6th grade Math Review Exam

6th grade Math Review Exam

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Section 1: Ratios

Total: 10 Points

1. In a basket, there are 8 apples and 12 oranges. What is the ratio of apples to total fruit? Write it in simplest form.
   Answer: ______ : ______
2. A class has 15 girls and 10 boys. What is the ratio of boys to the whole class? Write it in simplest form.
   Answer: ______ : ______
3. The ratio of dogs to cats at a shelter is 3:2. If there are 18 dogs, how many cats are there?
   Work:
   Answer: ______ cats
4. For every 4 blue marbles, there are 5 green marbles. If there are 32 blue marbles, how many green marbles are there?
   Work:
   Answer: ______ green marbles
5. A map scale is 1 inch : 20 miles. If two towns are 3.5 inches apart on the map, how many miles apart are they in real life?
   Work:
   Answer: ______ miles
6. A lemonade recipe calls for 2 cups of lemon juice for every 5 cups of water. If you want to use 8 cups of lemon juice, how many cups of water will you need?
   Work:
   Answer: ______ cups

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Section 2: Rates and Percentages

Total: 10 Points

7. If 6 pounds of bananas cost $4.50, what is the cost per pound?
   Answer: $______
8. A car travels 240 miles in 4 hours. What is its speed in miles per hour?
   Answer: ______ mph
9. Write $\frac{3}{8}$83​ as a decimal and a percent.
   Decimal: ______ Percent: ______%
10. Write 0.65 as a fraction in simplest form and as a percent.
    Fraction: ______ Percent: ______%
11. What is 30% of 80?
    Answer: ______
12. 15 is what percent of 60?
    Answer: ______%
13. A shirt costs $25. It is on sale for 20% off. What is the sale price?
    Work:
    Answer: $______

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Section 3: Negative Numbers

Total: 26 Points

Adding and Subtracting (10 Points)

14. $-5+8=$−5+8= ______
15. $3-7=$3−7= ______
16. $-4+(-6)=$−4+(−6)= ______
17. $-9-(-2)=$−9−(−2)= ______
18. $5+(-12)=$5+(−12)= ______
19. $-8-4=$−8−4= ______
20. $-1+10=$−1+10= ______
21. $-7-(-7)=$−7−(−7)= ______
22. $0+(-15)=$0+(−15)= ______
23. $-3-8=$−3−8= ______

Multiplying and Dividing (6 Points)

24. $(-4)\times 5=$(−4)×5= ______
25. $6\times (-3)=$6×(−3)= ______
26. $(-7)\times (-2)=$(−7)×(−2)= ______
27. $18÷(-3)=$18÷(−3)= ______
28. $(-24)÷(-6)=$(−24)÷(−6)= ______
29. $(-10)÷2=$(−10)÷2= ______

Word Problems (6 Points)

30. The temperature at 6 a.m. was -3°F. By noon, it had risen 12 degrees. What was the temperature at noon?
    Answer: ______°F
31. A scuba diver is at -50 feet. She ascends 20 feet, then descends 15 feet. What is her new depth?
    Work:
    Answer: ______ feet
32. A bank account has a balance of -$25. You deposit $40. What is the new balance?
    Answer: $______

Negative Fractions and Decimals (4 Points)

33. $-2.5+4.1=$−2.5+4.1= ______
34. $\frac{-3}{4}+\frac{1}{2}=$4−3​+21​= ______
35. $-1.2-0.8=$−1.2−0.8= ______
36. $-\frac{5}{6}-(-\frac{1}{3})=$−65​−(−31​)= ______

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Section 4: Equations and Inequalities

Total: 15 Points

Solving Equations (5 Points)

37. $x+8=15$x+8=15
    Answer: $x=$x= ______
38. $3y=27$3y=27
    Answer: $y=$y= ______
39. $\frac{m}{4}=6$4m​=6
    Answer: $m=$m= ______
40. $2p-5=13$2p−5=13
    Answer: $p=$p= ______
41. $7=1+2k$7=1+2k
    Answer: $k=$k= ______

Inequalities (4 Points)

42. $x-4>9$x−4>9
    Answer: $x$x ______
43. $3n\le 21$3n≤21
    Answer: $n$n ______
44. $-2y<10$−2y<10
    Answer: $y$y ______
45. $5+a\ge 12$5+a≥12
    Answer: $a$a ______

Word Problems (2 Points)

46. Tia wants to save at least $100 for a new video game. She has saved $35. Write an inequality to show how much more money, $m$m, she needs to save.
    Inequality: ______
47. The maximum number of people allowed in an elevator is 12. If $p$p people are in the elevator, write an inequality to represent this situation.
    Inequality: ______

Two-Step Inequalities (4 Points)

48. $2x+7<19$2x+7<19
    Answer: ______
49. $\frac{y}{3}-4\ge 2$3y​−4≥2
    Answer: ______
50. $-5m+1>16$−5m+1>16
    Answer: ______
51. $8\le 3w-1$8≤3w−1
    Answer: ______

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Section 5: Plane Figures

Total: 14 Points

Parallelograms (2 Points)

52. Find the area of a parallelogram with a base of 10 cm and a height of 7 cm.
    Answer: ______ cm²
53. A parallelogram has an area of 48 in² and a height of 6 in. What is the length of its base?
    Answer: ______ in

Triangles (3 Points)

54. A triangle has an area of 24 m² and a base of 8 m. What is its height?
    Answer: ______ m
55. Find the area of a triangle with a base of 12 ft and a height of 5 ft.
    Answer: ______ ft²
56. A triangle has an area of 45 cm² and a height of 9 cm. What is the length of its base?
    Answer: ______ cm

Trapezoids (5 Points)

57. Find the area of a trapezoid with bases of 5 in and 9 in, and a height of 4 in.
    Answer: ______ in²
58. A trapezoid has an area of 60 yd², a height of 6 yd, and one base of 8 yd. What is the length of the other base?
    Work:
    Answer: ______ yd
59. Find the area of a trapezoid with bases of 7 cm and 11 cm, and a height of 6 cm.
    Answer: ______ cm²
60. A trapezoid has an area of 100 ft², a height of 10 ft, and one base of 12 ft. Find the other base.
    Work:
    Answer: ______ ft
61. Find the area of a trapezoid with bases of 15 m and 20 m, and a height of 8 m.
    Answer: ______ m²

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End of Exam
Great job working through all these problems! Remember to check your work.

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Answer Key

Section 1: Ratios

1. 2:5
2. 2:5
3. 12
4. 40
5. 70
6. 20

Section 2: Rates and Percentages

7. $0.75
8. 60
9. 0.375, 37.5%
10. 13/20, 65%
11. 24
12. 25%
13. $20

Section 3: Negative Numbers

14. 3
15. -4
16. -10
17. -7
18. -7
19. -12
20. 9
21. 0
22. -15
23. -11
24. -20
25. -18
26. 14
27. -6
28. 4
29. -5
30. 9°F
31. -45 feet
32. $15
33. 1.6
34. -0.25 or -1/4
35. -2.0 or -2
36. -0.5 or -1/2

Section 4: Equations and Inequalities

37. 7
38. 9
39. 24
40. 9
41. 3
42. $x>13$x>13
43. $n\le 7$n≤7
44. $y>-5$y>−5
45. $a\ge 7$a≥7
46. $m\ge 65$m≥65
47. $p\le 12$p≤12
48. $x<6$x<6
49. $y\ge 18$y≥18
50. $m<-3$m<−3
51. $w\ge 3$w≥3

Section 5: Plane Figures

52. 70 cm²
53. 8 in
54. 6 m
55. 30 ft²
56. 10 cm
57. 28 in²
58. 12 yd
59. 54 cm²
60. 8 ft
61. 140 m²