Year 9 NAPLAN Numeracy Prep — Set 2
This is a second practice set with 10 brand-new questions covering real numbers & surds, financial maths, algebra, linear and non-linear relationships, measurement, trigonometry, similarity, 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 (Set 2)
NAPLAN Style10 brand-new questions covering a fresh mix of topics, mixing calculator and non-calculator sections.
Question 1
Non-calculator — Real Numbers & SurdsSimplify: √72
Question 2
Calculator allowed — Financial MathematicsBen invests $1,500 at 5% per annum compound interest, compounded annually, for 2 years. What is the total value of the investment, to the nearest cent?
Question 3
Non-calculator — Expanding & FactorisingFactorise: x² + 7x + 10
Question 4
Non-calculator — Linear RelationshipsA line passes through the points (1, 2) and (4, 11). What is the gradient of the line?
Question 5
Non-calculator — Non-Linear RelationshipsWhat is the y-intercept of the parabola y = x² - 4x - 5?
Question 6
Calculator allowed — Surface Area & VolumeA rectangular prism (box) has length 8 cm, width 5 cm and height 3 cm. What is its volume?
Question 7
Calculator allowed — TrigonometryIn a right-angled triangle, the hypotenuse is 15 cm and one angle is 40°. Using sin(40°) = 0.643, find the length of the side opposite the 40° angle. Round to one decimal place.
Question 8
Calculator allowed — SimilarityTriangle ABC is similar to triangle DEF. Side AB = 6 cm corresponds to side DE = 9 cm. If side BC = 8 cm, what is the length of the corresponding side EF?
Question 9
Non-calculator — StatisticsHere are the ages (in years) of 7 people in a family:
12, 45, 8, 39, 41, 15, 10
What is the median age?
Question 10
Non-calculator — ProbabilityA bag contains 4 red marbles and 6 blue marbles. A marble is drawn at random, its colour noted, then put back in the bag before a second marble is drawn. What is the probability that both marbles drawn are red?
Key Concepts Summary
- ●Surds: To simplify √n, find the largest perfect square factor of n and split it out, e.g. √72 = √36 x √2 = 6√2.
- ●Compound interest: A = P(1 + r)^n. Unlike simple interest, compound interest is calculated on the growing balance each year.
- ●Factorising: For x² + bx + c, find two numbers that multiply to c and add to b. Always check your answer by expanding it back out.
- ●Linear relationships: Gradient = rise ÷ run = (y2 - y1) ÷ (x2 - x1).
- ●Non-linear relationships: For a parabola y = x² + bx + c, the y-intercept is always c (substitute x = 0).
- ●Surface area & volume: Volume of a rectangular prism = length x width x height. Do not confuse volume with surface area.
- ●Trigonometry: SOH CAH TOA. Identify which sides and angles you have, and which you need to find.
- ●Similarity: Find the scale factor from a known pair of corresponding sides, then multiply (not divide) to find an unknown side.
- ●Statistics & probability: Sort data before finding the median. For independent events, multiply probabilities: P(A and B) = P(A) x P(B).