Band 8

Geometry, NAP-L4-CA14v1

Hannah is walking in the city, heading due East.

She makes quarter turn left and keeps walking.

After this, Hannah makes another quarter turn left and continues to walk.

In what direction is Hannah now walking?

North	South	East	West

Show Answers Only

`text(West)`

Show Worked Solution

`text{Directions (in order): East → North → West}`

`:.\ text(Hannah is walking due West.)`

Measurement, NAP-I4-CA17v1

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

The wheel turns 3 times.

Approximately how many metres has the bicycle travelled?

`text(2 m)`	`text(5 m)`	`text(10 m)`	`text(25 m)`

Show Answers Only

`5\ text(m)`

Show Worked Solution

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

`:.\ text{Distance (3 rotations)}`

`= 3 xx (pi xx d)`

`= 3 xx (pi xx 0.530)`

`= 4.99…\ text(m)`

`=5\ text{m (nearest m)}`

Measurement, NAP-F4-CA16v1

A car tyre has a circumference of 120 cm.

Which of these is closest to the radius of the tyre?

`9.5\ text(cm)`	`19.1\ text(cm)`	`38.0\ text(cm)`	`753.6\ text(cm)`

Show Answers Only

`19.1\ text(cm)`

Show Worked Solution

`C`	`= 2 pi r`
`120`	`=2 xx pi xx r`
`r`	`=120/(2 pi)`
	`~~19.1\ text(cm)`

Number, NAP-L4-CA27 SA v1

Gary is painting his house over 3 days.

He paints `1/3` of the house on the first day.
He paints `5/12` of the house on the second day.

In order to finish, what percentage of the house does Gary need to paint on the third day?

Show Answers Only

`25 text(%)`

Show Worked Solution

`text(Fraction painted)`	`= 1/3 + 5/12`
	`= (4 + 5)/12`
	`= 9/12`
	`=3/4`
	`=75 text(%)`

`:. 25 text(% needs to be painted on the third day.)`

Number, NAP-F3-NC25v1

`5/6+ 1/4 = ?`

`1 1/24`	`5/24`	`1 5/24`	`11/12`

Show Answers Only

`1 1/24`

Show Worked Solution

`5/6 + 1/4`	`=20/24 + 6/24`
	`=26/24`
	`= 1 1/12`

Number, NAP-F3-CA22v1

Which number will complete this number sentence correctly?

`2.5 =`

`xx 4.5`

`4/7`	`5/9`	`1 1/5`	`3 1/7`

Show Answers Only

`5/9`

Show Worked Solution

`2.5`	`= n xx 4.5`
`5/2`	`=n xx 9/2`
`n`	`=5/2 -: 9/2`
	`=5/2 xx 2/9`
	`=5/9`

Number, NAP-B3-CA22 SA v1

This calculation gives the population of quokkas on Rottnest Island in April 2021.

`(74.219 - 7.019)/0.08`

What was the population in April 2021?

quokkas

Show Answers Only

`840`

Show Worked Solution

`(74.219 – 7.019)/0.08`	`= 67.2/0.08`
	`= 840\ text(quokkas)`

Number, NAP-C3-CA22v1

Which of these numbers is a multiple of both 3 and 11?

`616`	`666`	`3113`	`3333`

Show Answers Only

`3333`

Show Worked Solution

`text(Test if each option is divisible by both 3 and 11.)`

`3333/4 = 1111`

`3333/11 = 303`

`:. 3333\ text(is divisible by 4 and 11.)`

Number and Algebra, NAP-D2-31 SA v1

A ticket to Leyland Brothers World for two adults costs $42 in total.

A ticket to Leyland Brothers World for one child is one third the cost of an adult ticket.

What is the cost of a ticket for one child?

Show Answers Only

`$7`

Show Worked Solution

`text(C)text(ost of 1 adult ticket)`

`= 42 -: 2`

`= $21`

`:.\ text(C)text(ost of 1 child ticket)`

`= 1/3 xx 21`

`= $7`

Algebra, NAPX-p115106v02

A broadband provider offers 3 types of broadband plans: Standard, High Speed and Fibre To The Door.

The Standard plan costs $50.40 less than the High Speed plan.

The Standard plan costs $72.60 less than the Fibre To The Door plan.

Which of these equations correctly states the cost of the High Speed plan?

	Cost of High Speed plan = Cost of Fibre To The Door plan – $72.60
	Cost of High Speed plan = Cost of Fibre To The Door plan – $50.40
	Cost of High Speed plan = Cost of Fibre To The Door plan – $32.80
	Cost of High Speed plan = Cost of Fibre To The Door plan – $22.20

Show Answers Only

`text{C}text{ost of High Speed plan = Cost of Fibre To The Door plan − $22.20}`

Show Worked Solution

`text{Fibre To The Door plan cost over High Speed plan}`

`= 72.60 – 50.40`

`= $22.20`

`:.\ text{C}text{ost of High Speed plan = Cost of Fibre To The Door plan − $22.20}`

Algebra, NAPX-p115106v01

A food delivery company provides 3 levels of service: Regular, Moderate and Premium.

Regular service costs $15.50 less than Moderate service.

Regular service costs $45.80 less than Premium service.

Which of these equations correctly represents the cost of Moderate service?

	Cost of Moderate Service = Cost of Premium service – $15.50
	Cost of Moderate Service = Cost of Premium service – $30.30
	Cost of Moderate Service = Cost of Premium service – $20.70
	Cost of Moderate Service = Cost of Premium service – $45.80

Show Answers Only

`text{C}text{ost of Moderate Service = Premium service – $30.30}`

Show Worked Solution

`text{Extra cost of Premium service over Moderate service}`

`= 45.80 – 15.50`

`= $30.30`

`:.\ text{C}text{ost of Moderate Service = Premium service – $30.30}`

Algebra, NAPX-p170065v02

Ashley makes $152 for every 19 beauty kits she sells online.

Which expression shows how much Ashley would earn if she sells `k` beauty kits?

	`(19 × 152) ÷ k`
	`(152 ÷ 19) × k`
	`(19 ÷ 152) × k`
	`(152 + 19) ÷ k`

Show Answers Only

`(152 ÷ 19) xx k`

Show Worked Solution

`152\ → 19\ text(kits)`

`152 -: 19 → \ text(1 kit)`

`:. (152 ÷ 19) xx k\ → \ k\ text(kits)`

Algebra, NAPX-p170065v01

A salesman earns $84 for every 7 litres of paint he sells.

Which expression shows how much would he would earn for selling `x` litres?

	`(84 × 7) ÷ x`
	`(84 ÷ 7) ÷ x`
	`(84 ÷ 7) × x`
	`(84 - 7) × x`

Show Answers Only

`(84 ÷ 7) xx x`

Show Worked Solution

`84\ → 7\ text(litres)`

`84 -: 7 → \ text(1 litre)`

`:. (84 ÷ 7) xx x\ → \ x\ text(litres)`

Geometry, NAPX-p170037v02

In the diagram below, line XYZ is a straight line.

What is the measurement of angle XYS?

	31°
	36°
	47°
	103°

Show Answers Only

`31^@`

Show Worked Solution

`text{Sum of angles in triangle} = 180^@`

`angle ZYT`	`= 180 – 102 – 42`
	`= 36^@`

`angle XYZ\ text{(straight line)} = 180^@`

`angle XYS`	`= 180 – 113 – 36`
	`= 31^@`

`therefore angle XYS = 31^@`

Geometry, NAPX-p170037v01

From the diagram shown below, Line ABC is a straight line.

What is the size of angle DBC?

	63°
	93°
	117°
	297°

Show Answers Only

`117^@`

Show Worked Solution

`text{Sum of angles in triangle} = 180^@`

`angle DBA`	`= 180 – 53 – 64`
	`= 63^@`

`angle ABC\ text{(straight line)} = 180^@`

`angle DBC`	`= 180 – 63`
	`= 117^@`

Statistics, NAPX-p108432v02

The graph below represents data gathered from 9 professional workers.

What kind of data could be represented in the graph shown above?

	Vertical Axis	Horizontal Axis
	Age	Salary
	Kind of Job	Salary
	Name of Company	Age
	Favourite food	Years of Experience

Show Answers Only

`text{Vertical Axis: Age}`

`text{Horizontal Axis: Salary}`

Show Worked Solution

`text(Age and Salary.)`

`text(Each data category needs to have a number of)`

`text(possibilities and the chosen pair need a general)`

`text(relationship where one moves higher at the same )`

`text(time as the other. Age and slary is the most likely.)`

`text{The graph represents varying numerical values. }`

Statistics, NAPX-p108432v01

Cyrene collected some data from 10 of her friends.

The graph represents the data gathered by Cyrene but no labels are used

What kind of data could Cyrene be showing in her graph?

	Vertical Axis	Horizontal Axis
	Age	Name
	Gender	Weight
	Height	Favourite food
	Height	Weight

Show Answers Only

`text{Vertical Axis: Height}`

`text{Horizontal Axis: Weight}`

Show Worked Solution

`text(Height and Weight.)`

`text(Each data category needs to have a number of)`

`text(possibilities and the chosen pair need a general)`

`text(relationship where one moves higher at the same )`

`text(time as the other.)`

`text(Height and weight is the most likely.)`

Geometry, NAPX-p110293v02

A quadrilateral FGHI is moved to a new position labelled LMJK.

Which of these processes resulted in the new position of the quadrilateral?

	Rotate quadrilateral FGHI 180° counter-clockwise about the origin.
	Reflect quadrilateral in the `y`-axis and then translate 8 units downward.
	Rotate quadrilateral FGHI 90° clockwise about the origin.
	Reflect quadrilateral FGHI in the `x`-axis and then translate 9 units to the left.

Show Answers Only

`text{Reflect triangle ABC in the}\ y text{-axis and then translate 5 units downward}`

Show Worked Solution

`text{Reflection in the}\ x text{-axis}`

`FGHI \ rightarrow \ F′G′H′I′`

`text{Translate the triangle 9 units to the left}`

`F′G′H′I′\ rightarrow \ KJML`

Geometry, NAPX-p110293v01

The triangle ABC is moved to the new position labelled XYZ.

Which of these processes resulted in the new position of the triangle?

	Rotate triangle ABC 180° counter-clockwise about the origin.
	Reflect triangle ABC in the `y`-axis and then translate 5 units downward
	Reflect triangle ABC in the `x`-axis and then translate 9 units to the right
	Rotate triangle ABC 270° clockwise about the origin.

Show Answers Only

`text{Reflect triangle ABC in the}\ y text{-axis and then translate 5 units downward.}`

Show Worked Solution

`text{Reflection in the}\ y text{-axis:}`

`A B C \ rightarrow \ A′ B′ C′`

`text{Translate the triangle 5 units downward:}`

`A′ B′ C′ \ rightarrow \ X Y Z`

Algebra, NAPX-p109130v02

On a given day, the RSPCA had 87 lost dogs and cats in its care.

If there was 11 more dogs than cats, how many dogs were there?

	38
	49
	53
	76

Show Answers Only

`49`

Show Worked Solution

`text(Strategy 1)`

`text{There are 11 more dogs than cats.}`

`text{Let} \ D \ = \ text{number of dogs}`

`D+ (D – 11)`	`= 87`
`2D`	`= 98`
`:. D`	`= 49`

`text(Strategy 2)`

`text{Check each option:}`

`38 + (38 – 11) = 65 \ text{(Incorrect)}`

`49+ (49-11) = 87 \ text{(Correct)}`

`53 + (53 – 11) = 95 \ text{(Incorrect)}`

`76 + (76 – 11) = 141 \ text{(Incorrect)}`

Algebra, NAPX-p109130v01

A college marching band is made up of 102 people.

There are 24 more men than women.

How many women are there?

	30
	39
	65
	78

Show Answers Only

`39`

Show Worked Solution

`text(Strategy 1)`

`text{There are 24 more men than women.}`

`text{Let}\ \ W \ = \ text{number of women}`

`W + (W + 24)`	`= 102`
`2W`	`= 78`
`:. W`	`= 39`

`text(Strategy 2)`

`text{Check each option:}`

`30 + (30 + 24) = 84 \ text{(Incorrect)}`

`39 + (39 + 24) = 102 \ text{(Correct)}`

`65 + (65 + 24) = 154 \ text{(Incorrect)}`

`78 + (78 + 24) = 180 \ text{(Incorrect)}`

Number, NAPX-p169769v02

Select a number line which correctly represents the following values: 0.255, 0.65, 0.45 and 0.85.

Show Answers Only

Show Worked Solution

Number, NAPX-p169769v01

Select a number line which correctly represents the following values: 0.09, 0.755, and 0.85.

Show Answers Only

Show Worked Solution

`text{The line graph shows the smallest number from left to right.}`

Probability, NAPX-p110739v02 SA

Shawn has a bag that holds one blue ball, one red ball and one green ball.

Shawn picks one ball without looking, records its colour and puts it back in the bag.

He repeated this process 60 times and summarises the results in the table below.

What is the difference between the expected and actual number of red balls picked?

Show Answers Only

`3`

Show Worked Solution

`text(Probability of grabbing a red ball) = 1/3`

`text(Expected number of red balls)`	`= 1/3 xx 60`
	`= 20`

`:.\ text(Difference)`	`= 23 – 20`
	`= 3`

Probability, NAPX-p110739v01 SA

Elaine rolled a regular die 100 times.

She recorded if an even or odd number appeared each time.

The table below represents the recorded data.

What is the difference between the expected number of odd rolls to the actual odd rolls recorded?

Show Answers Only

`8`

Show Worked Solution

`text(Probability of odd number) = 3/6 = 50text(%)`

`text(Expected number of odd rolls)`

`= 50text(%) xx 100`

`= 50`

`:.\ text(Difference)`	`= 50 – 42`
	`= 8`

Number, NAPX-p109848v02

Which of these number has 7 in the thousandths place?

	167.23
	12.537
	42.6667
	96.873

Show Answers Only

`12.537`

Show Worked Solution

`text{Digits in the decimal places are (in order):}`

`text(Tenths, hundredths, thousandths, …)`

`:. 12.537\ text(is correct.)`

Number, NAPX-p109848v01

Which of these number has 3 in the hundredths place?

	12.35
	321.223
	0.253
	12.43

Show Answers Only

`text(12.43)`

Show Worked Solution

`text{Digits in the decimal places are (in order):}`

`text(Tenths, hundredths, thousandths, …)`

`text(Therefore, 12.43 is correct.)`

Algebra, NAPX-p109760v01

The corners of a certain parallelogram are shown below.

Which point in the graph represents the fourth point?

	`(1, – 4)`
	`(3, – 4)`
	`(– 4, 1)`
	`(4, – 3)`

Show Answers Only

`(1, – 4)`

Show Worked Solution

`text{Consider the top left point on the graph (– 1, – 1),}`

`text(The point below is 3 grid lines down and three left.)`

`text{Consider the top right point on the graph (4, – 1),}`

`text{The point (1, – 4) is 3 grid lines down and three left.}`

Measurement, NAPX-p106471v02 SA

Martin has a piece of wire that measures 1.32 metres.

He cuts off a 470 millimetre piece of it.

How long is the remaining wire in millimetres?

Show Answers Only

`850\ text(mm)`

Show Worked Solution

`text(Conversion: 1 metre = 1000 millimetres)`

`text(Length remaining)`	`= (1.320 xx 1000) – 468`
	`= 1320 – 470`
	`= 850\ text(mm)`

Measurement, NAPX-p106471v01 SA

Henry is 175 centimetre tall.

He stands on top of a 425 millimetres chair.

How tall is Henry now in centimetres?

Show Answers Only

`text(217.5 centimetres)`

Show Worked Solution

`text(Conversion: 10 millimetres = 1 centimetre)`

`text(Total height)`	`= (425 ÷ 10) + 175`
	`= 42.5 + 175`
	`= 217.5\ text(cm)`

Number, NAPX-p169124v02

Deirdre walks to work which is 6 km from her home.

She walks there at a constant speed of 5 kilometres per hour.

How many minutes does it take Deirdre to walk to work from her home?

`1 1/4`	`70`	`72`	`84`

Show Answers Only

`72\ text(minutes)`

Show Worked Solution

`text(Time)`	`= text(Distance)/(text(S)text(peed))`
	`= 6/5\ text(hours)`
	`= 6/5 xx 60\ text(minutes)`
	`= 72\ text(minutes)`

Number, NAPX-p169124v01

Oggy's gym is 3 kilometres away from his apartment.

He jogs there at a constant speed of 10 kilometres per hour.

How many minutes does it take for Oggy to get to the gym from his apartment?

`1 2/3`	`18`	`24`	`36`

Show Answers Only

`18\ text(minutes)`

Show Worked Solution

`text(Time)`	`= text(Distance)/(text(S)text(peed))`
	`= 3/10\ text(hr)`
	`= 3/10 xx 60\ text(minutes)`
	`= 18\ text(minutes)`

Probability, NAPX-p167310v04

A man spins a wheel with 5 different coloured sections and records which colour it lands on each time.

He repeats the process multiple times.

The table below shows the results.

Using the table, what is the probability that the next spin will be yellow?

	`6/31`
	`16/84`
	`1/7`
	`2/5`

Show Answers Only

`1/7`

Show Worked Solution

`P(text(Yellow))`	`= text(Number of yellow)/text(Total number of throws)`
	`= 24/(42 + 24 + 38 + 27 + 37)`
	`= 24/168`
	`=1/7`

Probability, NAPX-p167310v03

Andrei has a stack of cards that contains only Aces, Kings, Queens, Jacks and Jokers.

He picks one card without looking, records the card and puts it back again with the others.

He repeated this process 62 times.

Using the table, what are the chances of Andrei randomly selecting the Joker in his next pick?

	`8/33`
	`6/31`
	`11/62`
	`6/25`

Show Answers Only

`6/31`

Show Worked Solution

`P(text(Joker))`	`= text(Number of Jokers)/text(Total number of draws)`
	`= 12/62`
	`= 6/31`

Probability, NAPX-p167310v02

Marie grabs a coloured ball from a bag and records the colour. She then puts the ball back to the bag and repeats this process 96 times.

The results are shown in the table below.

Using the table, what is the probability that the next ball picked up by Marie will be yellow?

	`5/48`
	`6/25`
	`5/43`
	`7/36`

Show Answers Only

`5/48`

Show Worked Solution

`P(5)`	`= text(Number of yellow)/text(Total number)`
	`= 10/96`
	`= 5/48`

Probability, NAPX-p167310v01

A biased die has 6 faces numbered from 1 to 6.

Raven throws the die 50 times and recorded the results in the table below.

Using the table, what is the probability that Raven will be throwing a 5 on her next throw?

	`6/44`
	`2/17`
	`11/25`
	`3/25`

Show Answers Only

`3/25`

Show Worked Solution

`P(5)`	`= text(Number of 5’s)/text(Total number of throws)`
	`= 6/50`
	`= 3/25`

Algebra, NAPX-p115542v02

Shane is drawing a repeated pattern in the grid.

Which of these points will be part of Shane’s pattern?

	(8, 3)
	(2, 7)
	(7, 3)
	(2, 6)

Show Answers Only

`(8, 3)`

Show Worked Solution

`text(If the pattern continues:)`

`text{The point (8, 3) will be part of the pattern.}`

Algebra, NAPX-p115542v01

Patricia is drawing a repeating pattern on the grid pictured below.

Which of these points will be part of Patricia’s pattern?

	(16, 6)
	(14, 8)
	(14, 7)
	(16, 8)

Show Answers Only

`(16, 8)`

Show Worked Solution

`text(If the pattern continues:)`

`:.\ text{The point (16, 8) will be part of the pattern.}`

Number, NAP-L4-NC06

In 100 grams of the alloy electrum, there are 87.5 grams of gold and 12.5 grams of other metals.

Of the other metals, 2.1 grams are silver.

Which of these fractions is the closest to the proportion of silver among the other metals?

`1/8`	`1/5`	`1/10`	`1/4`

Show Answers Only

`1/5`

Show Worked Solution

`text(Fraction)`	`= 2.1/12.5`
	`= 21/125`
	`~~ 1/5`

Number, NAP-L4-NC05 SA

A menu requires 600 grams of curry paste.

Three satchels are emptied that provide 120 grams of curry paste.

How many more satchels are required?

Show Answers Only

`12`

Show Worked Solution

`text(Paste per satchel)`

`= 120/3 = 40\ text(grams)`

`text(Total satchels required)`	`= 600/40`
	`= 15 `

`:.\ text(An extra 12 satchels are required.)`

Number, NAP-L4-NC04 SA

Albert buys six donuts at a bakery.

He pays with a $5 note and gets 80 cents change.

How much does each donut cost?

cents

Show Answers Only

`70`

Show Worked Solution

`text(C)text(ost of donuts)= 5.00 – 0.80=$4.20`

`:.\ text(C)text(ost of 1 donut)`	`=420/6`
	`=70\ text(cents)`

Number, NAP-L4-CA31

Earthquakes are measured using the Richter scale which calculates the amount of energy (in ergs) the earthquake releases.

An earthquake measuring 4 on the Richter scale releases `32^4` ergs of energy.

An earthquake measuring 8 on the Richter scale releases `32^8` ergs of energy.

An earthquake measuring 8 on the Richter scale releases how many times as much energy as an earthquake measuring 4?

`10^2`	`10^4`	`32^2`	`32^4`

Show Answers Only

`32^4`

Show Worked Solution

`text(Energy)\ (4) = 32 xx 32 xx 32 xx 32\ text(ergs)`

`text(Energy)\ (8) = 32 xx 32 xx 32 xx 32 xx 32 xx 32 xx 32 xx 32\ text(ergs)`

`:.\ text{Times of energy (8 ÷ 4)}`

`= 32^8/32^4`

`= 32^4`

Number, NAP-L4-CA27 SA

Alan is fertilising his lawn over 2 days.

He fertilises `1/4` of the lawn on the morning of the first day.
He fertilises `2/5` of the lawn on the afternoon of the first day.

If Alan does no more work on the first day, what percentage of his lawn is fertilised after 1 day?

Show Answers Only

`65 text(%)`

Show Worked Solution

`text(Fraction fertilised)`	`= 2/5 + 1/4`
	`= (8 + 5)/20`
	`= 13/20`

`:. 65 text(% is fertilised after Day 1.)`

Number, NAP-L4-CA26 SA

Petrol costs 158.5 cents per litre.

How much does 12 litres of petrol cost?

Show Answers Only

`$19.02`

Show Worked Solution

`text(1 litre costs $1.585)`

`:.\ text(12 litres cost)`	`= 12 xx 1.585`
	`= 19.02`

Measurement, NAP-L4-CA25

Rogan has a square and a rectangle.

He cuts the rectangle along the dotted line as shown below.

Rogan then joins these 3 pieces to make a parallelogram.

Which of these calculations could Rogan use to find the area of the parallelogram?

`3\ text(cm) xx 6\ text(cm)`	`9\ text(cm) xx 6\ text(cm)`	`12\ text(cm) xx 6\ text(cm)`	`21\ text(cm) xx 3\ text(cm)`

Show Answers Only

`9\ text(cm) xx 6\ text(cm)`

Show Worked Solution

`text(Area)`	`= text(area of square) + text(area of rectangle)`
	`= 6 xx 6 + 3 xx 6`
	`= 9 xx 6\ text(cm)`

Probability, NAP-L4-CA22

A restaurant menu has the following different options available for a 3-course meal.

- 3 entrees
- 6 mains
- 4 desserts

How many different combinations of options are there for a 3-course meal?

13	16	36	72

Show Answers Only

`72`

Show Worked Solution

`text(Combinations)`	`= 3 xx 6 xx 4`
	`= 72`

Statistics, NAP-L4-CA20

The stem-and-leaf plot shows the number of koalas in a wildlife sanctuary each day during two weeks of bushfires.

On how many days were there at least 30 koalas in the sanctuary?

2	3	6	8	14

Show Answers Only

`6`

Show Worked Solution

`text(The plot shows 6 data points that)`

`text(are 30 or greater)`

`=> 6`

Measurement, NAP-L4-CA19 SA

Nathan is on a hike from Nords Wharf to Burwood Beach.

The trail is 38 kilometres in length.

On the first day, Nathan walks 8300 metres to Little Pelican.

The next day, he walks 16 900 metres to Redhead Beach.

How many kilometres remain for Nathan to complete this trail?

Give your answer in kilometres, to one decimal place.

kilometres

Show Answers Only

`12.8\ text(km)`

Show Worked Solution

`text(Convert distances to km:)`

`8300\ text(m) -> 8.3\ text(km)`

`16\ 900\ text(m) -> 16.9\ text(km)`

`:.\ text(Distance remaining)`	`= 38 – (8.3 + 16.9)`
	`= 12.8\ text(km)`

Statistics, NAP-L4-CA16

This graph shows the number of people in Australia, in millions, in part time work, from 1998 to 2018.

Which of these statements about the graph is true?

	More than three times as many people were in part time work in 2018 as in 1998.
	The number of people in part time work increased by more than 500 000 from 2003 to 2008
	The number of people in part time work increased more per year between 2008 and 2013 than at any other time.

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`text(The number of people in part time work increased by)`

`text(more than 500 000 from 2003 to 2008)`

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`text(People in part-time work in 2003 ≈ 2.85 million)`

`text(People in part-time work in 2008 ≈ 3.5 million)`

`:.\ text(Increased by more than 500 000 between 2003 and 2008)`

Number, NAP-L3-NC07 SA

A solar panel grid on a school roof produces an average of 8.6 kWh of energy per day.

How much energy will the grid produce for the school on average over 7 days?

kWh

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`60.2`

Show Worked Solution

`text(One multiplication strategy:)`

`7xx8=56`

`7 xx 0.6 = 4.2`

`7 xx 8.6 = 56+4.2=60.2`

`:.\ text(It produces 60.2 kWh over 7 days.)`

Number, NAP-L3-NC06 SA

Mount Kosciusko is 2228 metres high.

Mount Daligo is 1247 metres high.

How many metres higher is Mount Kosciusko than Mount Daligo?

metres

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`981`

Show Worked Solution

`text(Metres higher)`	`= 2228 – 1247`
	`= 981`

Geometry, NAP-L4-CA14

Roger starts walking due West.

He makes a quarter turn right and keeps walking.

Then, he makes another quarter turn right and stops.

What direction is Roger now facing?

North	South	East	West

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`text(East)`

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`:.\ text(Roger now facing due East.)`

Number, NAP-L3-NC04 SA

Year 7 students at a school collected aluminium cans to recycle.

There were 50 students in Year 7.
Each student collected 30 kilograms of aluminium cans.
Every 1000 kilograms of aluminium cans is worth $800.

In total, how much are the cans collected by all of Year 7 worth?

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`$1200`

Show Worked Solution

`text(Kilograms collected)`	`= 50 xx 30`
	`= 1500\ text(kg)`

`text(Cans worth)`	`= 1.5 xx $800`
	`= $1200`

Geometry, NAP-L3-CA39 SA

Two sailing boats set sail from an island.

The direction that each boat sailed is shown in the diagram below.

The angle between the direction of the two boats has been shaded.

What is the size of the shaded angle?

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`69°`

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`text(Shaded angle)`	`= 360 – (229 + 62)`
	`= 360 – 291`
	`= 69°`

Number, NAP-L3-CA31

Sapphire has 65 chocolates to pack into gift bags.

She puts 13 chocolates in each gift bag.

Which of the statements below are true?

Select three statements.

	13 × 65 = (the number of gift bags Sapphire packs)
	13 × (the number of gift bags Sapphire packs) = 65
	65 ÷ 13 = (the number of gift bags Sapphire packs)
	65 ÷ (the number of gift bags Sapphire packs = 13

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13 × (the number of gift bags Sapphire packs) = 65

65 ÷ 13 = (the number of gift bags Sapphire packs)

65 ÷ (the number of gift bags Sapphire packs) = 13

Show Worked Solution

`text(True statements are:)`

13 × (the number of gift bags Sapphire packs) = 65

65 ÷ 13 = (the number of gift bags Sapphire packs)

65 ÷ (the number of gift bags Sapphire packs) = 13

Geometry, NAP-L3-CA28

Rochelle drew a pattern which is pictured below.

Rochelle rotates the pattern.

How much does Rochelle to turn the pattern until it looks exactly the same?

`1/8\ text(turn)`	`1/4\ text(turn)`	`1/2\ text(turn)`	`text(1 turn)`

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`1/4\ text(turn)`

Show Worked Solution

`text(Outer pattern looks the same every)\ \ 1/8\ \ text(turn).`

`text(Inner cross pattern looks the same every)\ \ 1/4\ \ text(turn).`

`:.\ text(Whole pattern looks the same every)\ \ 1/4\ \ text(turn).`

Geometry, NAP-L3-CA27

Rodin glues 5 triangle prisms together to make a sculpture.

How many faces, including the base, does Rodin's sculpture have?

15	19	21	25

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`21`

Show Worked Solution

`text(Faces on bottom prism = 5)`

`text(Faces of other prisms = 4)`

`:.\ text(Total faces)`	`= 5 + 4 xx 4`
	`= 21`

Number, NAP-L4-CA17

Stephan makes 14 loaves of bread to sell at his bakery.

Each loaf takes `1/4` cup of sugar.

After he makes each loaf, he counts how many cups of sugar he uses in total.

`1/4, \ 1/2, \ 3/4, \ 1, \ 1 1/4, \ 1 1/2, …`

Which is the last number he will count?

`4`	`3 3/4`	`3 1/2`	`3 1/4`

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`3 1/2`

Show Worked Solution

`text(Last number)`	`= 14/4`
	`= 3 1/2`

Number, NAP-L3-CA26

Stephan makes 14 loaves of bread to sell at his bakery.

Each loaf takes `1/4` cup of sugar.

After he makes each loaf, he counts how many cups of sugar he uses in total.

`1/4, \ 1/2, \ 3/4, \ 1, \ 1 1/4, \ 1 1/2, …`

Which is the last number he will count?

`4`	`3 3/4`	`3 1/2`	`3 1/4`

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`3 1/2`

Show Worked Solution

`text(Last number)`	`= 14/4`
	`= 3 1/2`

Measurement, NAP-L3-CA25

A water container has 5 litres of water in it.

Kate pours water into her dog's bowl.

She pours the water into the 250 cubic centimetre bowl until it is full.

How much water is left in the container?

250 millilitres	475 millilitres	4500 millilitres	4750 millilitres

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`text(4750 millilitres)`

Show Worked Solution

`text(1 cm³ = 1 mL)`

`text(5 litres = 5000 mL)`

`:.\ text(Water left)`	`= 5000 – 250`
	`= 4750\ text(millilitres)`