6th grade math

Sections: Ratios, Rates & Percentages, Negative Numbers, Equations & Inequalities, Plane Figures

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Section 1: Ratios (6 questions, 12 points)

Part-to-Whole Ratios

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 blue shirts, what is the ratio of students wearing blue to the whole class?
   Answer: ______ : ______

Ratios with Tape Diagrams & Word Problems

3. The ratio of cats to dogs at a pet shelter is 3:5. If there are 24 dogs, how many cats are there?
   Answer: ______ cats
4. For every 4 pencils, there are 2 erasers. If you have 16 pencils, how many erasers do you have?
   Answer: ______ erasers

Ratios and Measurements

5. A map scale is 1 inch : 20 miles. How many miles apart are two cities that are 3.5 inches apart on the map?
   Answer: ______ miles

Ratios in Recipes (Word Problem)

6. A lemonade recipe calls for 2 cups of lemon juice for every 5 cups of water. If you want to use 15 cups of water, how many cups of lemon juice do you need?
   Answer: ______ cups

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Section 2: Rates and Percentages (6 questions, 12 points)

Solving Unit Rate/Price Problems

7. If 6 oranges cost $4.50, what is the cost per orange?
   Answer: $______ per orange
8. A car travels 240 miles in 5 hours. What is its speed in miles per hour?
   Answer: ______ mph

Fraction, Decimal, and Percent Converting

9. Write $\frac{3}{8}$83​ as a decimal and a percent.
   Decimal: ______ Percent: ______%
10. Convert 0.65 to a fraction in simplest form and a percent.
    Fraction: ______ Percent: ______%

Percent of a Number

11. Find 30% of 80.
    Answer: ______

Finding Common Percentages

12. What is 50% of 120?
    Answer: ______

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Section 3: Negative Numbers (20 questions, 20 points)

Adding and Subtracting Negative Numbers

13. $(-8)+5=$(−8)+5= ______
14. $12+(-15)=$12+(−15)= ______
15. $(-7)-(-3)=$(−7)−(−3)= ______
16. $4-9=$4−9= ______
17. $(-10)+(-6)=$(−10)+(−6)= ______
18. $(-5)-8=$(−5)−8= ______
19. $0+(-13)=$0+(−13)= ______
20. $(-4)-(-10)=$(−4)−(−10)= ______

Multiplying and Dividing Negative Numbers

21. $(-6)\times 3=$(−6)×3= ______
22. $8\times (-2)=$8×(−2)= ______
23. $(-5)\times (-4)=$(−5)×(−4)= ______
24. $(-15)÷3=$(−15)÷3= ______
25. $24÷(-6)=$24÷(−6)= ______
26. $(-18)÷(-3)=$(−18)÷(−3)= ______

Negative Numbers in Word Problems

27. The temperature at 6 a.m. was –4°F. By noon, it rose 11°F. What was the temperature at noon?
    Answer: ______°F
28. A scuba diver is at –30 feet. She ascends 12 feet, then descends 8 feet. What is her final depth?
    Answer: ______ feet

Negative Fractions and Decimals

29. $(-2.5)+1.8=$(−2.5)+1.8= ______
30. $\frac{-3}{4}+\frac{1}{2}=$4−3​+21​= ______
31. $(-0.6)\times 4=$(−0.6)×4= ______
32. $\frac{-5}{6}-\frac{1}{3}=$6−5​−31​= ______

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Section 4: Equations and Inequalities (13 questions, 26 points)

Solving Equations

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

Inequalities – Solve each inequality.

37. $x-4>9$x−4>9
    Solution: $x$x ______
38. $3n\le 21$3n≤21
    Solution: $n$n ______
39. $-2k<10$−2k<10
    Solution: $k$k ______

Inequalities in Word Problems

40. Emily has at most $50 to spend. She buys a book for $18. Write an inequality to find how much money $m$m she has left.
    Inequality: ______

Two-Step Inequalities – Solve.

41. $5x+2\ge 17$5x+2≥17
    Solution: $x$x ______
42. $\frac{m}{3}-1<4$3m​−1<4
    Solution: $m$m ______
43. $-4y+7>15$−4y+7>15
    Solution: $y$y ______

Graphing Inequalities – Choose the correct graph option (a, b, or c).

44. $x\le 3$x≤3
    a) ●––––––––––––>
    b) <––––––––––––●
    c) <––––●–––––––>
    Choice: ______
45. $x>-2$x>−2
    a) ○––––––––––––>
    b) <––––––––––––○
    c) <––––○–––––––>
    Choice: ______

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Section 5: Plane Figures (10 questions, 40 points)

Parallelogram Models

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

Areas of Triangles (Missing Height or Base)

48. A triangle has area 24 m² and base 8 m. Find the height.
    Answer: ______ m
49. A triangle has area 45 cm² and height 9 cm. Find the base.
    Answer: ______ cm

Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)

50. Find the area of a trapezoid with bases 5 ft and 9 ft, and height 4 ft.
    Answer: ______ ft²
51. A trapezoid has an area of 60 yd², height 6 yd, and one base 8 yd. Find the other base.
    Answer: ______ yd

Composite Figures

52. Find the area of the shape: A rectangle (8 in by 5 in) with a right triangle on top (base 8 in, height 3 in).
    Answer: ______ in²
53. Find the area: A square (side 6 cm) with a semicircle on top (diameter 6 cm). Use $\pi \approx 3.14$π≈3.14.
    Answer: ______ cm²

Missing Side Given Area

54. A rectangle has area 56 ft² and length 8 ft. Find the width.
    Answer: ______ ft
55. A rhombus has area 75 m² and height 5 m. Find the base.
    Answer: ______ m

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End of Test – Please review your work.

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Answer Key (For Teacher Use)

Section 1:

1. 5:12
2. 7:18
3. 9
4. 8
5. 70
6. 6

Section 2:
7. 0.75
8. 48
9. 0.375, 37.5%
10. 13/20, 65%
11. 24
12. 60

Section 3:
13. –3
14. –3
15. –4
16. –5
17. –16
18. –13
19. –13
20. 6
21. –18
22. –16
23. 20
24. –5
25. –4
26. 6
27. 7
28. –26
29. –0.7
30. –1/4 or –0.25
31. –2.4
32. –7/6 or ≈ –1.167

Section 4:
33. 8
34. 9
35. 20
36. 7
37. $x>13$x>13
38. $n\le 7$n≤7
39. $k>\text{–}5$k>–5
40. $m\le 32$m≤32
41. $x\ge 3$x≥3
42. $m<15$m<15
43. $y<\text{–}2$y<–2
44. b
45. a

Section 5:
46. 70
47. 8
48. 6
49. 10
50. 28
51. 12
52. 52
53. 56.13
54. 7
55. 15