NAPLAN NAPLAN Numeracy Year 9 Practice 1 — Questions and Answers
Question 1: A rectangular swimming pool is 25 m long and 10 m wide. What is the perimeter of the pool?
- 35 m
- 50 m
- 70 m (Correct answer)
- 250 m
Correct answer: 70 m
Perimeter = 2 × (length + width) = 2 × (25 + 10) = 2 × 35 = 70 m
The perimeter of a rectangle is P = 2 × (length + width). Here, P = 2 × (25 + 10) = 2 × 35 = 70 m. Note that 250 m² would be the area, not the perimeter.
Question 2: A store sells a jacket for $180. During a sale, the price is reduced by 25%. What is the sale price?
- $45
- $135 (Correct answer)
- $145
- $155
Correct answer: $135
25% of $180 = $45. Sale price = $180 − $45 = $135
To find 25% of $180: 0.25 × 180 = $45. This is the discount amount. Sale price = $180 − $45 = $135. Alternatively, the sale price is 75% of the original: 0.75 × $180 = $135.
Question 3: The table shows students who chose each sport: Cricket: 12, Football: 18, Netball: 15, Swimming: 9, Tennis: 6. What percentage of students chose Football?
- 25%
- 30% (Correct answer)
- 35%
- 40%
Correct answer: 30%
Total = 12+18+15+9+6 = 60. Football % = (18 ÷ 60) × 100 = 30%
Total students = 12 + 18 + 15 + 9 + 6 = 60. Percentage who chose Football = (18 ÷ 60) × 100 = 0.30 × 100 = 30%.
Question 4: Solve for x: 3x + 7 = 22
- x = 3
- x = 4
- x = 5 (Correct answer)
- x = 6
Correct answer: x = 5
3x = 22 − 7 = 15, so x = 15 ÷ 3 = 5
Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Check: 3(5) + 7 = 22 ✓
Question 5: The mean of five test scores is 72. Four of the scores are 65, 78, 80 and 69. What is the fifth score?
- 68 (Correct answer)
- 70
- 72
- 74
Correct answer: 68
Sum of 5 scores = 72 × 5 = 360. Sum of 4 known = 65+78+80+69 = 292. Fifth = 360 − 292 = 68
If the mean of 5 scores is 72, then total sum = 72 × 5 = 360. Sum of the four known scores = 65 + 78 + 80 + 69 = 292. Fifth score = 360 − 292 = 68.
Question 6: A cylinder has a radius of 4 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
- 125.6 cm³
- 251.2 cm³
- 502.4 cm³ (Correct answer)
- 1256 cm³
Correct answer: 502.4 cm³
V = π × r² × h = 3.14 × 16 × 10 = 502.4 cm³
V = π × r² × h = 3.14 × 4² × 10 = 3.14 × 16 × 10 = 502.4 cm³. Remember to square the radius (not the diameter).
Question 7: A map uses a scale of 1 : 50 000. On the map, two towns are 6 cm apart. What is the actual distance in kilometres?
- 3 km (Correct answer)
- 6 km
- 30 km
- 300 km
Correct answer: 3 km
Actual = 6 cm × 50 000 = 300 000 cm = 3 000 m = 3 km
Actual distance = 6 × 50 000 = 300 000 cm. Convert: 300 000 cm ÷ 100 = 3 000 m ÷ 1 000 = 3 km.
NAPLAN NAPLAN Numeracy Year 9 Practice 1
A rectangular swimming pool is 25 m long and 10 m wide.
What is the perimeter of the pool?