6th Grade Math Midterm Review Exam

Grade 6 Mathematics Midterm Review Exam

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Section 1: Ratios

Total: 16 Points

Part-to-Whole Ratios (5 Points)

Write each ratio in simplest form.

1. In a basket of fruit, there are 8 apples and 12 oranges. What is the ratio of apples to the total pieces of fruit?
   Answer: ______ : ______
2. A classroom has 15 girls and 10 boys. What is the ratio of boys to the total number of students?
   Answer: ______ : ______
3. A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. What is the ratio of green marbles to the total marbles?
   Answer: ______ : ______
4. In a parking lot, 7 cars are silver and 13 are black. What is the ratio of silver cars to the total number of cars?
   Answer: ______ : ______
5. A box has 9 pencils and 6 pens. What is the ratio of pens to the total number of writing tools?
   Answer: ______ : ______

Ratios with Tape Diagrams & Word Problems (5 Points)

Solve. You may draw a tape diagram in the workspace.

6. The ratio of dogs to cats at a shelter is 3:2. If there are 18 dogs, how many cats are there?
   Work Space:
   Answer: ______ cats
7. The ratio of fiction to nonfiction books on a shelf is 5:4. If there are 35 fiction books, how many nonfiction books are there?
   Answer: ______ books
8. For every 4 miles Sam runs, he walks 1 mile. If he ran 12 miles, how many miles did he walk?
   Answer: ______ miles
9. The ratio of adults to children at a park is 2:7. If there are 16 adults, how many children are there?
   Answer: ______ children
10. In a recipe, the ratio of flour to sugar is 3:1. If you use 9 cups of flour, how many cups of sugar do you need?
    Answer: ______ cups

Ratios and Measurements (5 Points)

Convert and write the ratio of the first unit to the second unit in simplest form.

11. Convert 3 feet to inches. (1 foot = 12 inches)
    Answer: ______ : ______
12. Convert 2 gallons to quarts. (1 gallon = 4 quarts)
    Answer: ______ : ______
13. Convert 5 meters to centimeters. (1 meter = 100 cm)
    Answer: ______ : ______
14. Convert 60 minutes to seconds. (1 minute = 60 seconds)
    Answer: ______ : ______
15. Convert 4 pounds to ounces. (1 pound = 16 ounces)
    Answer: ______ : ______

Ratios in Recipes (Word Problem) (1 Point)

16. A lemonade recipe calls for 2 cups of lemon juice for every 5 cups of water.
    a) What is the ratio of lemon juice to water in simplest form?
    Answer: ______ : ______
    b) If you want to make 28 cups of lemonade total, how many cups of lemon juice do you need?
    Work Space:
    Answer: ______ cups
    c) How many cups of water do you need?
    Answer: ______ cups

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Section 2: Rates and Percentages

Total: 20 Points

Solving Unit Rate/Price Problems (5 Points)

17. If 5 pounds of apples cost $7.50, what is the price per pound?
    Answer: $ ______
18. A car travels 240 miles in 4 hours. What is the unit rate (miles per hour)?
    Answer: ______ mph
19. A 12-ounce bag of chips costs $3.60. What is the price per ounce?
    Answer: $ ______
20. A printer can print 30 pages in 2 minutes. How many pages does it print per minute?
    Answer: ______ pages
21. You buy 8 pencils for $4.00. What is the cost per pencil?
    Answer: $ ______

Fraction, Decimal, and Percent Conversion (5 Points)

22. Write $\frac{3}{5}$53​ as a decimal and a percent.
    Decimal: ______ Percent: ______ %
23. Write 0.72 as a fraction in simplest form and a percent.
    Fraction: ______ Percent: ______ %
24. Write 45% as a fraction in simplest form and a decimal.
    Fraction: ______ Decimal: ______
25. Write $\frac{7}{8}$87​ as a decimal and a percent.
    Decimal: ______ Percent: ______ %
26. Write 0.06 as a fraction in simplest form and a percent.
    Fraction: ______ Percent: ______ %

Percent of a Number (5 Points)

27. What is 30% of 80?
    Answer: ______
28. What is 15% of 200?
    Answer: ______
29. 40% of what number is 24?
    Answer: ______
30. 75% of what number is 45?
    Answer: ______
31. 18 is what percent of 90?
    Answer: ______ %

Finding Common Percentages (5 Points)

32. Find 10% of 150.
    Answer: ______
33. Find 25% of 48.
    Answer: ______
34. Find 50% of 1,200.
    Answer: ______
35. Find 75% of 64.
    Answer: ______
36. Find 100% of 89.
    Answer: ______

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Section 3: Negative Numbers

Total: 29 Points

Adding and Subtracting Negative Numbers (10 Points)

37. $-5+8=$−5+8= ______
38. $3+(-10)=$3+(−10)= ______
39. $-7-4=$−7−4= ______
40. $-2-(-6)=$−2−(−6)= ______
41. $9+(-9)=$9+(−9)= ______
42. $-12+5=$−12+5= ______
43. $4-7=$4−7= ______
44. $-8-(-3)=$−8−(−3)= ______
45. $0+(-15)=$0+(−15)= ______
46. $-1-9=$−1−9= ______

Multiplying and Dividing Negative Numbers (10 Points)

47. $(-4)\times 5=$(−4)×5= ______
48. $6\times (-3)=$6×(−3)= ______
49. $(-7)\times (-2)=$(−7)×(−2)= ______
50. $(-18)÷3=$(−18)÷3= ______
51. $24÷(-4)=$24÷(−4)= ______
52. $(-30)÷(-5)=$(−30)÷(−5)= ______
53. $(-9)\times 0=$(−9)×0= ______
54. $(-14)÷(-2)=$(−14)÷(−2)= ______
55. $8\times (-1)=$8×(−1)= ______
56. $(-100)÷10=$(−100)÷10= ______

Negative Numbers in Word Problems (4 Points)

57. The temperature at noon was 5°F. By midnight, it dropped 12 degrees. What was the temperature at midnight?
    Answer: ______ °F
58. A submarine is 250 feet below sea level. It rises 75 feet. What is its new position relative to sea level?
    Answer: ______ feet
59. A hiker starts at an elevation of 30 feet above sea level, then descends 45 feet. What is her new elevation?
    Answer: ______ feet
60. In a game, you lose 7 points, then gain 10 points, then lose 3 points. What is your total score change?
    Answer: ______ points

Negative Fractions and Decimals (5 Points)

61. $-\frac{1}{4}+\frac{3}{4}=$−41​+43​= ______
62. $-0.5-0.75=$−0.5−0.75= ______
63. $-\frac{2}{3}-(-\frac{1}{3})=$−32​−(−31​)= ______
64. $1.2+(-2.8)=$1.2+(−2.8)= ______
65. $-\frac{5}{6}+\frac{1}{6}=$−65​+61​= ______

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Section 4: Equations and Inequalities

Total: 20 Points

Solving Equations (5 Points)

66. $x+8=15$x+8=15
    Answer: $x=$x= ______
67. $y-3=10$y−3=10
    Answer: $y=$y= ______
68. $4m=28$4m=28
    Answer: $m=$m= ______
69. $\frac{n}{5}=9$5n​=9
    Answer: $n=$n= ______
70. $2p+7=19$2p+7=19
    Answer: $p=$p= ______

Inequalities (5 Points)

Solve and graph the solution on the number line provided below each problem.

71. $x+5>12$x+5>12
    Answer: ______
72. $3y\le 21$3y≤21
    Answer: ______
73. $a-4<2$a−4<2
    Answer: ______
74. $\frac{b}{2}\ge 6$2b​≥6
    Answer: ______
75. $2c+1\ge 11$2c+1≥11
    Answer: ______

(Number lines for graphing are omitted here for brevity in text format. In a Word doc, they would be included.)

Inequalities in Word Problems (5 Points)

Write an inequality to represent each situation. Use $x$x for the unknown number.

76. Katie has at least $20.
    Inequality: ______
77. A number decreased by 4 is less than 10.
    Inequality: ______
78. Five times a number is at most 30.
    Inequality: ______
79. The sum of a number and 7 is greater than 15.
    Inequality: ______
80. One-third of a number is no more than 12.
    Inequality: ______

Two-Step Inequalities (5 Points)

Solve each inequality.

81. $3x-5>10$3x−5>10
    Answer: ______
82. $\frac{y}{4}+2\le 5$4y​+2≤5
    Answer: ______
83. $2a+7<19$2a+7<19
    Answer: ______
84. $5-m\ge 1$5−m≥1
    Answer: ______
85. $4b-3>9$4b−3>9
    Answer: ______

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Section 5: Plane Figures (Area)

Total: 15 Points

Parallelograms (3 Points)

86. Find the area of a parallelogram with base 10 cm and height 6 cm.
    Answer: ______ cm²
87. Find the height of a parallelogram with area 48 in² and base 8 in.
    Answer: ______ in
88. Find the base of a parallelogram with area 63 m² and height 9 m.
    Answer: ______ m

Triangles (3 Points)

89. Find the area of a triangle with base 12 ft and height 5 ft.
    Answer: ______ ft²
90. Find the height of a triangle with area 24 cm² and base 6 cm.
    Answer: ______ cm
91. Find the base of a triangle with area 35 in² and height 10 in.
    Answer: ______ in

Trapezoids (4 Points)

92. Find the area of a trapezoid with bases 5 cm and 9 cm, and height 4 cm.
    Answer: ______ cm²
93. Find the height of a trapezoid with bases 8 m and 12 m, and area 50 m².
    Answer: ______ m
94. Find the missing base of a trapezoid if one base is 7 in, height is 6 in, area is 45 in², and the other base is unknown.
    Answer: ______ in
95. A trapezoid has an area of 72 ft², height 8 ft, and one base 10 ft. Find the other base.
    Answer: ______ ft

ANSWER KEY

Total Points: 100 Points

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Section 1: Ratios

Total: 16 Points

Part-to-Whole Ratios (5 Points)

1. 2:5
2. 2:5
3. 1:4
4. 7:20
5. 2:5

Ratios with Tape Diagrams & Word Problems (5 Points)

6. 12 cats
7. 28 books
8. 3 miles
9. 56 children
10. 3 cups

Ratios and Measurements (5 Points)

11. 1:12
12. 1:4
13. 1:100
14. 1:60
15. 1:16

Ratios in Recipes (Word Problem) (1 Point)

16. a) 2:5
    b) 8 cups
    c) 20 cups

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Section 2: Rates and Percentages

Total: 20 Points

Solving Unit Rate/Price Problems (5 Points)

17. $1.50
18. 60 mph
19. $0.30
20. 15 pages
21. $0.50

Fraction, Decimal, and Percent Conversion (5 Points)

22. Decimal: 0.6, Percent: 60%
23. Fraction: 18/25, Percent: 72%
24. Fraction: 9/20, Decimal: 0.45
25. Decimal: 0.875, Percent: 87.5%
26. Fraction: 3/50, Percent: 6%

Percent of a Number (5 Points)

27. 24
28. 30
29. 60
30. 60
31. 20%

Finding Common Percentages (5 Points)

32. 15
33. 12
34. 600
35. 48
36. 89

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Section 3: Negative Numbers

Total: 29 Points

Adding and Subtracting Negative Numbers (10 Points)

37. 3
38. -7
39. -11
40. 4
41. 0
42. -7
43. -3
44. -5
45. -15
46. -10

Multiplying and Dividing Negative Numbers (10 Points)

47. -20
48. -18
49. 14
50. -6
51. -6
52. 6
53. 0
54. 7
55. -8
56. -10

Negative Numbers in Word Problems (4 Points)

57. -7°F
58. -175 ft
59. -15 ft
60. 0 points

Negative Fractions and Decimals (5 Points)

61. 1/2
62. -1.25
63. -1/3
64. -1.6
65. -2/3

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Section 4: Equations and Inequalities

Total: 20 Points

Solving Equations (5 Points)

66. x = 7
67. y = 13
68. m = 7
69. n = 45
70. p = 6

Inequalities (5 Points)

71. x > 7
72. y ≤ 7
73. a < 6
74. b ≥ 12
75. c ≥ 5

Inequalities in Word Problems (5 Points)

76. x ≥ 20
77. x – 4 < 10
78. 5x ≤ 30
79. x + 7 > 15
80. x/3 ≤ 12

Two-Step Inequalities (5 Points)

81. x > 5
82. y ≤ 12
83. a < 6
84. m ≤ 4
85. b > 3

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Section 5: Plane Figures (Area)

Total: 15 Points

Parallelograms (3 Points)

86. 60 cm²
87. 6 in
88. 7 m

Triangles (3 Points)

89. 30 ft²
90. 8 cm
91. 7 in

Trapezoids (4 Points)

92. 28 cm²
93. 5 m
94. 8 in
95. 8 ft