6th grade math - EduBird

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

Section 1: Ratios (6 questions, 12 points)

Part-to-Whole Ratios

In a basket of 12 fruits, there are 5 apples. What is the ratio of apples to total fruits?
Answer: ______
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

The ratio of dogs to cats at a pet shelter is 3:2. If there are 15 dogs, how many cats are there?
Answer: ______
For every 4 pencils in a desk, there is 1 eraser. If there are 6 erasers, how many pencils are there?
Answer: ______

Ratios and Measurements

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)

A lemonade recipe 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 do you need?
Answer: ______ cups

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

Solving Unit Rate/Price Problems

If 6 pounds of apples cost $12, what is the cost per pound?
Answer: $______
A printer can print 120 pages in 4 minutes. What is the unit rate (pages per minute)?
Answer: ______ pages/minute

Fraction, Decimal, and Percent Converting

Write $\frac{3}{8}$ 83 as a decimal and a percent.
Decimal: ______ Percent: ______
Write 0.45 as a fraction in simplest form and as a percent.
Fraction: ______ Percent: ______

Percent of a Number

What is 30% of 80?
Answer: ______

Finding Common Percentages

A shirt originally costs $40. It is on sale for 25% off. What is the sale price?
Answer: $______

Section 3: Negative Numbers (24 questions, 24 points)

Adding and Subtracting Negative Numbers

$- 5 + 8 =$ −5+8= ______
$3 - 7 =$ 3−7= ______
$- 4 + (- 6) =$ −4+(−6)= ______
$- 9 - (- 2) =$ −9−(−2)= ______
$5 + (- 12) =$ 5+(−12)= ______
$- 8 - 4 =$ −8−4= ______
$- 1 + 10 =$ −1+10= ______
$6 - (- 3) =$ 6−(−3)= ______
$- 7 + (- 7) =$ −7+(−7)= ______
$0 - 15 =$ 0−15= ______

Multiplying and Dividing Negative Numbers

$(- 4) \times 5 =$ (−4)×5= ______
$6 \times (- 3) =$ 6×(−3)= ______
$(- 7) \times (- 2) =$ (−7)×(−2)= ______
$18 \div (- 3) =$ 18÷(−3)= ______
$(- 24) \div (- 6) =$ (−24)÷(−6)= ______
$(- 10) \div 2 =$ (−10)÷2= ______

Negative Numbers in Word Problems

The temperature at 6 a.m. was -3°F. By noon, it had risen 12 degrees. What was the temperature at noon?
Answer: ______°F
A scuba diver is at -15 feet. She descends another 10 feet. What is her new depth?
Answer: ______ feet
A penalty in a game gives a score of -5 points. If a team gets 3 penalties, what is their total penalty score?
Answer: ______ points
You have $20 in your bank account. You write a check for $35. What is your new balance, represented as a negative number if you are overdrawn?
Answer: $______

Negative Fractions and Decimals

$- \frac{1}{2} + \frac{3}{4} =$ −21+43= ______
$- 0.6 - 0.1 =$ −0.6−0.1= ______
$(- \frac{2}{3}) \times 6 =$ (−32)×6= ______
$- 1.5 \div (- 0.5) =$ −1.5÷(−0.5)= ______

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

Solving Equations

$x + 8 = 15$ x+8=15
$x =$ x= ______
$3 y = 27$ 3y=27
$y =$ y= ______
$\frac{m}{4} = 5$ 4m=5
$m =$ m= ______
$2 p - 3 = 11$ 2p−3=11
$p =$ p= ______

Inequalities – Solve each inequality.

$n - 5 > 7$ n−5>7
Solution: $n$ n ______
$4 k \leq 20$ 4k≤20
Solution: $k$ k ______
$- 2 x < 10$ −2x<10
Solution: $x$ x ______

Inequalities in Word Problems

To ride a roller coaster, you must be at least 48 inches tall. If $h$ h represents height, write an inequality.
Inequality: ______
You can spend at most $30 on snacks. If each snack costs $3, write an inequality to find how many snacks $s$ s you can buy.
Inequality: ______

Multi-Step Inequalities – Solve.

$3 a + 7 \leq 22$ 3a+7≤22
Solution: $a$ a ______
$\frac{b}{2} - 4 > 1$ 2b−4>1
Solution: $b$ b ______
$- 5 x + 2 \geq 17$ −5x+2≥17
Solution: $x$ x ______
$2 (y - 3) < 10$ 2(y−3)<10
Solution: $y$ y ______
$8 - 3 m \leq - 1$ 8−3m≤−1
Solution: $m$ m ______
$4 + \frac{c}{3} \leq 6$ 4+3c≤6
Solution: $c$ c ______

Section 5: Plane Figures (9 questions, 27 points)

Parallelogram Models

Find the area of a parallelogram with a base of 10 cm and a height of 6 cm.
Answer: ______ cm²
A parallelogram has an area of 42 in² and a height of 7 in. What is the length of its base?
Answer: ______ in

Areas of Triangles (Missing Height or Base)

Find the area of a triangle with a base of 12 m and a height of 5 m.
Answer: ______ m²
A triangle has an area of 24 ft² and a base of 8 ft. What is its height?
Answer: ______ ft
Find the area of a triangle with a base of 9 cm and a height of 4 cm.
Answer: ______ cm²

Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)

Find the area of a trapezoid with bases of 5 in and 9 in, and a height of 4 in.
Answer: ______ in²
A trapezoid has an area of 35 cm², a height of 5 cm, and one base of 6 cm. Find the length of the other base.
Answer: ______ cm
Find the area of a trapezoid with bases of 8 m and 11 m, and a height of 7 m.
Answer: ______ m²
A trapezoid has an area of 60 ft², bases of 10 ft and 14 ft. What is its height?
Answer: ______ ft

End of Test – Please check your work before submitting.

Answer Key (For Teacher Use)

Section 1:

5:12
7:18
10
24
70
20

Section 2:
7. 2
8. 30
9. 0.375, 37.5%
10. 9/20, 45%
11. 24
12. 30

Section 3:
13. 3
14. -4
15. -10
16. -7
17. -7
18. -12
19. 9
20. 9
21. -14
22. -15
23. -20
24. -18
25. 14
26. -6
27. 4
28. -5
29. 9
30. -25
31. -15
32. -15
33. ¼ or 0.25
34. -0.7
35. -4
36. 3

Section 4:
37. 7
38. 9
39. 20
40. 7
41. $n > 12$ n>12
42. $k \leq 5$ k≤5
43. $x > - 5$ x>−5
44. $h \geq 48$ h≥48
45. $3 s \leq 30$ 3s≤30 or $s \leq 10$ s≤10
46. $a \leq 5$ a≤5
47. $b > 10$ b>10
48. $x \leq - 3$ x≤−3
49. $y < 8$ y<8
50. $m \geq 3$ m≥3
51. $c \leq 6$ c≤6

Section 5:
52. 60
53. 6
54. 30
55. 6
56. 18
57. 28
58. 8
59. 66.5
60. 5