NAPX-MultipleChoice

Number, NAPX-I4-CA01

Raina earns $15 per hour.

How much will he be paid for working 5 hours?

`$3`	`$20`	`$30`	`$75`

Show Answers Only

`$75`

Show Worked Solution

`text(Pay)`	`= 5 xx 15`
	`= $75`

Number, NAPX-J4-NC06, NAPX-J3-NC06

`9 + (13 - 4 xx 2 + 3) =`

What number does

represent?

`2`	`17`	`30`	`54`

Show Answers Only

`17`

Show Worked Solution

`9 + (13 – 4 xx 2 + 3)`	`=`	?
`9 + (13 – 8 + 3)`	`=`	?
`9 + 8`	`=`	?
`17`	`=`	?

Number, NAPX-J4-NC04

Crystal is making red cordial for her daughter's birthday party.

She needs to add 280 millilitres of concentrate to every 2 liters of water.

If Crystal only has 0.5 litres of water left, how many millilitres of concentrate should she add?

14 mL	70 mL	140 mL	280 mL	560 mL

Show Answers Only

`70\ text(mL)`

Show Worked Solution

`text(Given)\ \ 280\ text(mL)`	`=> 2\ text(litres)`
`140\ text(mL)`	`=> 1\ text(litre)`
`70\ text(mL)`	`=> 0.5\ text(litre)`

Number, NAPX-J4-NC02

The diameter of Jupiter is approximately 139 000 kilometres.

Which of these shows 139 000 in scientific notation?

`1.39 xx 10^4`	`1.39 xx 10^5`	`1.39 xx 10^6`	`1.39 xx 10^7`

Show Answers Only

`1.39 xx 10^5`

Show Worked Solution

`139\ 000`	`= 1.39 xx 100\ 000`
	`= 1.39 xx 10^5`

Number, NAPX-J4-NC01

Terry makes 500 kilograms of concrete by combining 100 kg of cement mix with 200 kg of sand and 200 kg of aggregate.

What percentage of the concrete is made up of cement mix?

	`text(0.04%)`
	`text(0.2%)`
	`text(2%)`
	`text(5%)`
	`text(20%)`
	`text(40%)`

Show Answers Only

`text(40%)`

Show Worked Solution

`text(Percentage)`	`= 100/500 xx 100`
	`= 1/5 xx 100`
	`= 20 text(%)`

Statistics and Probability, NAPX-J4-CA38, NAPX-J3-CA37

The Strikers and the Hurricanes are playing cricket in a 20 over competition.

The stem-and-leaf plots show the number of runs each side has scored in their last 15 games.

Select the true statement about the data.

	The Strikers had the lowest run score.
	The Hurricanes had the highest run score.
	The Strikers scored over 136 runs more times than the Hurricanes.
	The median score for The Strikers is higher than the median score for The Hurricanes.
	The range of scores for The Strikers is smaller than the range of scores for The Hurricanes.

Show Answers Only

`text{The range of scores for The Strikers is smaller than the}`

`text{range of scores for The Hurricanes.}`

Show Worked Solution

`text(Striker’s range) = 148-110 = 38`

`text(Hurricane’s range) = 144-103 = 41`

`:.\ text(Striker’s range) < text(Hurricane’s range)`

Algebra, NAPX-J4-CA32

A Greek wedding reception area has pillars that are `x` cm wide and the gap between pillars is `y` cm.

If the reception area has 9 pillars on one side, the length of that side can be represented by which expression?

`8x + 9y`	`8(x + y)`	`9x + y`	`9x + 8y`	`9(x + y)`

Show Answers Only

`9x + 8y`

Show Worked Solution

`text(The length of the side)`

`=\ text(width of 9 pillars + width of 8 gaps)`

`= 9x + 8y`

Measurement, NAPX-J4-CA31

Rebel walks for 5 minutes from her home to Century City Station.

She then travels by train to Malibu Station.

From Malibu Station, Rebel then walks for 16 minutes to the beach for a swim.

What is the latest time Rebel can leave home to arrive at the beach by 7:00?

`05:50`	`05:55`	`06:00`	`06:05`	`06:10`

Show Answers Only

`06:05`

Show Worked Solution

`text(Working backwards from arriving at the beach at 07:00,)`

`07:00\ text(less 16 minutes walking = 06:44)`

`text(1st train to arrive before 06:44 leaves Century City at 06:15.)`

`:.\ text{Rebel must leave at 06:10 (5 minutes before 06:15).}`

Measurement, NAPX-J4-CA28, NAPX-J3-CA36

A square table top has an area of 9025 square centimetres.

What is the area of the table top in square millimetres?

	9.025 square millimetres
	90.25 square millimetres
	90 250 square millimetres
	902 500 square millimetres

Show Answers Only

`text(902 500 square millimetres)`

Show Worked Solution

`text(Solution 1:)`

`text(Dimensions of square with area 9025 cm² is:)`

`text(95 cm × 95 cm)`

`text(Converting to millimetres:)`

`950\ text(mm) xx 950\ text(mm) = 902\ 500\ text(square millimetres)`

`text(Solution 2:)`

`text(Scale factor of converting cm to mm = 10)`

`text(Scale factor of converting cm² to mm²)\ = 10 xx 10 = 100`

`:. 9025\ text(cm²) xx 100 = 902\ 500\ text(mm²)`

Geometry, NAPX-J4-CA27, NAPX-J3-CA29

This shape is reflected across the line and then rotated 90° anti-clockwise.

Which image shows the appearance of the shape after these transformations?

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Show Worked Solution

`text(After reflection):`

`text(After rotation):`

Measurement, NAPX-J4-CA25

Zappa is making a scale model of his music studio.

The height of the studio in the scale model is 5 centimetres.
The height of Zappa's actual studio is 2 metres.

What does 1 centimetre in Zappa's scale model represent in his real studio?

`text(1000 cm)`	`text(250 cm)`	`text(100 cm)`	`text(40 cm)`

Show Answers Only

`text(40 cm)`

Show Worked Solution

`text(5 cm)`	`= 2\ text(m)`
	`= 200\ text(cm)`
`:. 1\ text(cm)`	`= 200 ÷ 5`
	`= 40\ text(cm)`

Measurement, NAPX-J4-CA23

Buzz is placing door trim on the top and both sides of a double door entrance, as pictured below.

How many metres of door trim does he need?

`text(4.44 m)`	`text(6.45 m)`	`text(8.88 m)`	`text(64.5 m)`

Show Answers Only

`text(64.5 m)`

Show Worked Solution

`text(Metres of door trim needed)`

`= (2010 xx 2) + 2430`

`= 6450\ text(mm)`

`= 6.45\ text(m)`

Algebra, NAPX-J4-CA22

Phoenix drew a straight line through the points `text{(−2, 2)}` and `(3, 0)` as shown in the diagram below.

What is the gradient of the line that Phoenix drew?

`5/2`	`2/5`	`−2/5`	`−5/2`

Show Answers Only

`−2/5`

Show Worked Solution

`text(Gradient)`	`= text(rise)/text(run)`
	`= (y_2 – y_1)/(x_2 – x_1)`
	`= (2 – 0)/(-2 – 3)`
	`= −2/5`

Algebra, NAPX-J4-CA21

Which expression is equivalent to `12x + 24`?

`3(4x + 8)`	`3(4x + 21)`	`6(2x + 18)`	`12(x + 24)`

Show Answers Only

`3(4x + 8)`

Show Worked Solution

`3 (4x + 8)`	`= 3 xx 4x + 3 xx 8`
	`= 12x + 24`

Statistics and Probability, NAPX-J4-CA19, NAPX-J3-CA26

This graph shows a company's profit over a four year period.

Which conclusion can be reached from the graph?

	The profit in Year 2 was double of the profit in Year 1.
	The profit in Year 4 was one quarter the profit in Year 3.
	The profits were positive in Years 2 and 3, and negative in Years 1 and 4.
	The profits were greater than $20 000 in the period between Year 1 and Year 4.

Show Answers Only

The profits were greater than $20 000 in the period between Year 1 and Year 4.

Show Worked Solution

`text(Important to note that profits in this table begin at $25 000, not zero.)`

`:.\ text(Profits were greater than $20 000 in the period)`

`text(between Year 1 and Year 4.)`

Number, NAPX-J4-CA18

The weight of a gold bar is 1.0247 kg.

What is the weight of the gold bar rounded to the nearest hundredth of a kilogram?

`text(1.02 kg)`	`text(1.03 kg)`	`text(1.024 kg)`	`text(1.025 kg)`

Show Answers Only

`text(1.02 kg)`

Show Worked Solution

`text(Nearest hundredth kg)`

`= 1.02\ text(kg)`

Statistics and Probability, NAPX-J4-CA17

Marley is comparing the average daily rainfall in the towns of Byron Bay and Coffs Harbour in January.

What method below is the most valid?

	Ask 1 in 10 residents in each town how much rain they received each day in January
	Research the total rainfall each town received in January and divide by 31.
	Research the weekly high and low rainfall each town received in January.
	Research the total rainfall each town received over the past year and divide by 12.

Show Answers Only

`text(Research the total rainfall each town received in January)`

`text(and divide by 31.)`

Show Worked Solution

`text(Research the total rainfall each town received in January)`

`text(and divide by 31.)`

Measurement, NAPX-J4-CA16

Wyatt is designing a rectangular lawn for a landscaping project.

He wants the lawn to be at least 400 square metres.

He has marked out two sides, each 25.5 metres in length.

What is the smallest possible length of each of the other two sides, rounded to one decimal place?

`text(15 metres)`	`text(15.6 metres)`	`text(15.7 metres)`	`text(16 metres)`

Show Answers Only

`text(15.7 metres)`

Show Worked Solution

`text(Smallest possible length)`

`= 400 ÷ 25.5`

`= 15.68…`

`= 15.7\ text(metres)`

`text(Note: this distance must be rounded up due to the)`

`text{context of the question (area “at least” 400 m²).}`

Algebra, NAPX-J4-CA14

Dom and Marty each bought saffron from the local farmers' market.

Dom bought 4 grams for $5.

Marty bought 6 grams for $7.50.

Which graph best represents the cost of saffron at the farmers' market?

Show Answers Only

Show Worked Solution

`text{Plot (4,5) and (6, 7.5) on each grid and see which graph is correct.}`

Measurement, NAPX-J4-CA13

Jayden measures the width of his car parking space. It is 2525 millimetres wide.

An equivalent car park width is:

	25 metres and 25 centimetres
	2 metres and 525 centimetres
	25 centimetres and 25 millimetres
	2 metres and 525 millimetres

Show Answers Only

`text(2 metres and 525 millimetres)`

Show Worked Solution

`2525\ text(mm)`	`= 2525/1000 text(m)`
	`= 2.525\ text(m)`
	`= 2\ text(metres and 525 millimetres)`

Number, NAPX-J4-CA12, NAPX-J3-CA21

Which number line correctly shows the positions of 0.05, 0.405 and 0.45.

Show Answers Only

Show Worked Solution

Statistics and Probability, NAPX-J4-CA10

Peggy picks a marble from a bag and records its colour before placing it back in the bag.

She repeats this 20 times.

Her results are in the table below.

Using the table, what is the probability that the next marble Peggy picks will be black?

`1/4`	`1/5`	`2/5`	`1/10`

Show Answers Only

`1/5`

Show Worked Solution

`text{Pr(Black)}`	`= text(number of black picked)/text(total picks)`
	`= 4/20`
	`= 1/5`

Geometry, NAPX-J4-CA09, NAPX-J3-CA20

Which of these is the front view of this object made from cubes?

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Show Worked Solution

Algebra, NAPX-J4-CA08, NAPX-J3-CA16

Ringo places a disc at (−5, −1).

He then moves the disc up 2 units.

What are the coordinates of the new position of the disc?

`text{(−7, −1)}`	`text{(−5, −3)}`	`text{(−3, −1)}`	`text{(−5, 1)}`

Show Answers Only

`text{(−5, 1)}`

Show Worked Solution

`text{New position is (−5, 1)}`

Algebra, NAPX-J4-CA07, NAPX-J3-CA15

Alfred writes the sequence:

`3, 0.3, 0.03, 0.003, …`

Describe the rule he uses to write the next number in this sequence.

	`text(divide by 2.7)`
	`text(divide by 10)`
	`text(subtract 2.7)`
	`text(divide by 0.1)`
	`text(multiply by 10)`
	`text(multiply by 0.01)`

Show Answers Only

`text(divide by 10)`

Show Worked Solution

`3 ÷ 10`	`= 0.3`
`0.3 ÷ 10`	`= 0.03`
`0.03 ÷ 10`	`= 0.003`

`:.\ text(Rule: divide by 10).`

Number, NAPX-J4-CA06

Ticka is a baker and sells 50 loaves of bread at the markets. Each loaf costs him $3.75 to make.

He sells 40 loaves for $7.95 each.

In the last hour of the market, he sells the last 10 loaves for $2.50 each.

What is the total profit or loss of the 50 loaves?

`−$12.50`	`$155.50`	`$180.50`	`$343.00`

Show Answers Only

`$155.50`

Show Worked Solution

`text(Total profit/loss)`	`=\ text(sales revenue – costs)`
	`=(40 xx 7.95 + 10 xx 2.50) – (50 xx 3.75)`
	`= 343 – 187.50`
	`= $155.50`

Number, NAPX-J4-CA05, NAPX-J3-CA12

Mallory has `3/8` cup of raisins.

She needs `3/4` cup of raisins for a fruit cake she is making.

How many more cups of raisins does Mallory need for the recipe?

`1/8\ text(cup)`	`1/4\ text(cup)`	`3/8\ text(cup)`	`1/2\ text(cup)`

Show Answers Only

`3/8\ text(cup)`

Show Worked Solution

`text(Raisins needed)`	`= 3/4 – 3/8`
	`= 3/8\ text(cup)`

Statistics and Probability, NAPX-J4-CA04, NAPX-J3-CA08

Emma works Monday till Friday. She gets the bus to work 4 days per week and catches the ferry on the other day.

Today is a work day.

What is the probability that Emma catches the ferry to work?

`0.25`	`1/7`	`5/7`	`text(20%)`

Show Answers Only

`text(20%)`

Show Worked Solution

`text(Probability)`	`= 1/5`
	`= 0.20`
	`= 20 text(%)`

Statistics and Probability, NAPX-J4-CA03

A survey was conducted to determine the number of children who have a dog or a cat as a pet.

The results are shown below.

How many children have a cat as pet, but not a dog?

`8`	`11`	`42`	`60`	`71`

Show Answers Only

`42`

Show Worked Solution

`42`

Number, NAPX-J4-CA02

It takes Charles 2.4 minutes to ride his bike one full lap around a lake track.

How many laps does Charles complete in 12 minutes?

`5`	`6`	`28`	`29`

Show Answers Only

`5`

Show Worked Solution

`text(Laps completed)`	`= 12 ÷ 2.4`
	`= 5\ text(laps)`

Measurement, NAPX-J4-CA01, NAPX-J3-CA02

The digital clock below tells the time in the 24-hour system.

What is the equivalent time in the 12-hour system?

`text(6:25 am)`	`text(6:25 pm)`	`text(8:25 am)`	`text(8:25 pm)`

Show Answers Only

`text(6:25 pm)`

Show Worked Solution

`text(18:25 in 12 hour system ⇒ deduct 12 hours.)`

`text(6:25 pm)`

Number, NAPX-F4-NC05

`8 xx (2 + 7)`

`7 xx 2 + 9`

Which symbol `( <, = , >)` makes the number sentence correct?

`<`	`=`	`>`

Show Answers Only

`>`

Show Worked Solution

`text(Evaluate each side:)`

`8 xx (2 + 7)`	`= 8 xx 9 = 72`
`7 xx 2 +9`	`= 14 + 9 = 23`

`:. 8 xx (2 + 7)`	`> 7 xx 2 + 9`

Number, NAP-A4-NC22

The distance from `A` to `B` is three times the distance from `B` to `C`.

The distance from `A` to `C` is 180 metres.

What is the distance from `B` to `C`?

30 metres	40 metres	45 metres	60 metres

Show Answers Only

`45\ text(metres)`

Show Worked Solution

`AB:BC = 3:1`

`text(Ratio has 4 parts) \ => \ 1\ text(part) = 180/4 = 45`

`:. BC`	`= 1 xx 45`
	`=45\ text(m)`

Algebra, NAP-G4-CA15

Alan earns $55 for making 11 deliveries.

Which expression shows how much he will earn for making `n` deliveries?

`(55 xx 11) xx n`	`(55 ÷ 11) ÷ n`	`(55 xx 11) ÷ n`	`(55 ÷ 11) xx n`

Show Answers Only

`(55 ÷ 11) xx n`

Show Worked Solution

`55\ → 11\ text(deliveries)`

`55 -: 11 → \ text(1 delivery)`

`:. (55 ÷ 11) xx n\ → \ n\ text(deliveries)`