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Year 10 Mathematics sample

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Question 1 of 5 Space and geometry

For a swimming carnival roster, what is the straight-line distance between \((2,3)\) and \((10,18)\)?

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

Question 2 of 5 Number and arithmetic

During a school athletics tally, the value \(y\) is directly proportional to \(x\). When \(x=2\), \(y=4\). What is \(y\) when \(x=3\)?

Direct proportion

x	y
2	4
3	?

A 6 B 5 C 12 D 7

Question 3 of 5 Measures and units

In a classroom floor-plan sketch, a block has mass 15 g and volume 5 cm³. What is its density?

Mass and volume of a block

Quantity	Value
Mass	15 g
Volume	5 cm^3

A 75 g/cm^3 B 20 g/cm^3 C 2 g/cm^3 D 3 g/cm^3

Question 4 of 5 Chance and data

During a school athletics tally, a spinner shows red on 2 of 6 equal sections. It is spun twice. What is the probability of at least one red?

Spinner spun twice

Outcome	Equal sections
Red	2
Not red	4
Total	6

A \(\frac{1}{3}\) B \(\frac{5}{9}\) C \(\frac{1}{9}\) D \(\frac{2}{3}\)

Question 5 of 5 Number and arithmetic

In an index-laws question from a blue-team peer-marking exercise, simplify \(\frac{3^{6} \times 3^{12}}{3^2}\).

A \(3^{18}\) B \(3^{16}\) C \(3^{70}\) D \(3^{15}\)

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