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Year 12 Mathematics sample

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Question 1 of 5 Space and geometry

At a community garden stall, what is the straight-line distance between \((1,3)\) and \((9,18)\)?

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

Question 2 of 5 Number and arithmetic

For a local sports roster, the value \(y\) is directly proportional to \(x\). When \(x=4\), \(y=8\). What is \(y\) when \(x=5\)?

Direct proportion

x	y
4	8
5	?

A 10 B 9 C 40 D 13

Question 3 of 5 Measures and units

In a classroom floor-plan sketch, a block has mass 25 g and volume 5 cm³. What is its density?

Mass and volume of a block

Quantity	Value
Mass	25 g
Volume	5 cm^3

A 125 g/cm^3 B 30 g/cm^3 C 5 g/cm^3 D 1 g/cm^3

Question 4 of 5 Chance and data

During a house-points review, a spinner shows red on 3 of 4 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	1
Total	4

A \(\frac{15}{16}\) B \(\frac{3}{4}\) C \(\frac{9}{16}\) D \(\frac{3}{2}\)

Question 5 of 5 Number and arithmetic

In an index-laws question from a gold-team peer-marking exercise, simplify \(\frac{7^{6} \times 7^{12}}{7^2}\).

A \(7^{16}\) B \(7^{18}\) C \(7^{70}\) D \(7^{15}\)

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