6th Grade Math Review & Assessment

6th Grade Math Review & Assessment

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Section 1: Ratios

Total: 8 Points

1. In a basket of 12 fruits, 5 are apples. Write the ratio of apples to total fruits.
   Answer: ______ : ______
2. A class has 18 students. If 7 are wearing glasses, what is the ratio of students with glasses to the whole class?
   Answer: ______ : ______
3. The ratio of dogs to cats at a pet shelter is 3:2. If there are 15 dogs, how many cats are there?
   Work:
   Answer: ______ cats
4. For every 4 red marbles, there are 5 blue marbles. If there are 36 red marbles, how many blue marbles are there?
   Work:
   Answer: ______ blue marbles
5. A map scale is 1 inch : 20 miles. How many miles are represented by 3.5 inches on the map?
   Work:
   Answer: ______ miles
6. A lemonade recipe calls for 2 cups of lemon juice for every 5 cups of water. If you use 8 cups of lemon juice, how many cups of water do you need?
   Work:
   Answer: ______ cups

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Section 2: Rates and Percentages

Total: 10 Points

7. If 6 notebooks cost $12.90, what is the cost per notebook?
   Work:
   Answer: $______
8. A car travels 210 miles in 3.5 hours. What is its speed in miles per hour?
   Work:
   Answer: ______ mph
9. Write $\frac{2}{5}$52​ as a decimal and a percent.
   Decimal: ______ Percent: ______ %
10. Write 0.72 as a fraction in simplest form and as a percent.
    Fraction: ______ Percent: ______ %
11. Find 30% of 80.
    Answer: ______
12. What is 15% of 200?
    Answer: ______
13. A shirt costs $40. It is on sale for 25% off. What is the sale price?
    Work:
    Answer: $______

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Section 3: Negative Numbers

Total: 22 Points

Adding and Subtracting (5 Points)

14. $-8+5=$−8+5= ______
15. $12+(-15)=$12+(−15)= ______
16. $-4-7=$−4−7= ______
17. $-3-(-9)=$−3−(−9)= ______
18. $6+(-10)-(-2)=$6+(−10)−(−2)= ______

Multiplying and Dividing (5 Points)

19. $(-5)\times 4=$(−5)×4= ______
20. $6\times (-3)=$6×(−3)= ______
21. $(-24)÷(-6)=$(−24)÷(−6)= ______
22. $18÷(-2)=$18÷(−2)= ______
23. $(-7)\times (-2)=$(−7)×(−2)= ______

Word Problems (3 Points)

24. The temperature at 6 a.m. was -4°F. By noon, it had risen 11 degrees. What was the temperature at noon?
    Answer: ______°F
25. A scuba diver is at -30 feet. She ascends 12 feet, then descends 8 feet. Where is she now?
    Work:
    Answer: ______ feet
26. A bank account has a balance of -$15. If $40 is deposited, what is the new balance?
    Answer: $______

Negative Fractions and Decimals (9 Points)

27. $-\frac{1}{2}+\frac{3}{4}=$−21​+43​= ______
28. $-1.2+3.5=$−1.2+3.5= ______
29. $-0.6\times 2=$−0.6×2= ______
30. $(-\frac{1}{4})\times (-8)=$(−41​)×(−8)= ______
31. $-3.4-1.8=$−3.4−1.8= ______
32. $\frac{1}{2}-(-\frac{3}{4})=$21​−(−43​)= ______
33. $-2.5÷0.5=$−2.5÷0.5= ______

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Section 4: Equations and Inequalities

Total: 15 Points

Solving Equations (4 Points)

34. $x+8=15$x+8=15
    Answer: $x=$x= ______
35. $3y=27$3y=27
    Answer: $y=$y= ______
36. $\frac{z}{4}=5$4z​=5
    Answer: $z=$z= ______
37. $2p-7=11$2p−7=11
    Answer: $p=$p= ______

Inequalities (3 Points)

38. $x+3>7$x+3>7
    Answer: $x$x ______
39. $2n\le 16$2n≤16
    Answer: $n$n ______
40. $-5k<20$−5k<20
    Answer: $k$k ______

Word Problems (2 Points)

41. Lisa needs at least $50 to buy a game. She has $22 saved. Write an inequality to show how much more money, $m$m, she needs.
    Inequality: ______
42. A bus can hold at most 48 students. If 31 are already on, write an inequality for how many more, $s$s, can get on.
    Inequality: ______

Two-Step Inequalities (6 Points)

43. $3x+4\ge 13$3x+4≥13
    Answer: ______
44. $\frac{y}{2}-5<1$2y​−5<1
    Answer: ______
45. $-2m+7>3$−2m+7>3
    Answer: ______
46. $6-4n\le 18$6−4n≤18
    Answer: ______
47. $5+3p<20$5+3p<20
    Answer: ______
48. $\frac{a}{3}+4\ge 7$3a​+4≥7
    Answer: ______

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Section 5: Plane Figures

Total: 15 Points

49. Find the area of a parallelogram with base 10 cm and height 7 cm.
    Answer: ______ cm²
50. A parallelogram has an area of 54 in² and a height of 6 in. What is the length of its base?
    Answer: ______ in
51. Find the area of a triangle with base 12 m and height 5 m.
    Answer: ______ m²
52. A triangle has an area of 28 ft² and a base of 8 ft. What is its height?
    Answer: ______ ft
53. Find the area of a trapezoid with bases 9 cm and 15 cm, and height 4 cm.
    Answer: ______ cm²
54. A trapezoid has an area of 75 yd², height 5 yd, and one base of 10 yd. Find the length of the other base.
    Work:
    Answer: ______ yd
55. Find the area of a trapezoid with bases 6 in and 14 in, and height 3 in.
    Answer: ______ in²

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End of Exam
Great job! You’ve worked through some challenging problems. Now, check your answers carefully.

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Answer Key

Section 1: Ratios

1. 5:12
2. 7:18
3. 10
4. 45
5. 70
6. 20

Section 2: Rates and Percentages

7. $2.15
8. 60
9. 0.4, 40%
10. 18/25, 72%
11. 24
12. 30
13. $30

Section 3: Negative Numbers

14. -3
15. -3
16. -11
17. 6
18. -2
19. -20
20. -18
21. 4
22. -9
23. 14
24. 7°F
25. -26 feet
26. $25
27. ¼ or 0.25
28. 2.3
29. -1.2
30. 2
31. -5.2
32. 1¼ or 1.25 or 5/4
33. -5

Section 4: Equations and Inequalities

34. 7
35. 9
36. 20
37. 9
38. $x>4$x>4
39. $n\le 8$n≤8
40. $k>-4$k>−4
41. $m\ge 28$m≥28
42. $s\le 17$s≤17
43. $x\ge 3$x≥3
44. $y<12$y<12
45. $m<2$m<2
46. $n\ge -3$n≥−3
47. $p<5$p<5
48. $a\ge 9$a≥9

Section 5: Plane Figures

49. 70 cm²
50. 9 in
51. 30 m²
52. 7 ft
53. 48 cm²
54. 20 yd
55. 30 in²