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Geometry, NAPX-F3-CA03

There are six cubes in this 3D puzzle.
 

  
The puzzle is completely dipped into red paint.

When the cubes are separated, how many faces will be red?

`36` `31` `28` `26` `21`
 
 
 
 
 
Show Answers Only

`26`

Show Worked Solution

`text(The number of red faces on each cube is:)`

`:.\ text(Total faces red)`

`= 5 + 5 + 3 + 4 + 4 + 5`

`= 26` 

Number, NAPX-G3-NC11

The Park Run is a 5 kilometre fun run.

Olive completes the Park Run in 35 minutes.

Popeye runs at the same speed as Olive.

How long will it take him to run 3 kilometres?

`text(15 minutes)` `text(18 minutes)` `text(20 minutes)` `text(21 minutes)`
 
 
 
 
Show Answers Only

`text(21 minutes)`

Show Worked Solution

`text(Olive’s speed)`

`= 35 ÷ 5`

`= 7\ text(mins/km)`

 

`:.\ text(Time for Popeye to run 3 kilometres)`

`= 3 xx 7`

`= 21\ text(minutes)`

Algebra, NAPX-G3-NC08

Lief uses sticks to make a pattern.

He starts with 2 sticks for Design 1.

 

How many sticks does Lief need for Design 5?

`28` `30` `32` `36`
 
 
 
 
Show Answers Only

`30`

Show Worked Solution

`text(Strategy One)`

`text(Drawing design 5:)`

 
`:.\ text(30 sticks are required for design 5)`
 

`text(Strategy Two)`

`text(Design 2 has 4 more sticks than design 1.)`

`text(Design 3 has 6 more sticks than design 2.)`

`text(Design 4 has 8 more sticks than design 3.)`

`text(Continuing this pattern,)`

`text(Design 5 will have 10 more sticks than design 4 = 30 sticks.)`

Algebra, NAPX-G3-NC07

Which of these patterns fits the rule, "Double the previous number and deduct 2"?

 
 `3, 4, 5, 6, 9, …`
 
 `3, 6, 12, 24, 48, …`
 
 `4, 6, 10, 18, 34, …`
 
 `4, 10, 22, 46, 94, …`
Show Answers Only

`4, 6, 10, 18, 34, …`

Show Worked Solution

`text(By trial and error, consider option 3:)`

`4 xx 2 – 2 = 6`

`6 xx 2 – 2 = 10`

`10 xx 2 – 2 = 18`
 

`:.\ 4, 6, 10, 18, 34, …\ text(fits the rule.)`

Geometry, NAPX-G3-NC05

Rufus made a sculpture.

This is a drawing of the front view and the side view.
  

 
Which of these is a correct top view?

 
 
  
 
 
 
  
 
Show Answers Only

Show Worked Solution

`text(The two views indicate the sculpture is a sphere sitting)`

`text(on top of a cylinder.)`

Number, NAPX-G3-NC04

Korin collects 150 carrots from his vegetable garden.

He puts the carrots in bunches of 12 carrots.

How many full bunches can he make?

`5` `9` `12` `13`
 
 
 
 
Show Answers Only

`12`

Show Worked Solution

`text(Number of full bunches)`

`= 150 ÷ 12`

`= 12\ text(remainder)\ 6`
 

`:.\ text(Korin can make 12 full bunches.)`

Algebra, NAPX-G3-NC01

Mike and Georgia saved $90 together.

Georgia saved twice as much money as Mike.

How much money did Georgia save?

`$30` `$50` `$60` `$180`
 
 
 
 
Show Answers Only

`$60`

Show Worked Solution

`text(Let)\ \ x =\ text(Mike’s savings)`

`x + 2x` `= 90`
`3x` `= 90`
`x` `= 30`

 

`:.\ text(Georgia saved $60.)`

Number, NAPX-G3-CA32

Dawn had a bag of different coloured marbles.

`1/4` of the marbles were clear and `1/3` of the marbles were black.

Her bag contained 5 more black marbles than clear marbles.

How many marbles were in Dawn's bag?

`36` `48` `60` `72`
 
 
 
 
Show Answers Only

`60`

Show Worked Solution

`text(Let)\ \ n = text(number of marbles in bag)`

`1/3n – 1/4n` `= 5`
`4/12n – 3/12n` `= 5`
`1/12n` `= 5`
`:. n` `= 60`

Algebra, NAPX-G3-CA24

Isaac dropped an apple from the top of a bridge into the water below.

He uses the following equation to calculate the distance the apple travels in metres,

distance = 4.9 x (time)²

where time is the number of seconds it takes the apple to reach the water.

Which of these is closest to the distance if it took the apple a time of 3.3 seconds to reach the water?

`text(12 metres)` `text(16 metres)` `text(32 metres)` `text(53 metres)` `text(261 metres)`
 
 
 
 
 
Show Answers Only

`text(53 metres)`

Show Worked Solution
`text(Distance)` `= 4.9 xx (3.3)^2`
  `= 4.9 xx 10.89`
  `= 53.361`
  `~~ 53\ text(metres)`

Measurement, NAPX-G3-CA22

Miley is driving from Byron Bay to Noosa via Southport.

Her estimated travel times are in the table below.
 

 
Miley plans to leave Byron Bay at 6:30 am and take a 20 minute rest stop in Southport.

Using these driving times and rest time, when should Miley arrive in Noosa?

about 9:00 am about 9:30 am about 10:00 am about 10:30 am
 
 
 
 
Show Answers Only

`text(about 10:30 am)`

Show Worked Solution
`text(Travel time)` `= 3\ text(h 35 mins)`
`text(Rest time)` `= 20\ text(mins)`

 

`:.\ text(Arrival time)` `= 6:30\ text(am plus 3 h 55 mins)`
  `~~ 6:30\ text(am plus 4 hours)`
  `~~ 10:30\ text(am)`

Algebra, NAPX-G3-CA21

Soup is sold in cans of 3 sizes: small, medium, and large.

A small can of soup costs $1.40 less than a medium can.

A small can of soup costs $4.20 less than a large can.

Which equation correctly states the cost of a medium can of soup?

 
 cost of a medium can = cost of a large can – $1.40
 
 cost of a medium can = cost of a large can – $2.80
 
 cost of a medium can = cost of a large can – $4.20
 
 cost of a medium can = cost of a large can – $5.60
Show Answers Only

`text(C)text(ost of a medium can = cost of a large can – $2.80)`

Show Worked Solution

`text(Extra cost of a large can over a medium)`

`=$4.20 – $1.40`

`=$2.80`
 

`:.\ text(C)text(ost of a medium can = cost of a large can – $2.80)`

Number, NAPX-G3-CA15

Crisco takes part in a walkathon to raise money for charity.

His grandmother sponsors him $30 in total.

His sister sponsors him $1.50 for each kilometre he walks.

In order to raise $120, how many kilometres does Crisco need to walk?

`20`  `40` `60` `80` `90`
 
 
 
 
 
Show Answers Only

`60\ text(laps)`

Show Worked Solution

`text(Let)\ \ x = text(number of kilometres Crisco walks)`

`120` `= 1.5x + 30`
`1.5x` `= 90`
`:. x` `= 90/1.5`
  `= 60\ text(laps)`

Number, NAPX-G3-CA14

Butch has only 5-cent, 10-cent, 20-cent and 50-cent coins in his pocket.

He buys a doughnut that costs him $2.65 and pays the exact price.

What is the smallest number of coins he could use to pay for his doughnut?

`5`    `6`   `7` `8` `9`
 
 
 
 
 
Show Answers Only

`7\ text(coins)`

Show Worked Solution

`text(The minimum number of coins are:)`

`5 xx 50 text(-cent)` `= $2.50`
`1 xx 10 text(-cent)` `= $0.10`
`1 xx 5 text(-cent)` `=$0.05` 

 

`:.\ text(Minimum coins to make $2.65 = 7 coins)`

Geometry, NAPX-G3-CA10

 
Pogo is staying at the Dead Dingo Inn.

Which of these directions should Pogo follow to get to the hardware store?

 
 Go south-west to Come By Chance then turn right.
 
 Go south-east to Come By Chance then turn right.
 
 Go south-west to Come By Chance then turn left.
 
 Go south-east to Come By Chance then turn left.
Show Answers Only

`text(Go south-west to Come By Chance then turn left.)`

Show Worked Solution

`text(Go south-west to Come By Chance then turn left.)`

Number, NAPX-G3-CA09

Renee has $5.

A doughnut costs $1.20.

How many doughnuts can Renee buy?

`3`    `4`   `5`   `6`
 
 
 
 
Show Answers Only

`4`

Show Worked Solution

`text(Strategy 1)`

`3 xx $1.20` `= $3.60`
`4 xx $1.20` `= $4.80`
`5 xx $1.20` `= $6.00`

 

`text(Strategy 2)`

`5/1.20 = 4.166…\ \ text{(round down)}`

 

`:.\ text(Renee can only buy 4.)`

Number, NAPX-G3-CA07

Ming bought 7 apples and 5 oranges.

He used this calculation to work out the total cost

`5 × 0.70 + 7 × 0.85`

How much did one apple cost?

`$0.70` `$0.85` `$5` `$7`
 
 
 
 
Show Answers Only

`$0.85`

Show Worked Solution

`text(S)text(ince 7 apples were bought, the cost)`

`text(of one is $0.85.)`

Geometry, NAPX-G4-CA05, NAPX-G3-CA06

A rectangle is cut along its diagonals to produce four triangles.

These triangles are best described as

 
 scalene
 
 equilateral
 
 right angled
 
 isosceles
Show Answers Only

`text(isosceles)`

Show Worked Solution

`text(S)text(ince the diagonals of a rectangle bisect)`

`text(each other)`

`=>\ text(the 4 triangles are isosceles.)`

 

Statistics and Probability, NAPX-G3-CA05

Rocky rolls a standard 6-sided dice once.

Which of the following is Rocky most likely to roll?

 
 a number greater than or equal to 3
 
 an odd number
 
 a number less than 4
 
 the number 4 or 6
Show Answers Only

`text(a number greater than or equal to 3)`

Show Worked Solution

`text(Consider the probability of each option:)`

`text{P(greater than or equal to 3)} = 4/6 = 2/3`

`text{P(odd)} =3/6 = 1/2`

`text{P(less than 4)} = 3/6 = 1/2`

`text{P(4 or 6)} = 2/6 = 1/3`
 

`:.\ text(A number greater than or equal to 3 is the most likely.)`

Statistics and Probability, NAPX-H3-NC29

Dippa arrived at Toorak station at 11:00 am and caught the next train to Southbank.
 

 
At what time did Dippa arrive at Southbank station?

`11:22` `11:30` `11:46` `11:58`
 
 
 
 
Show Answers Only

`11:58`

Show Worked Solution

`text(Arriving at Toorak at 11:00 am,)`

`=>\ text(Train A has already left)`

`=>\ text(Train B doesn’t stop at Southbank)`

`=>\ text(Train C doesn’t stop at Toorak)`

`=>\ text(Train D arrives at 11:58 am)`

`:.\ text(He arrives at 11:58 am.)`

Measurement, NAPX-H3-NC24, NAPX-H2-37

Crystal drew a shape as pictured below.

   

What is the perimeter of this shape in centimetres?

`73` `90` `108` `112` `122`
 
 
 
 
 
Show Answers Only

`112\ text(cm)`

Show Worked Solution

`text(Starting at the bottom left corner and)`

`text(moving clockwise:)`

`text(Perimeter)` `= 18 + 24 + 18 + 7 + 14 + 12 + 14 + 5`
  `= 112\ text(cm)`

Algebra, NAPX-H3-NC20

Trinity is a tile designer. He is repeating 4 symbols as shown in the picture below.

Trinity is using this pattern for a line of tiles that is 33 tiles long.
 

 
What will be the symbol on the 33rd tile?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(8 repeats of the 4 tile pattern make up the)`

`text(first 32 tiles.)`

`:.\ text(The 33rd tile is the first tile in the pattern.)`

Number, NAPX-H3-NC18

This table shows the prices of different kinds of nuts sold at a farmers' market.

   

Which one of these are the most expensive nuts per kilogram?

peanuts cashews hazelnuts walnuts
 
 
 
 
Show Answers Only

`text(Cashews)`

Show Worked Solution

`text(Consider each option:)`

`$1.50\ text(for 200 g = 5 × 1.50 = $7.50 per kg)`

`$3.60\ text(for 500 g = 2 × 3.60 = $7.20 per kg)`

`$7.60\ text(for 1 kg)`

`$1.75\ text(for 250 g = 4 × 1.75 = $7.00 per kg)`

 

`:.\ text(Hazelnuts are the most expensive.)`

Measurement, NAPX-H3-NC16

A pasta factory packs 350 gram packets of pasta into a box that can hold 7 kg in total.

Which one of these expressions shows how many packets of pasta will be needed to fill the box?

`350 ÷ 7` `7 xx 350` `7000 xx 350` `7000 ÷ 350`
 
 
 
 
Show Answers Only

`7000 ÷ 350`

Show Worked Solution

`text(S)text(ince 7 kg = 7000 grams,)`

`text(Packets of pasta) = 7000 ÷ 350`

Number, NAPX-H3-NC14

Bernard wants to buy a tennis racquet that has a normal price of $220.

He is given a 10% discount.

What is the value of the discount?

`$2.20` `$10` `$22` `$198` `$210`
 
 
 
 
 
Show Answers Only

`$22`

Show Worked Solution

`text(Value of the discount)`

`= 10 text(%) xx 220`

`=$22`

Statistics and Probability, NAPX-H3-NC13

Tranquilla's class were asked to choose their favourite vegetable among four choices.

  • 5 voted for zuccini
  • 5 voted for carrots
  • 6 voted for snow peas
  • The rest voted for spinach
     

 
How many students in Tranquilla's class chose spinach?

`7` `8` `9` `10`
 
 
 
 
Show Answers Only

`8`

Show Worked Solution

`text(S)text(ince snow peas are exactly one quarter of chart,)`

`=>\ text(Total students) = 4 xx 6 = 24`

 
`:.\ text(Votes for spinach)`

`=24-(5+5+6)`

`=8`

Number, NAPX-H3-NC12, NAPX-H2-22

The Sydney Opera House began construction in 1959.

Approximately how old was the Sydney Opera House in 2020?

`50` `60` `70` `80`
 
 
 
 
Show Answers Only

`60`

Show Worked Solution

`text(2020 – 60 years = 1960.)`

`:.\ text(Closest approximation is 60 years.)`

Number, NAPX-H3-NC05

Nug had a $10 note only.

At the service station, he bought 6 sherbert cones that cost $0.80 each.

How much change should he get?

`$4.40` `$4.80` `$5.20` `$5.60`
 
 
 
 
Show Answers Only

`$5.20`

Show Worked Solution
`text(Change)` `= 10 – (6 xx 0.80)`
  `= 10 – 4.80`
  `= $5.20`

Geometry, NAPX-H3-NC04

This is a view of a solid made by stacking 21 identical cubes.
 

 
How many cubes are completely hidden in this view?

`15` `14` `6` `5`
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text(One strategy:)`

`text{Cubes that can be seen (by row)}`

`= 5+5+5`

`= 15`

 
`:.\ text(Number hidden)\ =21-15=6`

Number, NAPX-H3-NC02

Kelsey threw a shot put in the school athletics carnival and landed it where the arrow marker is shown below.
 

 

 
Which of these is closest to the length of his throw?

`2 3/4 text(m)` `3 1/3 text(m)` `3 1/2 text(m)` `3 2/3 text(m)`
 
 
  
 
Show Answers Only

`3 2/3 text(m)`

Show Worked Solution

`3 2/3 text(m)`

Number, NAPX-H3-CA31

Jaco has a square billboard poster with an area of 9 m².

He enlarges the billboard poster to have an area of 81 m².

The enlargement multiplied the side lengths of the original billboard poster by a factor of

`text(three.)` `text(four.)` `text(six.)` `text(nine.)` `text(twelve.)`
 
 
 
 
 
Show Answers Only

`text(three)`

Show Worked Solution
`text(Let)\ \ \ s` `=\ text(side length of original poster)`
`s^2` `= 9`
`s` `= 3\ text(metres)`

 

`text(Let)\ \ \ S` `=\ text(side length of enlarged poster)`
`S^2` `= 81`
`S` `= 9`

 

`:.\ text(Side lengths have increased from 3 to 9,)`

`text(or by a factor of three.)`

Measurement, NAPX-H3-CA30

Squares with sides 5 cm are cut out from the corners of a rectangular piece of cardboard.

The sides are then folded to make a rectangular box with no lid.
 

 
What is the volume of the box?

`text(12 cm³)` `text(60 cm³)` `text(72 cm³)` `text(96 cm³)` `text(120 cm³)`
 
 
 
 
 
Show Answers Only

`60\ text(cm³)`

Show Worked Solution
`text(Volume)` `=\ text(base area × height)`
  `= (6 xx 2) xx 5`
  `= 60\ text(cm³)`

Statistics and Probability, NAPX-H3-CA25

Skylar records the number of students who can play different instruments in his class.

He records the results in the table below.

 

Some students play more than one instrument.

What is the least number of boys that could be in Skylar's class?

`1` `7` `12` `15`
 
 
 
 
Show Answers Only

`7`

Show Worked Solution

`text(S)text(ince students can play more than 1 instrument,)`

`text(Skylar’s class could have only 7 boys since this is)`

`text(the largest number of boys that play any single)`

`text(instrument.)`

Number, NAPX-H3-CA24

Tim lives 6 km from the park where he trains for soccer.

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

How many minutes does it take for Tim to get to the park?

`1 2/3` `24` `36` `60`
 
 
 
 
Show Answers Only

`36\ text(minutes)`

Show Worked Solution
`text(Time)` `= text(Distance)/(text(S)text(peed))`
  `= 6/10\ text(hr)`
  `= 6/10 xx 60\ text(minutes)`
  `= 36\ text(minutes)`

Measurement, NAPX-H3-CA23

 
Which of these could be used to calculate the area of the shape in square centimetres?

`(7 xx 2) + (10 xx 9)` `(10 xx 7) + (10 xx 2)`
 
 
`(10 xx 7) + (7 xx 3)` `(10 xx 9) - (3 xx 2)`
 
 
Show Answers Only

`(10 xx 9) – (3 xx 2)`

Show Worked Solution
`text(Area)` `=\ text(Area of large rectangle – Area of cut-out rectangle)`
  `=(10 xx 9) – (3 xx 2)`