6th grade math

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

Section 1: Ratios (20 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 of them are wearing glasses, what is the ratio of students wearing glasses to the total class size?
   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: ______
   (Draw a simple tape diagram below if needed.)
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 : 50 miles. How many miles are represented by 4.5 inches on this map?
Answer: ______

Ratios in Recipes (Word Problem)
6. A lemonade recipe calls for a ratio of 2 cups of lemon juice to 5 cups of water. If you use 8 cups of lemon juice, how many cups of water will you need to keep the same taste?
Answer: ______

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Section 2: Rates and Percentages (20 points)

Solving Unit Rate/Price Problems
7. If 6 pounds of bananas cost $4.50, what is the price per pound?
Answer: ______

8. A printer can print 120 pages in 3 minutes. What is its unit rate in pages per minute?
   Answer: ______

Fraction, Decimal, and Percent Converting
9. Convert $\frac{3}{5}$53​ to a decimal and a percent.
Answer: Decimal ______, Percent ______

10. Convert 0.08 to a fraction (in simplest form) and a percent.
    Answer: Fraction ______, Percent ______

Percent of a Number
11. Find 30% of 80.
Answer: ______

12. What is 15% of 200?
    Answer: ______

Finding Common Percentages
13. 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 (25 points)

Adding and Subtracting Negative Numbers
14. $-8+5=$−8+5= ______
15. $4+(-12)=$4+(−12)= ______
16. $-3-7=$−3−7= ______
17. $-5-(-9)=$−5−(−9)= ______
18. $10-15=$10−15= ______
19. $-6+(-4)=$−6+(−4)= ______
20. $0-8=$0−8= ______
21. $-1-(-1)=$−1−(−1)= ______

Multiplying and Dividing Negative Numbers
22. $(-4)\times 6=$(−4)×6= ______
23. $5\times (-3)=$5×(−3)= ______
24. $(-7)\times (-2)=$(−7)×(−2)= ______
25. $18÷(-3)=$18÷(−3)= ______
26. $(-24)÷(-6)=$(−24)÷(−6)= ______
27. $(-10)÷2=$(−10)÷2= ______

Negative Numbers in Word Problems
28. The temperature at noon was 5°F. By midnight, it had dropped 12 degrees. What was the temperature at midnight?
Answer: ______

29. A scuba diver is at 15 feet below sea level. She descends another 20 feet. What is her new depth?
    Answer: ______
30. A checking account has a balance of -$25. If you deposit $60, what is the new balance?
    Answer: ______

Negative Fractions and Decimals
31. $-\frac{1}{4}+\frac{1}{2}=$−41​+21​= ______
32. $-0.5-0.3=$−0.5−0.3= ______
33. $0.6+(-1.2)=$0.6+(−1.2)= ______

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Section 4: Equations and Inequalities (20 points)

Solving Equations
34. Solve for $x$x: $x+8=15$x+8=15
Answer: ______

35. Solve for $y$y: $3y=27$3y=27
    Answer: ______
36. Solve for $n$n: $n\mathrm{/}4=6$n/4=6
    Answer: ______
37. Solve for $a$a: $2a-5=11$2a−5=11
    Answer: ______

Inequalities
38. Solve and graph on a number line: $x+3>7$x+3>7
Answer: ______

39. Solve and graph on a number line: $2k\le 10$2k≤10
    Answer: ______
40. Solve: $-2x<8$−2x<8
    Answer: ______

Inequalities in Word Problems
41. Lisa needs to save at least $120 for a new game. She has already saved $45. Write and solve an inequality to find how much more money ($m$m) she needs to save.
Answer: Inequality: ______, Solution: ______

42. The maximum number of people allowed in an elevator is 12. If there are currently $p$p people in it, write an inequality to show how many more can enter.
    Answer: ______

Multi-Step Inequalities
43. Solve: $3x+7\le 22$3x+7≤22
Answer: ______

44. Solve: $2(y-4)>6$2(y−4)>6
    Answer: ______
45. Solve: $-5x+10\ge -15$−5x+10≥−15
    Answer: ______

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Section 5: Plane Figures (15 points)

Parallelogram Models
46. Find the area of a parallelogram with a base of 10 cm and a height of 6 cm.
Answer: ______

47. A parallelogram has an area of 48 square inches and a height of 6 inches. What is the length of its base?
    Answer: ______

Areas of Triangles (Missing Height or Base)
48. Find the area of a triangle with a base of 12 m and a height of 5 m.
Answer: ______

49. A triangle has an area of 24 square feet and a base of 8 feet. What is its height?
    Answer: ______

Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)
50. Find the area of a trapezoid with bases of 9 cm and 5 cm, and a height of 4 cm.
Answer: ______

51. A trapezoid has an area of 70 square yards. Its bases are 8 yards and 12 yards. What is its height?
    Answer: ______

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End of Exam
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Answer Key

(For teacher use)

Section 1: 1) 5:12, 2) 7:18, 3) 9, 4) 8, 5) 225 miles, 6) 20 cups
Section 2: 7) $0.75, 8) 40, 9) 0.6, 60%, 10) 2/25, 8%, 11) 24, 12) 30, 13) $30
Section 3: 14) -3, 15) -8, 16) -10, 17) 4, 18) -5, 19) -10, 20) -8, 21) 0, 22) -24, 23) -15, 24) 14, 25) -6, 26) 4, 27) -5, 28) -7°F, 29) -35 ft, 30) $35, 31) 1/4 or 0.25, 32) -0.8, 33) -0.6
Section 4: 34) 7, 35) 9, 36) 24, 37) 8, 38) x > 4, 39) k ≤ 5, 40) x > -4, 41) m ≥ 75, 42) p ≤ 12, 43) x ≤ 5, 44) y > 7, 45) x ≤ 5
Section 5: 46) 60 cm², 47) 8 in, 48) 30 m², 49) 6 ft, 50) 28 cm², 51) 7 yd