AzM2 Grade 6 Mathematics 2 — Questions and Answers

Question 1: What is the Greatest Common Factor (GCF) of 24 and 36?

6
8
12 (Correct answer)
18

Correct answer: 12

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. GCF = 12.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 3, 4, 6, 12. Greatest = 12 (C). Alternatively: 24 = 2³ × 3; 36 = 2² × 3². GCF = 2² × 3 = 12. Answer C is correct.

Question 2: The coordinates of a point are (-3, 4). In which quadrant is this point located?

Quadrant I
Quadrant II (Correct answer)
Quadrant III
Quadrant IV

Correct answer: Quadrant II

Quadrant II has negative x-values and positive y-values. (-3, 4) has x = -3 (negative) and y = 4 (positive), so it is in Quadrant II.

Coordinate plane quadrants: QI: (+, +); QII: (-, +); QIII: (-, -); QIV: (+, -). For (-3, 4): x = -3 (negative), y = 4 (positive) → Quadrant II (B). Students often confuse quadrants — remember they go counterclockwise from the upper right: I, II, III, IV. Answer B is correct.

Question 3: A school collected 360 cans for a food drive over 6 days, collecting the same number each day. Write an equation and solve: how many cans were collected each day?

54 cans
60 cans (Correct answer)
66 cans
72 cans

Correct answer: 60 cans

Equation: 6d = 360. Solve: d = 360 ÷ 6 = 60 cans per day.

Let d = cans per day. Equation: 6d = 360. Divide both sides by 6: d = 360 ÷ 6 = 60. Answer B is correct. Check: 60 × 6 = 360 ✓. This tests writing and solving one-step equations from word problems, a key 6th-grade algebra standard.

Question 4: What is the area of a triangle with a base of 14 cm and a height of 9 cm?

126 cm²
63 cm² (Correct answer)
46 cm²
23 cm²

Correct answer: 63 cm²

Area = ½ × base × height = ½ × 14 × 9 = ½ × 126 = 63 cm².

Triangle area = ½ × b × h = ½ × 14 × 9 = ½ × 126 = 63 cm². Answer B is correct. Answer A (126 cm²) is the result of forgetting to multiply by ½ (or divide by 2) — the most common error. The factor of ½ is essential because a triangle is half of a parallelogram.

Question 5: A data set has values: 12, 15, 11, 18, 14. What is the mean?

14 (Correct answer)
15
13
16

Correct answer: 14

Mean = sum ÷ count = (12 + 15 + 11 + 18 + 14) ÷ 5 = 70 ÷ 5 = 14.

Mean (average) = sum of all values ÷ number of values. Sum: 12 + 15 + 11 + 18 + 14 = 70. Count: 5 values. Mean = 70 ÷ 5 = 14. Answer A is correct. The mean is used to find the 'typical' value in a data set and is a core 6th-grade statistics concept.

Question 6: Which ratio is equivalent to 3:4?

6:9
9:12 (Correct answer)
12:15
4:3

Correct answer: 9:12

9:12 = 9/12 = 3/4 when simplified by dividing both by 3. So 9:12 is equivalent to 3:4.

Equivalent ratios are found by multiplying both terms by the same factor. 3:4 × 3 = 9:12. Verify: 9/12 = 3/4 ✓. Answer B is correct. 6:9 = 2:3 (not 3:4). 12:15 = 4:5 (not 3:4). 4:3 is the reciprocal of 3:4, not equivalent. Answer B is correct.

AzM2 Grade 6 Mathematics 2

What is the Greatest Common Factor (GCF) of 24 and 36?