YEAR 9 · REAL NUMBERS

Topic review.

Connect the key ideas, then choose a practice paper.

01 / QUICK RECAP

Connect the ideas.

Rational numbers are exact integer fractions; terminating and recurring decimals are rational.
A positive integer root is rational exactly when its input is a perfect square.
Use neighbouring squares and positive squared trial values to locate roots.
Negative positions reverse the order of their positive magnitudes.
Retain exact values until final rounding and include units.
Group complete root inputs and denominators, then check digital answers against an estimate.

02 / PRACTICE TESTS

Choose a paper and show your working.

Real numbers — Practice test 1
Classification, number-line order, root estimates and exact values.
16 questions · 38 marks · 50 minutes · Scientific calculator
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Real numbers — Practice test 2
Explain classifications and compare exact values with rounded measurements.
16 questions · 38 marks · 50 minutes · Scientific calculator
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Real numbers — Applications test
Use roots, pi, bounds and rounding to make practical decisions.
16 questions · 43 marks · 60 minutes · Scientific calculator
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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 9 real-number classification and applications; root bounds and sensible digital approximation. Full surd manipulation is developed in Year 10.