γ 7 =
6) 2 Γ 22 Γ 22 =
7) 53 Γ 52 Γ 5 Γ 5 =
8) 2π₯ Γ π₯ =
9) π₯3 Γ π₯2 =
10) π₯4 Γ π₯4 =
11) π₯2 Γ π₯2 Γ π₯2 =
12) 6π₯ Γ 6π₯ =
13) 2π₯2 Γ 2π₯2 =
14) 3π₯2 Γ π₯ =
15) 4π₯4 Γ 4π₯4 Γ 4π₯4 =
16) 2π₯2 Γ π₯2 =
17) π₯4 Γ 3π₯ =
18) π₯ Γ 2π₯2 =
19) 5π₯4 Γ 5π₯4 =
20) 2yπ₯2 Γ 2π₯ =
21) 3π₯4 Γ π¦2π₯4 =
22) π¦2π₯3 Γ π¦5π₯2 =
23) 4π¦π₯3 Γ 2π₯2π¦3 =
24) 6π₯2 Γ 6π₯3π¦4 =
25) 3π₯4π¦5 Γ 7π₯2π¦3 =
26) 7π₯2π¦5 Γ 9π₯π¦3 =
27) 7π₯π¦4 Γ 4π₯3π¦3 =
28) 3π₯5π¦3 Γ 8π₯2π¦3 =
29) 3π₯ Γ π¦5π₯3 Γ π¦4 =
30) π¦π₯2 Γ 2π¦2π₯2 Γ 2π₯π¦ =
31) 4π¦π₯4 Γ 5π¦5π₯ Γ π₯π¦3 =
32) 7π₯3 Γ 10π¦3π₯5 Γ 8π¦π₯3 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 91
Answers
Multiplication Property of Exponents
1) 23
2) 54
3) 34
4) 44
5) 76
6) 25
7) 57
8) 2π₯2
9) π₯5
10) π₯8
11) π₯6
12) 36π₯2
13) 4π₯4
14) 3π₯3
15) 64π₯12
16) 2π₯4
17) 3π₯5
18) 2π₯3
19) 25π₯8
20) 4π₯3π¦
21) 3π₯8π¦2
22) π₯5π¦7
23) 8π₯5π¦4
24) 36π₯5π¦4
25) 21π₯6π¦8
26) 63π₯3π¦8
27) 28π₯4π¦7
28) 24π₯7π¦6
29) 3π₯4π¦9
30) 4π₯5π¦4
31) 20π₯6π¦9
32) 560π₯11π¦4
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 92
Zero and Negative Exponents
Evaluate the following expressions.
1) 1β1 =
2) 2β2 =
3) 015 =
4) 1β10 =
5) 8β1 =
6) 8β2 =
7) 2β4 =
8) 10β2 =
9) 9β1 =
10) 3β2 =
11) 7β2 =
12) 3β4 =
13) 6β2 =
14) 5β3 =
15) 22β1=
16) 4β2 =
17) 5β2 =
18) 35β1 =
19) 4β3 =
20) 6β3 =
21) 3β5 =
22) 5β2 =
23) 2β3 =
24) 3β3 =
25) 7β3 =
26) 6β3 =
27) 8β3 =
28) 9β2 =
29) 10β3 =
30) 10β9 =
31) (1
2)β1
32) (1
2)β2 =
33) (1
3)β2 =
34) (2
3)β2 =
35) (1
5)β3 =
36) (3
4)β2 =
37) (2
5)β2 =
38) (1
2)β8 =
39) (2
5)β3 =
40) (3
7)β2 =
41) (5
6)β3 =
42) (4
9)β2 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 93
Answers
Zero and Negative Exponents
1) 1
2) 1
4
3) 0
4) 1
5) 1
8
6) 1
64
7) 1
16
8) 1
100
9) 1
9
10) 1
9
11) 1
49
12) 1
81
13) 1
36
14) 1
125
15) 1
22
16) 1
16
17) 1
25
18) 1
35
19) 1
64
20) 1
216
21) 1
243
22) 1
25
23) 1
8
24) 1
27
25) 1
343
26) 1
216
27) 1
512
28) 1
81
29) 1
1,000
30) 1
1,000,000,000
31) 2
32) 4
33) 9
34) 9
4
35) 125
36) 16
9
37) 25
4
38) 256
39) 125
8
40) 49
9
41) 216
125
42) 81
16
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 94
Division Property of Exponents
Simplify.
1) 22
23 =
2) 24
22 =
3) 55
5=
4) 3
35 =
5) π₯
π₯3 =
6) 3Γ33
32Γ34 =
7) 58
53 =
8) 5Γ56
52Γ57 =
9) 34Γ37
32Γ38 =
10) 5π₯
10π₯3 =
11) 3π₯3
2π₯5 =
12) 12π₯3
14π₯6 =
13) 12π₯3
9y8 =
14) 25π₯y4
5π₯6y2 =
15) 2π₯4
7π₯=
16) 16π₯2y8
4π₯3 =
17) 12π₯4
15π₯7π¦9 =
18) 12yπ₯4
10π¦π₯8 =
19) 16π₯4y
9π₯8y2 =
20) 5π₯8
20π₯8 =
21) 2π₯β5
9π₯β2 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 95
Answers
Division Property of Exponents
1) 1
2
2) 22
3) 54
4) 1
34
5) 1
π₯2
6) 1
32
7) 55
8) 1
9) 3
10) 1
2π₯2
11) 3
2π₯2
12) 6
7π₯3
13) 4π₯3
3π¦8
14) 5π¦2
π₯5
15) 2π₯3
7
16) 4π¦8
π₯
17) 4
5π₯3π¦9
18) 6
5π₯4
19) 16
9π₯4π¦
20) 1
4
21) 2
9π₯3
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 96
Powers of Products and Quotients
Simplify.
1) (42)2 =
2) (62)3 =
3) (2 Γ 23)4 =
4) (4 Γ 44)2 =
5) (33 Γ 32)3 =
6) (54 Γ 55)2 =
7) (2 Γ 24)2 =
8) (26)2 =
9) (11π₯5)2 =
10) (4π₯2π¦4)4 =
11) (2π₯4π¦4)3 =
12) (3π₯2π¦2)2 =
13) (3π₯4π¦3)4 =
14) (2π₯6π¦8)2 =
15) (12π₯3π₯)3 =
16) (2π₯9π₯6)3 =
17) (5π₯10π¦3)3 =
18) (4π₯3π₯3)2 =
19) (3π₯3. 5π₯)2 =
20) (10π₯11π¦3)2 =
21) (9π₯7π¦5)2 =
22) (4π₯4π¦6)5 =
23) (3π₯ . 4π¦3)2 =
24) (5π₯
π₯2)2 =
25) (π₯4y4
π₯2y2)3
=
26) (25π₯
5π₯6)2
=
27) (π₯8
π₯6y2)2
=
28) (π₯y2
π₯3y3)β2
=
29) (2π₯y4
π₯3 )2
=
30) (π₯y4
5π₯y2)β3
=
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 97
Answers
Powers of Products and Quotients
1) 44
2) 66
3) 216
4) 410
5) 315
6) 518
7) 210
8) 212
9) 121π₯10
10) 256π₯8π¦16
11) 8π₯12π¦12
12) 9π₯4π¦4
13) 81π₯16π¦12
14) 4π₯12π¦16
15) 1,728π₯12
16) 8π₯45
17) 125π₯30π¦9
18) 16π₯12
19) 225π₯8
20) 100π₯22π¦6
21) 81π₯14π¦10
22) 1,024π₯20π¦30
23) 144π₯2π¦6
24) 25
π₯2
25) π₯2π¦2
26) 25π¦4
π₯10
27) π₯4
π¦4
28) π₯4π¦2
29) 4π¦8
π₯4
30) 125
π¦6
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 98
Negative Exponents and Negative Bases
Simplify.
1) β6β1 =
2) β5β2 =
3) β2β4 =
4) βπ₯β3 =
5) 2π₯β1 =
6) β4π₯β3 =
7) β12π₯β5 =
8) β 5π₯β2π¦β3 =
9) 20π₯β4π¦β1 =
10) 14πβ6πβ7 =
11) β12π₯2π¦β3 =
12) β25
π₯β6=
13) β2π₯
aβ4=
14) (β1
3)β2 =
15) (β3
4)β2 =
16) β9
πβ7πβ2=
17) β5π₯
π₯β3=
18) βaβ3
bβ2=
19) β5
π₯β3=
20) 7π
β9cβ4=
21) 7ππ
πβ3πβ1=
22) β5πβ2
10πβ3=
23) 4ππβ2
β3πβ2=
24) (3π
2c)β2=
25) (β5π₯
3π¦π§)β3 =
26) 4ππβ2
β3πβ2=
27) (βπ₯3
π₯4)β2=
28) (βπ₯β2
3π₯2)β3 =
29) (βπ₯β4
π₯2)β2=
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 99
Answers
Negative Exponents and Negative Bases
1) β1
6
2) β1
25
3) β1
16
4) β1
π₯3
5) 2
π₯
6) β4
π₯3
7) β12
π₯5
8) β5
π₯5π¦3
9) 20
π₯4π¦
10) 14
π6π7
11) β12π₯2
π¦3
12) β25π₯6
13) β2π₯π4 14) 9
15) 16
9
16) β9π7π2
17) β5π₯4
18) βπ2
π3
19) β5π₯3
20) β7ππ4
9
21) 7π4π2
22) βπ3
2π2
23) β4ππ2
3π2
24) 4π2
9π2
25) β27π¦3π§3
125π₯3
26) β4ππ2
3π2
27) π₯2
28) β81π₯12
29) π₯12
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 100
Scientific Notation
Write each number in scientific notation.
1) 0.113 =
2) 0.02 =
3) 2.5 =
4) 20 =
5) 60 =
6) 0.004 =
7) 78 =
8) 1,600 =
9) 1,450 =
10) 91,000 =
11) 2,000,000 =
12) 0.0000006 =
13) 354,000 =
14) 0.000325 =
15) 0.00023 =
16) 56,000,000 =
17) 21,000 =
18) 78,000,000 =
19) 0.0000022 =
20) 0.00012 =
Write each number in standard notation.
21) 3 Γ 10β1 =
22) 5 Γ 10β2 =
23) 1.2 Γ 103 =
24) 2 Γ 10β4 =
25) 1.5 Γ 10β2 =
26) 4 Γ 103 =
27) 9 Γ 105 =
28) 1.12 Γ 104 =
29) 3 Γ 10β5 =
30) 8.3 Γ 10β5 =
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 101
Answers
Writing Scientific Notation
1) 1.13 Γ 10β1
2) 2 Γ 10β2
3) 2.5 Γ 100
4) 2 Γ 101
5) 6 Γ 101
6) 4 Γ 10β3
7) 7.8 Γ 101
8) 1.6 Γ 103
9) 1.45 Γ 103
10) 9.1 Γ 104
11) 2 Γ 106
12) 6 Γ 10β7
13) 3.54 Γ 105
14) 3.25 Γ 10β4
15) 2.3 Γ 10β4
16) 5.6 Γ 107
17) 2.1 Γ 104
18) 7.8 Γ 107
19) 2.2 Γ 10β6
20) 1.2 Γ 10β4
21) 0.3
22) 0.05
23) 1,200
24) 0.0002
25) 0.015
26) 4,000
27) 900,000
28) 11,200
29) 0.00003
30) 0.000083
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 102
Square Roots
Find the value each square root.
1) β0 = _____
2) β1 = _____
3) β4 = _____
4) β16 = _____
5) β9 = _____
6) β25 = _____
7) β49 = _____
8) β36 = _____
9) β64 = _____
10) β81 = _____
11) β121 = _____
12) β225 = _____
13) β144 = _____
14) β100 = _____
15) β256 = _____
16) β289 = _____
17) β324 = _____
18) β400 = _____
19) β900 = _____
20) β529 = _____
21) β90 = _____
22) β169 = _____
23) β196 = _____
24) β361 = _____
Evaluate.
25) β4 Γ β16 = __________
26) β25 Γ β64 = __________
27) β2 Γ β8 = __________
28) β6 Γ β6 = __________
29) β5 Γ β5 = __________
30) β8 Γ β8 = __________
31) β2 + β2 = __________
32) β8 + β8 = __________
33) 4β5 β 2β5 = __________
34) 3β3 Γ 2β3 = __________
35) 8β2 Γ 2β2 = __________
36) 6β3 β β12 = __________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 103
Answers
Square Roots
1) 0 2) 1 3) 2 4) 4 5) 3 6) 5 7) 7 8) 6 9) 8 10) 9 11) 11 12) 15 13) 12
14) 10 15) 16 16) 17 17) 18 18) 20 19) 30 20) 23
21) 3β10 22) 13 23) 14 24) 19 25) 8
26) 40 27) 4 28) 6 29) 5 30) 8
31) 2β2
32) 2β8
33) 2β5 34) 18 35) 32
36) 4β3
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 104
Angles
What is the value of π± in the following figures?
1)
2) 3)
4)
5)
6)
Solve. 7) Two complementary angles have equal measures. What is the measure of each angle?
______________________
8) The measure of an angle is two third the measure of its supplement. What is the measure
of the angle? ______________________
9) Two angles are complementary and the measure of one angle is 24 less than the other.
What is the measure of the bigger angle? ______________________
10) Two angles are complementary. The measure of one angle is half the measure of the
other. What is the measure of the smaller angle? ______________________
11) Two supplementary angles are given. The measure of one angle is 50Β° less than the
measure of the other. What does the bigger angle measure? ______________________
πΆ π΄ π΅
π₯Β° 112Β°
πΆ π΄ π΅
π₯Β° 91Β°
πΆ π΄ π΅
π₯Β° 128Β°
πΆ π΄ π΅ π₯Β°
163Β°
πΆ π΄ π΅ π₯Β°
35Β°
πΆ π΄ π΅ π₯Β°
62Β°
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 105
Answers
Angles
1) 68Β°
2) 89Β°
3) 52Β°
4) 17Β°
5) 55Β°
6) 28Β°
7) 45Β°
8) 72Β°
9) 57Β°
10) 30Β°
11) 115Β°
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 106
Pythagorean Relationship
Do the following lengths form a right triangle?
1)
2) 3) 4)
5) 6) 7) 8)
Find the missing side?
9)
10) 11) 12)
13) 14) 15) 16)
8
15
17
10 24
26 15
20
25
5
14
20 9
4
12
6
?
10
12
?
13 18
24
? 16
?
34
5 ?
13
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 107
Answers
Pythagorean Relationship
1) Yes 2) Yes 3) No 4) Yes 5) No 6) No
7) Yes 8) Yes 9) 5 10) 17 11) 15 12) 8
13) 5 14) 30 15) 30 16) 12
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 108
Triangles
Find the measure of the unknown angle in each triangle.
1) 2) 3) 4)
5) 6) 7) 8)
Find area of each triangle.
9)
10) 11) 12)
70Β°
95Β°
? Β°
50Β°
65Β° ? Β°
80Β°
85Β°
? Β°
40Β°
70Β° ? Β°
40Β° 85Β°
14 ππ
8 cm
16 cm
4 in
8 in
10 in
6
8
10
12
5
13
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 109
Answers
Triangles
1) 15Β° 2) 35Β° 3) 15Β° 4) 65Β°
5) 25Β° 6) 45Β° 7) 55Β° 8) 70Β°
9) 24 π ππ’πππ π’πππ‘ππ 10) 30 π ππ’πππ π’πππ‘ππ 11) 64 π ππ’πππ π’πππ‘ππ 12) 20 π ππ’πππ π’πππ‘ππ
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 110
Polygons
Find the perimeter of each shape.
1)
2) 3) 4) Square
5) Regular hexagon
6)
7) Parallelogram
8) Square
Find the area of each shape.
9) Parallelogram
10) Rectangle 11) Rectangle 12) Square
12 ft
12 ft
12 ft
12 ft
8 in
10 in
8 in
10 in
12 ft 12 ft
12 ft 12 ft
14 cm
5 m 5.5 cm
4.5 cm
4.5 cm
5.5 cm
5 in
4 in
6 m
8 in
10 in 7 in
6 m
6 m
6 m 5 km
7 km
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 111
Answers
Polygons
1) 48 ππ‘ 2) 36 ππ 3) 48 ππ‘ 4) 56 ππ 5) 30 π
6) 20 ππ 7) 18 ππ 8) 24 π 9) 36 π2
10) 80 ππ2 11) 35 ππ2 12) 49 ππ2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 112
Trapezoids
Find the area of each trapezoid.
1)
2) 3) 4)
5)
6)
7)
8)
Solve.
9) A trapezoid has an area of 60 cm2 and its height is 6 cm and one base is 8 cm.
What is the other base length? ______________________
10) If a trapezoid has an area of 65 ft2 and the lengths of the bases are 12 ft and
14 ft, find the height. ______________________
11) If a trapezoid has an area of 180 m2 and its height is 12 m and one base is 20 m,
find the other base length. ______________________
12) The area of a trapezoid is 625 ft2 and its height is 25 ft. If one base of the
trapezoid is 15 ft, what is the other base length? ______________________
9 cm
12 cm
6 cm
5 ft
7 ft
4 ft
14 m
18 m
10 m
7 cm
10 cm
5 cm
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 113
Answers
Trapezoids
1) 63 ππ2 2) 160 π2 3) 24 ππ‘2 4) 42.5 ππ2
5) 81 6) 94.5 7) 36 8) 18 9) 12 ππ
10) 5 ππ‘ 11) 10 π 12) 35 ππ‘
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 114
Circles
Find the area of each circle. (Ο = 3.14)
1)
2) 3) 4) 5) 6)
7)
8)
9)
10)
11)
12)
Complete the table below. (Ο = 3.14)
Radius Diameter Circumference Area
Circle 1 4 inches 8 inches 25.12 inches 50.24 square inches
Circle 2 12 meters
Circle 3 12.56 square ft
Circle 4 18.84 miles
Circle 5 5 kilometers
Circle 6 6 centimeters
Circle 7 8 feet
Circle 8 28.26 square meters
Circle 9 43.96 inches
Circle 10 5 feet
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 115
Answers
Circles
1) 50.24 ππ2 2) 113.04 ππ2 3) 12.56 ππ‘2 4) 314 π2
5) 28.26 ππ2 6) 200.96 πππππ 2 7) 12.56 ππ2 8) 3.14 ππ‘2
9) 50.24 π2 10) 78.5 ππ2 11) 113.04 πππππ 2 12) 19.63 ππ‘2
Radius Diameter Circumference Area
Circle 1 4 inches 8 inches 25.12 inches 50.24 square inches
Circle 2 6 meters 12 meters 37.68 meters 113.04 meters
Circle 3 2 square ft 4 square ft 12.56 square ft 12.56 square ft
Circle 4 3 miles 6 miles 18.84 miles 28.26 miles
Circle 5 2.5 kilometers 5 kilometers 15.7 kilometers 19.63 kilometers
Circle 6 6 centimeters 12 centimeters 37.68 centimeters 113.04 centimeters
Circle 7 4 feet 8 feet 25.12 feet 50.24 feet
Circle 8 3 square meters 6 square meters 18.84 square meters
28.26 square meters
Circle 9 7 inches 14 inches 43.96 inches 153.86 inches
Circle 10 5 feet 10 feet 31.4 feet 78.5 feet
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 116
Cubes
Find the volume of each cube.
1)
2) 3) 4) 5) 6)
7)
8)
9)
10)
11)
12)
Find the surface area of each cube.
13)
14) 15) 16) 17) 18)
2 cm 4 ft 6 m 3 miles 1 in
5 km 7 cm 10 ft 11 mm 8 in 9 km
5 m 2 ft 3 mm 4 cm 9 km
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 117
Answers
Cubes 1) 8 2) 8 ππ3 3) 64 ππ‘3 4) 216 π3 5) 1 ππ3 6) 27 πππππ 3
7) 125 ππ3 8) 343 ππ3 9) 1,000 ππ‘3 10) 1,331 ππ3 11) 512 ππ3 12) 729 ππ3
13) 24 14) 150 π2 15) 24 ππ‘2 16) 54 ππ2 17) 486 ππ2 18) 96 ππ2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 118
6 m
8 m
5 m
Rectangular Prism
Find the volume of each Rectangular Prism.
1)
2) 3)
4)
5)
6)
Find the surface area of each Rectangular Prism.
7)
8) 9) 10)
3 cm
10 cm 5 cm
7 m
6 m
5 m
10 in
8 in
4 in
6 ft
8 ft
12 ft
9 m
7 m
3 m
10 cm
5 cm
4 cm
4 ft
9 ft
3 ft
2 in
8 in 5 in 8 m
10 m
12 m
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 119
Answers
Rectangular Prism 1) 210 π3 2) 320 ππ3 3) 189 π3 4) 150 ππ3
5) 576 ππ‘3 6) 240 π3 7) 220 ππ2 8) 150 ππ‘2
9) 132 ππ2 10) 592 π2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 120
Cylinder
Find the volume of each Cylinder. Round your answer to the nearest tenth. (Ο = 3.14)
1)
2) 3)
4)
5)
6)
Find the surface area of each Cylinder. (Ο = 3.14)
7)
8) 9) 10)
6 m
8 m
4 in
6 in m
m
m
m
4 m
6 m
5 cm
8 cm
m
m
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 121
Answers
Cylinder 1) 2,009.6 π3 2) 50.24 ππ3 3) 565.2 ππ3 4) 2,575.4 π3
5) 904.3 π3 6) 301.4 ππ3 7) 251.2 π2 8) 408.2 ππ2
9) 75.4 ππ2 10) 904.3 π2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 122
Pyramids and Cone
Find the volume of each Pyramid and Cone. (Ο = 3.14)
1)
2) 3)
4)
5)
6)
Find the surface area of each Pyramid and Cone. (Ο = 3.14)
7)
8) 9) 10)
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 123
Answers Pyramids and Cone 1) 3,072 π¦π3
2) 400 π¦π3
3) 1,728 ππ3
4) 1,230.9 π3
5) 1,017.9 π3
6) 217.7 ππ3
7) 360 π¦π2
8) 864 π2
9) 64.34 ππ2
10) 417.4 ππ2
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 124
Mean and Median
Find Mean and Median of the Given Data.
1) 8, 12, 5, 3, 2
2) 3, 6, 3, 7, 4, 13
3) 13, 5, 1, 7, 9
4) 6, 4, 2, 7, 3, 2
5) 6, 5, 7, 5, 7, 1, 11
6) 6, 1, 4, 4, 9, 2, 19
7) 12, 4, 1, 5, 9, 7, 7, 19
8) 18, 9, 5, 4, 9, 6,12
9) 28, 25, 15, 16, 32, 44, 71
10) 10, 5, 1, 5, 4, 5, 8, 10
11) 18, 15, 30, 64, 42, 11
12) 44, 33, 56, 78, 41, 84
Solve.
13) In a javelin throw competition, five athletics score 56, 58, 63, 57 and 61
meters. What are their Mean and Median? _________________
14) Eva went to shop and bought 3 apples, 5 peaches, 8 bananas, 1 pineapple and 3
melons. What are the Mean and Median of her purchase?
_________________
15) Bob has 12 black pen, 14 red pen, 15 green pens, 24 blue pens and 3 boxes of
yellow pens. If the Mean and Median are 16 and 15 respectively, what is the
number of yellow pens in each box? _________________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 125
Answers
Mean and Median
1) Mean: 6, Median: 5
2) Mean: 6, Median: 5
3) Mean: 7, Median: 7
4) Mean: 4, Median: 3.5
5) Mean: 6, Median: 6
6) Mean: 8, Median: 4
7) Mean: 8, Median: 7
8) Mean: 9, Median: 9
9) Mean: 33, Median: 28
10) Mean: 6, Median: 5
11) Mean: 30, Median: 24
12) Mean: 56, Median: 50
13) Mean: 59, Median: 58
14) Mean: 4, Median: 3
15) 5
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 126
Mode and Range
Find Mode and Rage of the Given Data.
1) 8, 2, 5, 9, 1, 2
Mode: _____ Range: _____
2) 6, 6, 2, 3, 6, 3, 9, 12
Mode: _____ Range: _____
3) 4, 4, 3, 9, 7, 9, 4, 6, 4
Mode: _____ Range: _____
4) 12, 9, 2, 9, 3, 2, 9, 5
Mode: _____ Range: _____
5) 9, 5, 9, 5, 8, 9, 8
Mode: _____ Range: _____
6) 0, 1, 4, 10, 9, 2, 9, 1, 5, 1
Mode: _____ Range: _____
7) 6, 5, 6, 9, 7, 7, 5, 4, 3, 5
Mode: _____ Range: _____
8) 7, 5, 4, 9, 6, 7, 7, 5, 2
Mode: _____ Range: _____
9) 2, 2, 5, 6, 2, 4, 7, 6, 4, 9
Mode: _____ Range: _____
10) 7, 5, 2, 5, 4, 5, 8, 10
Mode: _____ Range: _____
11) 4, 1, 5, 2, 2, 12, 18, 2
Mode: _____ Range: _____
12) 6, 3, 5, 9, 6, 6, 3, 12
Mode: _____ Range: _____
Solve.
13) A stationery sold 12 pencils, 36 red pens, 44 blue pens, 12 notebooks, 18 erasers,
34 rulers and 32 color pencils. What are the Mode and Range for the stationery
sells?
Mode: _____ Range: _____
14) In an English test, eight students score 14, 13, 17, 11, 19, 20, 14 and 15. What are
their Mode and Range? ___________________
15) What is the range of the first 6 even numbers greater than 11? ________
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 127
Answers
Mode and Range
1) Mode: 2, Range: 8
2) Mode: 6, Range: 10
3) Mode: 4, Range: 6
4) Mode: 9, Range: 10
5) Mode: 9, Range: 4
6) Mode: 1, Range: 10
7) Mode: 5, Range: 6
8) Mode: 7, Range: 7
9) Mode: 2, Range: 7
10) Mode: 5, Range: 8
11) Mode: 2, Range: 17
12) Mode: 6, Range: 9
13) Mode: 12, Range: 32
14) Mode: 14, Range: 9
15) 10
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 128
Histograms
Use the following Graph to complete the table.
The following table shows the number of births in the US from 2007 to 2012 (in
millions).
Year Number of births (in millions)
2007 4.32
2008 4.25
2009 4.13
2010 4
2011 3.95
2012 3.95
Draw a histogram for the table.
Day Distance (km)
1
2
359
460
278
547
360
0
100
200
300
400
500
600
Day 1 Day 2 Day 3 Day 4 Day 5
Distance
Distance
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 129
Answers
Histograms
4.32
4.25
4.13
43.95 3.95
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
2007 2008 2009 2010 2011 2012
Nu
mb
er o
f B
irth
s (i
n m
illio
ns)
Year
Number of Births
Day Distance (km)
1 359
2 460
3 278
4 547
5 360
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 130
StemβandβLeaf Plot
Example:
56, 58, 42, 48, 66, 64, 53, 69, 45, 72
Stem leaf
4 2 5 8
5 3 6 8
6 4 6 9
7 2
Make stem ad leaf plots for the given data.
1) 74, 88, 97, 72, 79, 86, 95, 79, 83, 91
2) 37, 48, 26, 33, 49, 26, 19, 26, 48
3) 58, 41, 42, 67, 54, 65, 65, 54, 69, 53
Stem Leaf plot
Stem Leaf plot
Stem Leaf plot
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 131
Answers
StemβAndβLeaf Plot
1)
Stem leaf
7 2 4 9 9
8 3 6 8
9 1 5 7
2)
Stem leaf
1 9
2 6 6 6
3 3 7
4 8 8 9
3)
Stem leaf
4 1 2
5 3 4 4 8
6 5 5 7 9
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 132
Pie Graph
The circle graph below shows all Jasonβs expenses for last month. Jason spent $300 on his bills
last month.
Answer following questions based on the Pie graph.
1- How much did Jason spend on his car last month? ____________________
2- How much did Jason spend for foods last month? ____________________
3- How much did Jason spend on his rent last month? ___________________
4- What fraction is Jasonβs expenses for his bills and Car out of his total
expenses last month? ______________________
5- How much was Jasonβs total expenses last month? ___________________
Car
22%
Others
28%
Rent
28%
Bills
12%
Foods
10%
Jasonβs monthly expenses
Math Worksheets Name: __________
Date: ___________
Created by: Effortless Math Education www.EffortlessMath.com 133
Answers
Pie Graph
1) $550
2) $250
3) $700
4) 17
50
5) $2,500