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 the total number of fruits?
   Answer: ______
2. A class has 18 students. If 7 are wearing glasses, what is the ratio of students wearing glasses 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 4.5 inches apart on the map?
   Answer: ______ miles

Ratios in Recipes (Word Problem)

6. A lemonade recipe calls for 3 cups of water for every 1 cup of lemon juice. If you use 8 cups of lemon juice, how many total cups of lemonade will you make?
   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 printer can print 12 pages per minute. How many pages can it print in 15 minutes?
   Answer: ______ pages

Fraction, Decimal, and Percent Converting

9. Write $\frac{3}{5}$53​ as a decimal and a percent.
   Decimal: ______ Percent: ______
10. Write 0.08 as a fraction in simplest form and 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. What is the sale price?
    Answer: $______

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Section 3: Negative Numbers (23 questions, 23 points)

Adding and Subtracting Negative Numbers

13. $-8+5=$−8+5= ______
14. $4-9=$4−9= ______
15. $-3+(-7)=$−3+(−7)= ______
16. $-5-(-2)=$−5−(−2)= ______
17. $10+(-12)=$10+(−12)= ______
18. $-1-6=$−1−6= ______
19. $0+(-9)=$0+(−9)= ______
20. $-4-(-10)=$−4−(−10)= ______

Multiplying and Dividing Negative Numbers

21. $(-6)\times 3=$(−6)×3= ______
22. $8\times (-2)=$8×(−2)= ______
23. $(-4)\times (-5)=$(−4)×(−5)= ______
24. $15÷(-3)=$15÷(−3)= ______
25. $(-20)÷(-4)=$(−20)÷(−4)= ______
26. $(-14)÷2=$(−14)÷2= ______

Negative Numbers in Word Problems

27. The temperature at 6 a.m. was -3°F. By noon, it had risen 12 degrees. What was the temperature at noon?
    Answer: ______°F
28. A scuba diver is at 15 feet below sea level. She descends another 8 feet. What integer represents her new depth?
    Answer: ______ feet
29. A checking account has a balance of -$25. If you deposit $60, what is the new balance?
    Answer: $______
30. In a game, you lose 5 points for each wrong answer. If you answer 3 questions wrong, what is the total change in your score?
    Answer: ______ points

Negative Fractions and Decimals

31. $-\frac{1}{4}+\frac{1}{2}=$−41​+21​= ______
32. $-0.75-0.25=$−0.75−0.25= ______
33. $1.2+(-2.8)=$1.2+(−2.8)= ______
34. $-\frac{3}{5}\times 2=$−53​×2= ______
35. $-1.6÷(-0.4)=$−1.6÷(−0.4)= ______

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Section 4: Equations and Inequalities (12 questions, 36 points)

Solving Equations

36. Solve for $x$x: $x+7=15$x+7=15
    $x=$x= ______
37. Solve for $y$y: $3y=27$3y=27
    $y=$y= ______
38. Solve for $n$n: $\frac{n}{4}=6$4n​=6
    $n=$n= ______
39. Solve for $a$a: $2a-5=13$2a−5=13
    $a=$a= ______

Inequalities – Solve each inequality.

40. $x-4>1$x−4>1
    Solution: $x$x ______
41. $3k\le 12$3k≤12
    Solution: $k$k ______
42. $-2p<10$−2p<10
    Solution: $p$p ______

Inequalities in Word Problems – Write and solve.

43. Emily needs to save at least $120 for a new bike. She has already saved $45. Write and solve an inequality to find how much more she needs to save.
    Inequality: ________________
    Solution: ______
44. The maximum number of people allowed in an elevator is 12. If there are already 5 people in it, write and solve an inequality to find how many more can enter.
    Inequality: ________________
    Solution: ______

Multi-Step Inequalities – Solve.

45. $4m+3>19$4m+3>19
    Solution: $m$m ______
46. $2(x-5)\le 8$2(x−5)≤8
    Solution: $x$x ______
47. $-3y+7\ge 1$−3y+7≥1
    Solution: $y$y ______

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Section 5: Plane Figures (6 questions, 27 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 56 square inches and a height of 7 inches. What is the length of its base?
    Answer: ______ inches

Areas of Triangles (Missing Height or Base)

50. Find the area of a triangle with a base of 12 m and a height of 5 m.
    Answer: ______ m²
51. A triangle has an area of 24 square feet and a base of 8 feet. What is its height?
    Answer: ______ feet

Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)

52. Find the area of a trapezoid with bases of 9 cm and 15 cm, and a height of 4 cm.
    Answer: ______ cm²
53. A trapezoid has an area of 75 square yards. Its height is 6 yards and one base is 9 yards. What is the length of the other base?
    Answer: ______ yards

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End of Test – Please check your work before submitting.

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Answer Key (For Teacher Use)

Section 1:

1. 5:12
2. 7:18
3. 9
4. 8
5. 90
6. 32

Section 2:
7. 1.50
8. 180
9. 0.6, 60%
10. 2/25, 8%
11. 24
12. 30

Section 3:
13. -3
14. -5
15. -10
16. -3
17. -2
18. -7
19. -9
20. 6
21. -18
22. -16
23. 20
24. -5
25. 5
26. -7
27. 9
28. -23
29. 35
30. -15
31. ¼ or 0.25
32. -1.0
33. -1.6
34. -6/5 or -1.2
35. 4

Section 4:
36. 8
37. 9
38. 24
39. 9
40. $x>5$x>5
41. $k\le 4$k≤4
42. $p>-5$p>−5
43. $m\ge 75$m≥75, where $m$m = money needed
44. $p\le 7$p≤7, where $p$p = people who can enter
45. $m>4$m>4
46. $x\le 9$x≤9
47. $y\le 2$y≤2

Section 5:
48. 60
49. 8
50. 30
51. 6
52. 48
53. 16