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Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, NAP-B3-CA09

A resort has 4 pools.

Which pool has the largest surface area?
 

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Consider the surface area of each pool:)`

`text(1st pool) = 6 xx 19 = 114`

`text(2nd pool) = 7 xx 18 = 126`

`text(3rd pool) = 12.5 xx 12.5 = 156.25`

`text(4th pool) =10 xx 15 = 150`

 

 `:.\ text(The 3rd pool, 12.5 × 12.5, has the largest)`

`text(surface area.)`

Algebra, NAP-C4-NC03

Leo creates a pattern of triangles using sticks as shown below.

The number of sticks in the first four figures are 1, 3, 6 and 10.
 

 

 
What is the number of sticks needed for Figure 5?

`14` `15` `17` `21`
 
 
 
 
Show Answers Only

`15`

Show Worked Solution

`text(The pattern shows that:)`

`text(Figure 5 = Figure 4 + 5 sticks)`

 

`:.\ text(The number of sticks in figure 5)`

`=10+ 5 = 15`

Number, NAP-D3-CA15


 

Between 2007 and 2010, the number of people with type II diabetes in America increased by about

 
 `text(0.5 million people.)`
 
 `text(1 million people.)`
 
 `text(1.5 million people.)`
 
 `text(2 million people.)`
Show Answers Only

`text(2 million people.)`

Show Worked Solution

`33.21 – 31.16 = 2.05`

`:.\ text(The number increased by about 2 million people.)`

Measurement, NAP-C4-NC12

Which metric unit would a builder use to measure the area of a courtyard?
 

 
 

  
 `text(cubic centimetres)`
  
 `text(square centimetres)`
 
 `text(square metres)`
  
 `text(cubic metres)`
Show Answers Only

`text(square metres)`

Show Worked Solution

`text(The courtyard is a measurement of area and the)`

`text(most appropriate unit is square metres.)`

Geometry, NAP-C4-NC11

Danny was eating dinner and after finishing he took a photo of his plate and fork.
 

 
Which of the following measurements is closest to the length of the fork?

`9\ text(cm)` `10\ text(cm)` `12\ text(cm)` `15\ text(cm)`
 
 
 
 
Show Answers Only

`text(15 cm)`

Show Worked Solution

`text(The fork is approximately 75% the height)`

`text(of the plate,)`

`:.\ text(Fork height)` `= 75 text(%) xx 20`
  `=15\ text(cm)`

Number, NAP-C4-NC08

John weighs a small fish he caught in a net.

The net and fish together weighed 634 g.

The net by itself weighs 576 g.

What is the weight of the fish?

`48\ text(g)` `58\ text(g)` `146\ text(g)` `156\ text(g)`
 
 
 
 
Show Answers Only

`text(58 g)`

Show Worked Solution
`text(Weight of fish)` `= 634 – 576`
  `=58\ text(g)`

Geometry, NAP-C4-NC07

The picture below shows a flower.
 

 
The picture is 2 cm wide. The actual flower is 40 cm wide.

What scale is used in the picture?

 
 1 cm represents 80 cm
 
 4 cm represents 20 cm
 
 1 cm represents 20 cm
 
 1 cm represents 2 cm
Show Answers Only

`text(1 cm represents 20 cm)`

Show Worked Solution

`text(1 cm represents 20 cm)`

Measurement, NAP-C4-NC06

Kim bought these 5 items.
 

 
The total mass of Kim's items is closest to

`3\ text(kg)` `4\ text(kg)` `5\ text(kg)` `8\ text(kg)`
 
 
 
 
Show Answers Only

`text(5 kg)`

Show Worked Solution

`text(2 kg + 1.5 kg + 300 g + 350 g + 400 g)`

`=2\ text(kg + 1.5 kg + 0.3 kg + 0.35 kg +0.4 kg)`

`=4.55\ text(kg)`

`=5\ text{kg  (nearest kg)}`

Algebra, NAP-C4-NC05

Australia Post use formulas to calculate the cost of boxes sent in the post to local destinations.

They calculate the size of the box by the formula:
 

size = width + height + length

 
The minimum postage applies to boxes with a size of 110 cm or less.

Which box below is oversized?

  Length (cm) Height (cm) Width (cm)
 
 40 40 20
 
 60 10 45
 
 50 20 40
 
 40 40 30
Show Answers Only

`60 + 10 + 45 = 115`

Show Worked Solution

`text(Consider the calculation for each option:)`

`text(Option 1:  40 + 40 + 20 = 100 cm)`

`text(Option 2:  60 + 10 + 45 = 115 cm)`

`text(Option 1:  50 + 20 + 40 = 110 cm)`

`text(Option 1:  40 + 40 + 30 = 110 cm)`

 

`:.\ text(The  60 + 10 + 45  box is oversized.)`

Number, NAP-C4-NC04

A buoy is in the ocean recording the waves passing by.

At sea level it measures 0 m. It moves above and below sea level.

Which list gives four sea level recordings arranged in order lowest to highest?

 
 0 m, −2 m, 4 m,−4 m
 
 −2 m, −5 m, 0 m, 1 m
 
 −5 m, 2 m, −3 m, 0 m
 
 −5 m, −3 m, 0 m, 2 m
Show Answers Only

`text(−5m, −3m, 0m, 2m)`

Show Worked Solution

`text(−5 m, −3 m, 0 m, 2 m)`

Algebra, NAP-D4-NC09

George starts doing push-ups to get stronger.

The table below shows the number of push-ups he does each training session.
 

 
The number of push-ups he does each week increases and follows the rule:

Double the last session's number of push-ups and deduct 3.

What is the number of push-ups George did in session 4?

`12` `15` `17` `19`
 
 
 
 
Show Answers Only

`19`

Show Worked Solution

`text(Using the rule:)`

`text(Push-ups in session 4)`

`= (2 xx 11) – 3`

`= 22 – 3`

`= 19`

Algebra, NAP-D4-NC08

Jeremy sold ice creams out of his ice cream truck.

He drew the graph below to show how the number of ice creams he sells in a week is related to their price.
 

 
Which statement best describes the graph?

 
 As the ice cream price goes up, the number sold goes down.
 
 As the ice cream price goes up, the number sold goes up.
 
 As the ice cream price goes down, the number sold goes down.
 
 As the ice cream price goes down, the number sold stays the same.
Show Answers Only

`text(As the ice cream price goes up, the number)`

`text(sold goes down.)`

Show Worked Solution

`text(As the ice cream price goes up, the number)`

`text(sold goes down.)`

Measurement, NAP-D4-NC07

Tran lives in Sydney, but his mother lives in Bangkok.

When it is 1 pm in Sydney, it is 9 am in Bangkok on the same day.

At 7 pm in Sydney, Tran calls his mother in Bangkok.

What was the time in Bangkok when Tran called his mother?

`text(11 pm)` `text(3 am)` `text(11 am)` `text(3 pm)`
 
 
 
 
Show Answers Only

`text(3 pm)`

Show Worked Solution

`text(1 pm in Sydney is 9 am in Bangkok,)`

`=>\ text(Sydney is 4 hours ahead of Bangkok.)`

`:.\ text(7 pm in Sydney is 3 pm in Bangkok.)`

Number, NAP-D4-NC05

Leo took $72 to the 2nd hand book shop and bought a number of books.

All the books cost the same amount.

Leo paid for all the books and had no money left.

Which of these could be the amount that one book cost?

`$11` `$9` `$7` `$5`
 
 
 
 
Show Answers Only

`$9`

Show Worked Solution

`$72 ÷ 8 = $9`

`text($9 is the only amount that can be evenly)`

`text(divided into $72 with no remainder.)`

Number, NAP-D4-NC04

The results of a 400 metres running race final was recorded in the table below.
 

 
The time of the runner who came in 3rd place could be

 
 `text(52.57 seconds.)`
 
 `text(52.71 seconds.)`
 
 `text(53.21 seconds.)`
 
 `text(53.94 seconds.)`
Show Answers Only

`text(52.71 seconds)`

Show Worked Solution

`text{52.71 is slower than 2nd place (52.62)}`

`text{but faster than 4th place (53.19).}`

Geometry, NAP-D4-NC03

A cube can be made using plasticine balls and sticks as shown in the diagram below.
 

 

 How many plasticine balls and sticks would be needed to make a triangular prism?

 
 6 plasticine balls and 9 sticks 
 
 6 plasticine balls and 6 sticks
 
 4 plasticine balls and 8 sticks 
 
 4 plasticine balls and 6 sticks
Show Answers Only

`text(6 plasticine balls and 9 sticks)`

Show Worked Solution

`text(6 plasticine balls and 9 sticks)`

Measurement, NAP-D3-CA10

Eleanor and Rosalie measured the lengths of their smartphones.
 

 
How much longer is Rosalie's phone than Eleanor's?

`0.06\ text(cm)` `0.6\ text(mm)` `6\ text(mm)` `6\ text(cm)`
 
 
 
 
Show Answers Only

`6\ text(mm)`

Show Worked Solution

`14.6\ text(cm) – 14\ text(cm) = 0.6\ text(cm)`

`0.6\ text(cm) = 6\ text(mm)`

Number, NAP-D4-NC02

Which of the following changes is the smallest?

 
 `−8°text(C  to)\ −4°text(C)`
 
 `−5°text(C  to)\ −2°text(C)`
 
 `−2°text(C  to)\  3°text(C)`
 
 `3°text(C  to)\  7°text(C)`
Show Answers Only

`−5^@\ text(C to)\ −2^@text(C)`

Show Worked Solution

`text(Consider each option:)`

`text(– 8  to  – 4)` `=\ text(4° change)`
`text(– 5  to  – 2)` `=\ text(3° change)`
`text(– 2  to  3)` `=\ text(5° change)`
`text(3  to  7)` `=\ text(4° change)`

 

`:.\ −5^@\ text(C to)\ −2^@text(C is the smallest change.)`

Geometry, NAP-D4-NC01

Chevy drives from the car yard to the petrol station.
 

 
Which directions best describe his drive there?

 
 north-east, north, north-west then east
 
 north-west, north, north-east then east
 
 north-east, north, north-west, west
 
 north-west, north, north-east then west
Show Answers Only

`text(north-east, north, north-west, west)`

Show Worked Solution

`text(north-east, north, north-west, west)`

Number, NAP-D3-CA05

Bronwyn receives $1.85 in change at the shop.

She receives only coins.

What is the least number of coins that she could receive?

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

`5`

Show Worked Solution

`text($1.85 in the least number of coins is:)`

`1 xx $1, 1 xx 50text(c), 1 xx 20text(c)`

`1 xx 10text(c), 1 xx 5text(c).`

`:.\ text(Least coins) = 5`

Algebra, NAP-D3-NC10

Jeremy sold ice creams out of his ice cream truck.

He drew the graph below to show how the number of ice creams he sells in a week is related to their price.
 

 
Which statement best describes the graph?

 
 As the ice cream price goes up, the number sold goes down.
 
 As the ice cream price goes up, the number sold goes up.
 
 As the ice cream price goes down, the number sold goes down.
 
 As the ice cream price goes down, the number sold stays the same.
Show Answers Only

`text(As the ice cream price goes up, the number)`

`text(sold goes down.)`

Show Worked Solution

`text(As the ice cream price goes up, the number)`

`text(sold goes down.)`

Number, NAP-E3-CA06

Roger had tests to check his health that are summarised in the table below.
 

Test Normal range Roger's result
Resting heart rate 60 to 95 92
Blood sugar 4.2 to 6.1 4.1
Vitamin C 0.4 to 1.7 0.5

 
For which tests were Roger's results within the normal range?

 
 Resting heart rate and blood sugar
 
 Blood sugar and vitamin C only
 
 Resting heart rate only
 
 Resting heart rate and vitamin C only
Show Answers Only

`text(Resting heart rate and vitamin C only)`

Show Worked Solution

`text(Checking each test:)`

`text(92 is within 60 and 95)`

`text(4.1 is not within 4.2 and 6.1)`

`text(0.5 is within 0.4 and 1.7)`

`:.\ text(Resting heart rate and vitamin C only are within the normal range.)`

Measurement, NAP-D3-NC09

 

 
How much more water is needed to fill the jug to 2 L?

`text(400 mL)` `text(500 mL)` `text(600 mL)` `text(1500 mL)`
 
 
 
 
Show Answers Only

`text(500 mL)`

Show Worked Solution

`text(Volume of water in jug)`

`= 1.5\ text(L)`

`:.\ text(Extra water to be added)`

`= 2.0 – 1.5`

`= 0.5\ text(L)`

`= 500\ text(mL)`

Measurement, NAP-D3-NC08

Bob had a mini tennis court in his backyard, as shown in the diagram below.


 

What is the area of the mini tennis court?

 
 `6\ text(square metres)`
 
 `12\ text(square metres)`
 
 `24\ text(square metres)`
 
 `48\ text(square metres)`
Show Answers Only

`24\ text(m²)`

Show Worked Solution

`text(The mini tennis court has dimensions)`

`4 xx 6.`

`:.\ text(Area)` `= 4 xx 6`
  `= 24\ text(m²)`

Number, NAP-E3-CA11

Davis wants to make 7 pavlovas.

Each pavlova needs 7 eggs. He has no eggs so he goes to the shop.

The shop sells eggs in cartons of 12.

How many cartons of eggs does Davis need to buy?

`3`   `4`  `5`  `7`
 
 
 
 
Show Answers Only

`5`

Show Worked Solution

`text(Number of eggs needed)`

`= 7 xx 7`

`= 49`
 

`:.\ text(Number of cartons needed)`

`=49/12`

`= 4.083…`

`=5\ text(cartons)`

Geometry, NAP-E3-CA09

A gymnast does a move where she makes 3 full somersaults and lands back on her feet.

By how many degrees has the gymnast rotated her body in this move?

`270^@` `540^@` `720^@` `1080^@`
 
 
 
 
Show Answers Only

`1080^@`

Show Worked Solution

`text(One somersault rotates)\ 360^@.`

`:.3\ text(somersaults)` `= 3 xx 360^@`
  `= 1080^@`

Geometry, NAP-E3-CA08

A sculpture is pictured from 3 different angles below:
 

 
The sculpture is in the shape of

 
 a rectangle and a circle.
 
 two spheres.
 
 a cylinder and a circle.
 
 a cylinder and a sphere.
Show Answers Only

`text(A cylinder and a sphere.)`

Show Worked Solution

`text(A cylinder and a sphere.)`

Measurement, NAP-E3-CA03

A neighbourhood soccer oval is marked out with the dimensions shown below.
 

 
What is the area of the field?

 
 `298\ text(square metres)`
 
 `2842.75\ text(square metres)`
 
 `5261.25\ text(square metres)`
 
 `8123.25\ text(square metres)`
Show Answers Only

`5261.25\ text(m²)`

Show Worked Solution

`text(Area of the soccer field)`

`= 57.5 xx 91.5`

`= 5261.25\ text(m²)`

Number, NAP-B3-NC08 SA

A number is multiplied by itself and then 9 is added.

The answer is 18.

What is the number?
Show Answers Only

`3`

Show Worked Solution

`text(Reversing the order of operations:)`

`18-9=9`

`3 xx 3 = 9`
 

`text(Check answer:)`

`3 xx 3 +9=18`

`:.\ text(The number is 3.)`

Number and Algebra, NAP-B3-NC03

Which one of these has the same value as  `14 xx 2`?

`10 + 4 + 2` `10 xx 2 + 4` `10 xx 2 + 2` `10 xx 2 + 8`
 
 
 
 
Show Answers Only

`10 xx 2 + 8`

Show Worked Solution
`14 xx 2` `=28`
`10 xx 2 +8` `=20 +8`
  `=28`

Statistics, NAP-C3-CA09

This table shows the number of people who visited a war memorial on weekdays over 4 weeks.

 

Which day had the greatest total attendance over the 4 weeks?

`text(Monday)` `text(Tuesday)` `text(Wednesday)` `text(Thursday)`
 
 
 
  
Show Answers Only

`text(Tuesday)`

Show Worked Solution

`text(One strategy:)`

`text(At a glance, Thursday and Friday numbers look low.)`

`=>\ text(Checking total attendances on the 1st 3 days:)`

`text(Monday = 226)`

`text(Tuesday = 266)`

`text(Wednesday = 234)`

`:.\ text(Greatest total attendance on Tuesday.)`

Geometry, NAP-C3-CA08

This is part of the map of Hunter Street.

Jo Jo lives at number 2 which is the 1st house on the East side.
 

 
What is the number of the 16th house on Hunter Street on the east side?

`8`  `16` `32` `36`
 
 
 
 
Show Answers Only

`32`

Show Worked Solution

`text(1st house on East side is number 2.)`

`text(2nd house on East side is number 4.)`

`vdots`

`:.\ text(16th house on East side is number 32.)`

Number, NAP-F3-CA08

The shaded area on this graph shows how much of a computer file has loaded.
 

 

 
What percentage of the file has loaded?

`text(65%)` `text(70%)` `text(75%)` `text(80%)`
 
 
 
 
Show Answers Only

`text(75%)`

Show Worked Solution

`text(Total number of bars) = 20`

`text(Number of black bars) = 15`

`:.\ text(Percentage loaded)` `= 15/20`
  `=0.75`
  `=75text(%)`

Measurement, NAP-E3-NC13

Tenzing started his trek at 5:30 am.

He arrived at his destination `14 1/2` hours later.

At what time did he arrive at his destination?

`7:30\ text(pm)` `8:00\ text(pm)` `9:30\ text(pm)` `10:00\ text(pm)`
 
 
 
 
Show Answers Only

`text(8:00 pm)`

Show Worked Solution

`text(One strategy:)`

`5:30\ text(am plus)\ 14 1/2\ text(hours)` `=\ text(5:30 pm plus)\ 2 1/2\ text(hours)`
  `=\ text(8:00 pm)`

Geometry, NAP-E3-NC09

Irene placed three identical tiles together at their edges.

She drew around the outside to make this new shape.
 

 
Which of these could have been the shape of her tiles?

`text(triangles)` `text(rectangles)` `text(trapeziums)` `text(rhombuses)`
 
 
 
 
Show Answers Only

`text(rhombuses)`

Show Worked Solution

`text(rhombuses)`

Measurement, NAP-F3-CA06

Two sides of a triangle measure 6 cm and 12 cm.

Which one of these statements about the length of the third side is true?

 
 Its length is 6 cm.
 
 Its length is less than 6 cm.
 
 Its length is greater than 18 cm.
 
 Its length is greater than 6 cm but less than 18 cm.
Show Answers Only

`text(Its length is greater than 6 cm but less than 18 cm.)`

Show Worked Solution

`=>\ text(One side of a triangle cannot be longer than)`

`text(the sum of the 2 other sides.)`

`=>\ text(One side of a triangle cannot be shorter than)`

`text(the difference between the other 2 sides.)`

`:.\ text(Its length is greater than 6 cm but less)`

`text(than 18 cm)` 

Geometry, NAP-F3-NC12

Kimoko cut a regular pentagon into several identical pieces with no paper left over.
 

 
Which of these could be the shape of the pieces?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(A pentagon can be made up of 5 isosceles)`

`text(triangles as shown below.)`

`:.\ text(The shape of the pieces could only be:)`