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Year 11 Mathematics sample

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Question 1 of 5 Space and geometry

For a weekend training session, what is the straight-line distance between \((3,3)\) and \((11,18)\)?

A 23 units B 7 units C 18 units D 17 units

Question 2 of 5 Number and arithmetic

At a community garden stall, the value \(y\) is directly proportional to \(x\). When \(x=3\), \(y=6\). What is \(y\) when \(x=4\)?

Direct proportion

x	y
3	6
4	?

A 7 B 24 C 8 D 10

Question 3 of 5 Measures and units

At a weekend netball draw, a block has mass 20 g and volume 5 cm³. What is its density?

Mass and volume of a block

Quantity	Value
Mass	20 g
Volume	5 cm^3

A 100 g/cm^3 B 25 g/cm^3 C 1 g/cm^3 D 4 g/cm^3

Question 4 of 5 Chance and data

For a swimming carnival roster, a spinner shows red on 3 of 8 equal sections. It is spun twice. What is the probability of at least one red?

Spinner spun twice

Outcome	Equal sections
Red	3
Not red	5
Total	8

A \(\frac{3}{8}\) B \(\frac{9}{64}\) C \(\frac{39}{64}\) D \(\frac{3}{4}\)

Question 5 of 5 Number and arithmetic

In a same-base-powers problem from a green-team skills-checkpoint sheet, simplify \(\frac{5^{6} \times 5^{12}}{5^2}\).

A \(5^{18}\) B \(5^{70}\) C \(5^{16}\) D \(5^{15}\)

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