Band 8 – Page 7

Number, NAP-I4-NC11

The diameter of a pinhead is 0.0023 mm.

Which shows this measurement written in scientific notation?

`2.3 xx 10^(−3)`	`2.3 xx 10^(−2)`	`2.3 xx 10^2`	`2.3 xx 10^3`

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`2.3 xx 10^(−3)\ text{mm}`

Show Worked Solution

`0.0023 = 2.3 xx 10^(−3)\ text{mm}`

Geometry, NAP-I4-CA20

Lines `AB` and `CD` are parallel.

Line `EF` intersects lines `AB` and `CD` as shown.

Which pair of angles are equal?

	`/_ FQA and /_ FQB`
	`/_ CPQ and /_ AQE`
	`/_ DPE and /_ DPF`
	`/_ CPQ and /_ PQB`

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`/_ CPQ and /_ PQB`

Show Worked Solution

`/_ CPQ and /_ PQB`

`text{(Alternate angles)}`

Probability, NAP-I4-CA19

Zilda asked 45 eighteen year olds whether they work, go to school, do both or do neither.

The Venn diagram shows the results.

What is the probability that a person randomly selected from the group goes to school and works, rounded to three decimal places?

`0.778`	`0.158`	`0.093`	`0.079`	`0.067`

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`0.067`

Show Worked Solution

`P\ text{(go to school and works)}`

`= 3/45`

`= 0.067`

Measurement, NAP-I4-CA17

A wheel on a bicycle has a diameter of 530 mm.

The wheel turns 12 times.

Approximately how many metres has the bicycle travelled?

`text(6 m)`	`text(20 m)`	`text(40 m)`	`text(399 m)`

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`20\ text(m)`

Show Worked Solution

`text(Diameter)`	`=530\ text(mm)`
	`=0.530\ text(m)`

`:.\ text{Distance (12 circumferences)}`

`= 12 xx (pi xx d)`

`= 12 xx (pi xx 0.530)`

`= 19.98…\ text(m)`

`=20\ text{m (nearest m)}`

Geometry, NAP-I4-CA16 SA

What is the size of angle `x?`

degrees

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`135^@`

Show Worked Solution

`x`	`= 180 – 45`
	`= 135^@`

Number, NAP-I4-CA15

The table below lists the original price and the amount of discount of a pair of jeans at four different shops.

Which shop has the lowest sale price for the jeans?

`text(A)`	`text(B)`	`text(C)`	`text(D)`

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`text(Shop B)`

Show Worked Solution

`text(Consider the sale price at each shop:)`

`text(A)`	`= 20 – (25text{%} xx 20) = $15`
`text(B)`	`= 21 – (1/3 xx 21) = $14`
`text(C)`	`= 18 – (20 text{%} xx 18) = $14.40`
`text(D)`	`= 17 – 2 = $15`

`:.\ text(Shop B has the lowest sale price.)`

Measurement, NAP-I4-CA14 SA

A class is making ice-cubes for a science experiment.

One ice-cube container requires 0.35 litres of water to fill it.

How many millilitres of water would a student need to fill up one container?

millilitres

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`350\ text(millilitres)`

Show Worked Solution

`text(Volume)`	`= 0.35 xx 1000`
	`= 350\ text(millilitres)`

Number, NAP-I4-CA13

A christmas pudding recipe uses 3 cups of sugar for every 4 cups of sultanas.

Select the correct combination of sugar and sultanas for this recipe.

	`1/3` cup of sugar, `1/4` cup of sultanas
	`1` cup of sugar, `1.5` cups of sultanas
	`1.5` cups of sugar, `2` cups of sultanas
	`4` cups of sugar, `5` cups of sultanas

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`text(1.5 cups of sugar, 2 cups of sultanas.)`

Show Worked Solution

`text(Ratio)`	`= 3:4`
	`=1.5:2`

`:.\ text(1.5 cups of sugar, 2 cups of sultanas is)`

`text(in the correct ratio.)`

Statistics, NAP-I4-CA12 SA

Over 5 games, Ramesh recorded the following scores when playing cricket.

`28, \ 31, \ 33, \ 0, \ 18`

What was his mean score?

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`22`

Show Worked Solution

`text(Mean)`	`= (28 + 31 + 33 + 0 + 18)/5`
	`= 22`

Probability, NAP-I4-CA10

Kobe spins the arrow on the wheel to win a prize.

The arrow has an equal chance of landing on each section.

What is the probability that Kobe will win exactly $50?

`0.125`	`0.200`	`0.375`	`0.380`	`0.600`

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`0.375`

Show Worked Solution

`P text{(winning $50)} = 3/8 = 0.375`