6th grade math - EduBird

Section 1: Ratios (5 questions, 10 points)

In a basket of fruit, there are 9 apples and 15 pieces of fruit total. What is the ratio of apples to total fruit? Write it in simplest form.
Answer: ________
The ratio of dogs to cats at the pet shelter is 5:3. If there are 30 dogs, how many cats are there? Use a tape diagram in your thinking.
Answer: ________
A map scale says 1 inch : 20 miles. If two towns are 3.5 inches apart on the map, how many miles apart are they in real life?
Answer: ________
A recipe for lemonade 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 will you need?
Answer: ________
Write the ratio “12 to 18” in two other ways (as a fraction and using a colon).
Answer: Fraction ________, Colon ________

Section 2: Rates and Percentages (5 questions, 10 points)

If 4 pounds of apples cost $10, what is the unit price (cost per pound)?
Answer: ________
Convert the fraction ⅖ to a decimal and a percent.
Answer: Decimal ________, Percent ________
What is 30% of 120?
Answer: ________
A video game is on sale for 25% off its original price of $60. What is the sale price?
Answer: ________
Express 0.08 as a percent and as a fraction in simplest form.
Answer: Percent ________, Fraction ________

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

Compute each problem.

$7 + (- 10) =$ 7+(−10)= ________
$- 4 - 6 =$ −4−6= ________
$- 8 + 15 =$ −8+15= ________
$5 - (- 3) =$ 5−(−3)= ________
$- 12 - (- 7) =$ −12−(−7)= ________
$- 9 + (- 13) =$ −9+(−13)= ________
$- 2 \times 8 =$ −2×8= ________
$15 \div (- 3) =$ 15÷(−3)= ________
$(- 4) \times (- 6) =$ (−4)×(−6)= ________
$(- 18) \div (- 2) =$ (−18)÷(−2)= ________
$(- 5) \times 4 =$ (−5)×4= ________
$0 \div (- 5) =$ 0÷(−5)= ________
$(- 7) \times (- 1) =$ (−7)×(−1)= ________
$24 \div (- 8) =$ 24÷(−8)= ________

Word Problems

The temperature at noon was 5°F. By midnight, it had dropped 12 degrees. What was the temperature at midnight?
Answer: ________
A scuba diver is at 30 feet below sea level. She ascends 18 feet, then descends 7 feet. What is her final depth relative to sea level? (Use negative for below sea level)
Answer: ________

Negative Fractions & Decimals

$- \frac{1}{4} + \frac{1}{2} =$ −41+21= ________
$- 0.5 - 0.3 =$ −0.5−0.3= ________
$1.2 + (- 2.8) =$ 1.2+(−2.8)= ________
$- \frac{3}{4} - (- \frac{1}{4}) =$ −43−(−41)= ________

Section 4: Equations and Inequalities (15 questions, 30 points)

Solve for the variable.

$x + 8 = 15$ x+8=15
Answer: ________
$3 y = 27$ 3y=27
Answer: ________
$\frac{a}{4} = 6$ 4a=6
Answer: ________
$b - 12 = - 3$ b−12=−3
Answer: ________
$2 p + 5 = 19$ 2p+5=19
Answer: ________

Inequalities – Solve each inequality.

$x + 7 > 10$ x+7>10
Answer: ________
$3 n \leq 21$ 3n≤21
Answer: ________
$m - 4 < 1$ m−4<1
Answer: ________
$- 2 k \geq 8$ −2k≥8
Answer: ________
$5 t - 3 < 22$ 5t−3<22
Answer: ________

Word Problems – Write an equation or inequality and solve.

Six less than a number is 14. Write and solve an equation to find the number.
Equation: ________________
Solution: ________
Julie has at most $50 to spend on books. Each book costs $12. Write and solve an inequality to find how many books she can buy.
Inequality: ________________
Solution: ________
The sum of twice a number and 9 is 25. Find the number.
Equation: ________________
Solution: ________
A parking garage charges a flat fee of $5 plus $2 per hour. If you have $15, write and solve an inequality to find how many hours you can park.
Inequality: ________________
Solution: ________
Solve: $4 (x - 2) = 20$ 4(x−2)=20
Answer: ________

Section 5: Plane Figures (10 questions, 30 points)

What is the area of a parallelogram with a base of 10 cm and a height of 7 cm?
Answer: ________
A triangle has an area of 24 square inches and a base of 8 inches. What is its height?
Answer: ________
Find the area of a trapezoid with bases of 6 m and 10 m, and a height of 5 m.
Answer: ________
A parallelogram has a base of 12 ft and an area of 84 ft². Find its height.
Answer: ________
Find the area of a triangle with a base of 15 cm and a height of 6 cm.
Answer: ________
A trapezoid has an area of 45 yd², a height of 5 yd, and one base of 7 yd. Find the length of the other base.
Answer: ________
True or False: In a parallelogram, opposite sides are parallel.
Answer: ________
Find the area of a parallelogram with a base of 9 in and a height of 4.5 in.
Answer: ________
A triangle has a height of 10 m and an area of 35 m². What is the length of its base?
Answer: ________
A trapezoid has bases of 8 cm and 14 cm, and a height of 6 cm. What is its area?
Answer: ________

End of Test
Check your work before turning it in.

Answer Key (For Teacher Use)

Section 1:

3:5
18 cats
70 miles
20 cups
12/18, 12:18

Section 2:
6. $2.50 per pound
7. 0.4, 40%
8. 36
9. $45
10. 8%, 2/25

Section 3:
11. -3
12. -10
13. 7
14. 8
15. -5
16. -22
17. -16
18. -5
19. 24
20. 9
21. -20
22. 0
23. 7
24. -3
25. -7°F
26. -19 feet
27. ¼
28. -0.8
29. -1.6
30. -½

Section 4:
31. 7
32. 9
33. 24
34. 9
35. 7
36. x > 3
37. n ≤ 7
38. m < 5
39. k ≤ -4
40. t < 5
41. x – 6 = 14, x = 20
42. 12b ≤ 50, b ≤ 4.166…, 4 books
43. 2n + 9 = 25, n = 8
44. 5 + 2h ≤ 15, h ≤ 5
45. x = 7

Section 5:
46. 70 cm²
47. 6 in
48. 40 m²
49. 7 ft
50. 45 cm²
51. 11 yd
52. True
53. 40.5 in²
54. 7 m
55. 66 cm²