Year 9 NAPLAN Numeracy Prep
Challenge yourself with NAPLAN-style questions covering algebra, Pythagoras, trigonometry basics, financial maths, statistics and probability.
Exam Tips for Year 9 Numeracy
Calculator sections: Some questions allow an on-screen calculator, others do not. Practise mental maths strategies for non-calculator sections.
What Year 9 NAPLAN Numeracy Tests
Algebra
Expanding, factorising, solving linear equations, substitution, graphing linear relationships.
Pythagoras' Theorem
Finding unknown sides in right-angled triangles using a² + b² = c².
Trigonometry Basics
SOH CAH TOA — using sine, cosine and tangent to find sides and angles.
Financial Maths
Percentages, simple interest, discounts, profit/loss, GST calculations.
Statistics
Mean, median, mode, range, interpreting data displays, misleading graphs.
Probability
Theoretical probability, two-step experiments, tree diagrams, complementary events.
Knowledge Check
NAPLAN Style10 questions mixing calculator and non-calculator sections.
Question 1
Non-calculator — AlgebraExpand and simplify: 3(2x - 4) + 5x
Question 2
Calculator allowed — PythagorasA right-angled triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
Question 3
Non-calculator — Financial MathsA shop marks up items by 40%. If a shirt costs the shop $25, what is the selling price?
Question 4
Calculator allowed — TrigonometryIn a right-angled triangle, the angle is 35° and the adjacent side is 12 cm. Using cos(35°) = 0.819, find the hypotenuse. Round to one decimal place.
Question 5
Non-calculator — ProbabilityA fair six-sided die is rolled twice. What is the probability of getting a 6 on both rolls?
Question 6
Calculator allowed — Simple InterestEmma invests $2,000 at 4% per annum simple interest for 3 years. How much interest does she earn?
Question 7
Non-calculator — AlgebraSolve: 4(x + 3) = 2(x + 9)
Question 8
Calculator allowed — StatisticsThe scores of 8 students on a test are:
56, 72, 68, 85, 91, 78, 64, 82
What is the mean score (to 1 decimal place)?
Question 9
Non-calculator — Linear GraphsThe equation of a line is y = 2x - 3. What is the y-intercept?
Question 10
Calculator allowed — Pythagoras in ContextA ladder leans against a wall. The foot of the ladder is 1.5 m from the wall, and the ladder reaches 4 m up the wall. How long is the ladder? Round to 1 decimal place.
Key Concepts Summary
- ●Algebra: Expand brackets first, collect like terms, then solve. Always check by substituting back.
- ●Pythagoras: a² + b² = c² (where c is the hypotenuse). Know 3-4-5, 5-12-13, 6-8-10 triples.
- ●Trigonometry: SOH CAH TOA. Identify which sides you have and which you need to find.
- ●Simple interest: I = PRT. Make sure rate is a decimal and time is in years.
- ●Probability: For independent events, multiply. P(A and B) = P(A) x P(B).
- ●Linear graphs: y = mx + c. m = gradient (slope), c = y-intercept (where line crosses y-axis).