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, there are 5 apples. What is the ratio of apples to total fruits? Write the ratio in simplest form.
   Answer: ______
2. A class has 18 students. If 10 are girls, what is the ratio of boys to the total class?
   Answer: ______

Ratios with Tape Diagrams & Word Problems

3. The ratio of red marbles to blue marbles in a bag is 3:5. If there are 24 blue marbles, how many red marbles are there?
   Answer: ______
4. For every 2 adults on a field trip, there are 7 children. If there are 28 children, how many adults are there?
   Answer: ______

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 pancake recipe uses 2 cups of flour for every 3 cups of milk. If you want to use 9 cups of milk, how many cups of flour 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 5 pounds of apples cost $7.50, what is the cost per pound?
   Answer: $______
8. A car travels 240 miles in 4 hours. What is the car’s speed in miles per hour?
   Answer: ______ mph

Fraction, Decimal, and Percent Converting

9. Write $\frac{3}{4}$43​ as a decimal and a percent.
   Decimal: ______ Percent: ______
10. Write 0.08 as a fraction in simplest form and as a percent.
    Fraction: ______ Percent: ______

Percent of a Number

11. What is 30% of 80?
    Answer: ______

Finding Common Percentages

12. A shirt originally costs $40. It is on sale for 25% off. How much is the discount in dollars?
    Answer: $______

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

Adding and Subtracting Negative Numbers

13. $5+(\text{–}9)=$5+(–9)= ______
14. $\text{–}3\text{–}7=$–3–7= ______
15. $\text{–}4+10=$–4+10= ______
16. $6\text{–}(\text{–}2)=$6–(–2)= ______
17. $\text{–}8\text{–}(\text{–}5)=$–8–(–5)= ______
18. $\text{–}1+(\text{–}6)=$–1+(–6)= ______

Multiplying and Dividing Negative Numbers

19. $(\text{–}4)\times 3=$(–4)×3= ______
20. $5\times (\text{–}2)=$5×(–2)= ______
21. $(\text{–}6)\times (\text{–}4)=$(–6)×(–4)= ______
22. $15÷(\text{–}3)=$15÷(–3)= ______
23. $(\text{–}20)÷(\text{–}5)=$(–20)÷(–5)= ______
24. $(\text{–}18)÷6=$(–18)÷6= ______

Negative Numbers in Word Problems

25. The temperature at noon was 8°F. By midnight, it had dropped 15 degrees. What was the temperature at midnight?
    Answer: ______°F
26. A scuba diver is at –30 feet. She rises 12 feet. What is her new depth?
    Answer: ______ feet
27. A bank account has a balance of –$25. If $60 is deposited, what is the new balance?
    Answer: $______

Negative Fractions and Decimals

28. $\text{–}\frac{1}{2}+\frac{3}{4}=$–21​+43​= ______
29. $\text{–}0.5\text{–}1.2=$–0.5–1.2= ______
30. $(\text{–}0.8)\times 2=$(–0.8)×2= ______
31. $\text{–}2.4÷3=$–2.4÷3= ______
32. $\frac{3}{5}+(-\frac{4}{5})=$53​+(−54​)= ______

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Section 4: Equations and Inequalities (15 questions, 45 points)

Solving Algebraic 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-5=11$2p−5=11
    $p=$p= ______

Inequalities – Solve each inequality.

37. $x-3>4$x−3>4
    Solution: $x$x ______
38. $2n\le 10$2n≤10
    Solution: $n$n ______
39. $-3m<12$−3m<12
    Solution: $m$m ______

Inequalities in Word Problems

40. Katie has at least $20. Write an inequality to represent the amount of money $m$m Katie has.
    Inequality: ______
41. A number decreased by 5 is less than 12. Write and solve the inequality.
    Inequality: ______
    Solution: ______

Multi-Step Inequalities – Solve.

42. $4x+3\ge 19$4x+3≥19
    Solution: $x$x ______
43. $-2y-7>3$−2y−7>3
    Solution: $y$y ______
44. $5(z-1)\le 20$5(z−1)≤20
    Solution: $z$z ______
45. $\frac{x}{3}+4<7$3x​+4<7
    Solution: $x$x ______
46. $8-3m\ge 14$8−3m≥14
    Solution: $m$m ______
47. $2(p+5)>p+12$2(p+5)>p+12
    Solution: $p$p ______

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Section 5: Plane Figures (8 questions, 26 points)

Parallelogram Models

48. Find the area of a parallelogram with a base of 10 cm and a height of 6 cm.
    Answer: ______ cm²
49. A parallelogram has an area of 48 square inches and a height of 6 inches. What is the length of the base?
    Answer: ______ in

Areas of Triangles (Missing Height or Base)

50. A triangle has an area of 24 square meters and a base of 8 meters. What is its height?
    Answer: ______ m
51. A triangle has an area of 35 square feet and a height of 10 feet. What is the length of its base?
    Answer: ______ ft
52. Find the area of a triangle with a base of 12 cm and a height of 9 cm.
    Answer: ______ cm²

Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)

53. Find the area of a trapezoid with bases of 5 in and 9 in, and a height of 4 in.
    Answer: ______ in²
54. A trapezoid has an area of 60 square yards. The bases are 8 yards and 12 yards. What is the height?
    Answer: ______ yd
55. Find the area of a trapezoid with bases of 7 m and 11 m, and a height of 6 m.
    Answer: ______ m²

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End of Test – Please review your work before submitting.

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Answer Key (For Teacher Use)

Section 1:

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

Section 2:
7. 1.50
8. 60
9. 0.75, 75%
10. 2/25, 8%
11. 24
12. 10

Section 3:
13. –4
14. –10
15. 6
16. 8
17. –3
18. –7
19. –12
20. –10
21. 24
22. –5
23. 4
24. –3
25. –7
26. –18
27. 35
28. ¼ or 0.25
29. –1.7
30. –1.6
31. –0.8
32. –⅕ or –0.2

Section 4:
33. 8
34. 9
35. 20
36. 8
37. $x>7$x>7
38. $n\le 5$n≤5
39. $m>\text{–}4$m>–4
40. $m\ge 20$m≥20
41. $x\text{–}5<12$x–5<12, $x<17$x<17
42. $x\ge 4$x≥4
43. $y<\text{–}5$y<–5
44. $z\le 5$z≤5
45. $x<9$x<9
46. $m\le \text{–}2$m≤–2
47. $p>2$p>2

Section 5:
48. 60
49. 8
50. 6
51. 7
52. 54
53. 28
54. 6
55. 54