Year 9 NAPLAN numeracy requires confident reasoning across algebra, measurement, geometry, and statistics. Strong practice helps students move from recognising topics to solving unfamiliar problems efficiently.
Try each question first, then open the worked solution to check your answer and see how to reach it.
1.If a car travels at 60km/h, how far does it travel in 2.5 hours?
Answer: B (150km)
Use distance = speed × time. The car travels 60 km every hour, so in 2.5 hours it travels 60 × 2.5. Split the time: 60 × 2 = 120 km, plus 60 × 0.5 = 30 km, giving 150 km. The answer 120 km ignores the extra half hour, so always include every part of the time given.
2.Expand: 3(x + 4)
Answer: C (3x + 12)
Expanding means multiplying the number outside the brackets by every term inside. 3 × x = 3x and 3 × 4 = 12, so 3(x + 4) = 3x + 12. The answer 3x + 4 only multiplies the first term, which is the most common error. Check by substituting x = 1: 3(1 + 4) = 15 and 3(1) + 12 = 15.
3.Find the hypotenuse of a right-angled triangle with sides 3cm and 4cm.
Answer: A (5cm)
Use Pythagoras' theorem: the square of the hypotenuse equals the sum of the squares of the other two sides. 3² + 4² = 9 + 16 = 25, and the square root of 25 is 5, so the hypotenuse is 5 cm. This 3-4-5 triangle is worth memorising. Adding 3 + 4 = 7 cm skips the squaring step.
4.What is the gradient of the line y = 2x + 3?
Answer: A (2)
A straight line written as y = mx + c has gradient m and y-intercept c. In y = 2x + 3, the number multiplying x is 2, so the gradient is 2. That means y increases by 2 every time x increases by 1. The 3 is the y-intercept, where the line crosses the y-axis, not the gradient.
5.Factorise: x² + 5x + 6
Answer: A ((x+2)(x+3))
To factorise x² + 5x + 6, find two numbers that multiply to give 6 and add to give 5. The pair 2 and 3 works: 2 × 3 = 6 and 2 + 3 = 5. So x² + 5x + 6 = (x + 2)(x + 3). Check by expanding: x² + 3x + 2x + 6 = x² + 5x + 6.
6.Calculate the simple interest on $1000 at 5% p.a. for 3 years.
Answer: C ($150)
Simple interest = principal × rate × time. Here that is $1000 × 0.05 × 3. One year of interest is 5% of $1000 = $50, and three years is 3 × $50 = $150. The answer $50 is only one year. Simple interest is calculated on the original amount each year, unlike compound interest, which grows on the new total.
7.Solve for x: 3(x − 2) = 2x + 5
Answer: C (11)
Expand the brackets first: 3(x − 2) = 3x − 6, so the equation becomes 3x − 6 = 2x + 5. Subtract 2x from both sides: x − 6 = 5. Add 6 to both sides: x = 11. Check by substituting: 3(11 − 2) = 27 and 2(11) + 5 = 27, so both sides match.
8.The price of a phone increased from $400 to $460. What was the percentage increase?
Answer: C (15%)
Percentage increase = increase ÷ original amount × 100. The increase is $460 − $400 = $60. Divide by the original price: 60 ÷ 400 = 0.15, which is 15%. The answer 13% comes from dividing by the new price ($460) instead of the original. Always divide by the starting value when finding a percentage change.
9.What is the volume of a cylinder with radius 3 cm and height 10 cm? (Use π ≈ 3.14)
Answer: C (282.6 cm³)
The volume of a cylinder is πr²h: the area of the circular base multiplied by the height. The base area is 3.14 × 3² = 3.14 × 9 = 28.26 cm². Multiply by the height: 28.26 × 10 = 282.6 cm³. The answer 94.2 forgets to square the radius, and 188.4 is the curved surface area (2πrh).
10.A bag holds 4 red, 5 blue and 3 green marbles. One marble is chosen at random. What is the probability that it is not blue?
Answer: B (7/12)
There are 4 + 5 + 3 = 12 marbles in total. 'Not blue' means red or green, which is 4 + 3 = 7 marbles. So the probability is 7/12. You can also use the complement: P(blue) = 5/12, so P(not blue) = 1 − 5/12 = 7/12. The answer 5/12 is the chance of picking blue.
Practise multi-step problems where the first operation is not obvious.
Review data and graph questions separately from calculation-heavy questions.
Ask students to justify why an answer is reasonable.
Important topics include algebra, rates and ratios, measurement, geometry, statistics, probability, and multi-step problem solving.
Practice should use similar wording, mixed topics, and realistic difficulty so students build transfer skills for unfamiliar questions.