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Year 9 NAPLAN Preparation

Numeracy Study Notes
Linear Equations • Rates • Probability • Data • Measurement
Grade 9 | 2026

📐 1. Linear Equations

Solving Equations

Use inverse operations. Whatever you do to one side, do to the other.

3x + 5 = 20
3x = 20 - 5
3x = 15
x = 5

Writing Equations

"5 times a number plus 3 equals 18" → 5x + 3 = 18
Write: "A number divided by 2 minus 4 equals 6"

📊 2. Rates & Ratios

Understanding Rates

Rate compares two quantities with different units.

Speed = 60 km/h (distance ÷ time)
Cost = $3.50 per litre (price ÷ amount)

Using Rates

If 2 kg costs $10, then 5 kg costs $25 (× 2.5)
If you travel 100km in 2 hours, what is your average speed?

🎲 3. Probability

Probability Scale

WordsFractionDecimalPercentage
Impossible000%
Unlikely1/40.2525%
Even chance1/20.550%
Likely3/40.7575%
Certain11100%

Calculating Probability

P(event) = Number of favourable outcomes ÷ Total outcomes

Rolling a 4 on a die: 1/6
Drawing an Ace from 52 cards: __________

📈 4. Data & Statistics

Mean, Median, Mode

Data: 2, 3, 3, 5, 7, 8, 10
Mean = 38 ÷ 7 = 5.4 | Median = 5 | Mode = 3

Interpreting Data

Read graphs carefully. Note scales, labels, and trends.

📏 5. Measurement

Area & Volume

ShapeArea FormulaVolume Formula
Rectanglelength × width-
Triangle½ × base × height-
Circleπr²-
Rectangular prism-l × w × h
NAPLAN Year 9 | Numeracy