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Number and Algebra, NAP-G2-20

Rob uses sticks to make a pattern.

He starts with 3 sticks for Design 1.
 

 
How many sticks does Rob need for Design 5?

`39` `42` `45` `48`
 
 
 
 
Show Answers Only

`45`

Show Worked Solution

`text(One possible strategy:)`

`text(Each new row contains an extra triangle than the row above.)`

`=>\ text(Design 5 will have 5 triangles on the bottom row.)`
 

`:.\ text(Total sticks)` `= 30 + (5 xx 3)`
  `= 30 + 15`
  `= 45`

Geometry, NAP-G2-19

Sandra has a square piece of paper.

She folds it in half twice and then cuts a triangle piece as shown below.
 

What will the square piece of paper look like after Sandra unfolds it?

 
 
 
 
Show Answers Only

Show Worked Solution

Geometry, NAP-G2-16

Penny stuck some different shapes onto the back window of her car.

They look like this from the outside.
 

 
What do they look like from inside the car?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Consider the fish shape and the triangle.)`

`text(From the inside of the car:)`

`text(The fish tail will start from the left side, and it will be on top)`

`text(of the edge of the triangle.)`
 

Number and Algebra, NAP-H2-23

Riley had 3 bird cages that each contained 12 birds.

He then bought one more bird cage and spread the birds out evenly between the 4 cages.

How many birds were then in each cage?

`6` `9` `10` `12`
 
 
 
 
Show Answers Only

`9`

Show Worked Solution
`text(Total birds)` `= 3 xx 12`
  `= 36`

 

`:.\ text(Birds in each of 4 cages)`

`= 36 ÷ 4`

`= 9`

Number and Algebra, NAP-H2-19

Sharon bought 6 chocolate bars that cost $1.20 each.

She gave the shopkeeper a $10 note.

How much change should Sharon expect?

`$2.80` `$4` `$7.20` `$8.80`
 
 
 
 
Show Answers Only

`$2.80`

Show Worked Solution

`text(C) text(ost of 6 chocolate bars)`

`6 xx $1.20 = $7.20`

 

`:.\ text(Sharon’s change)` `=10.00 – 7.20`
  `=$2.80`

Number and Algebra, NAP-H2-13

Michelle, Lucy, Clare and Steph are sisters.

The years they were born are recorded in the table below.
 

 
Who is the second youngest sister?

`text(Michelle)` `text(Lucy)` `text(Clare)` `text(Steph)`
 
 
 
 
Show Answers Only

`text(Lucy)`

Show Worked Solution

`text(The order from oldest to youngest is:)`

`text{Clare (1977), Michelle (1978), Lucy (1987), Steph (1988).}`

`:.\ text(Lucy is the second youngest.)`

Number and Algebra, NAP-I2-27

Curly, Larry and Moe share a bag of oranges.

Curly and Larry get `1/5` of the oranges each.

What fraction of the bag of oranges does Moe get?

`4/5`  `3/5`  `2/5`  `1/5`
 
 
 
 
Show Answers Only

`3/5`

Show Worked Solution

`text(Fraction that Curly and Larry get)`

`= 1/5 + 1/5`

`= 2/5`

`:.\ text(Fraction left for Moe)`

`= 1 – 2/5`

`= 3/5`

Number and Algebra, NAP-I2-26

Bennelong writes a number on a piece of paper and hides it.

He gives his friend the following clues about his number.

  • The number is less than 500.
  • The number has 30 tens.
  • The digit in the ones place is one more than the digit in
    the hundreds place.

What is Bennelong's number?

`30` `34` `300` `304`
 
 
 
 
Show Answers Only

`304`

Show Worked Solution

`text(Consider the following clues,)`

`text(Number has 30 tens,)`

`=>\ text(Number is 3 digits, starting with 30_)`

 

`text(The “ones” digit is one more than the “hundreds” digit,)`

`:.\ text(Number must be 304.)`

Geometry, NAP-D2-23

Two plans of a sports complex can be seen below.
 

 
Which designated sports area is closest to the corner of Bone Street and Depp Street?

Karate Fencing Ping Pong Yoga
 
 
 
 
Show Answers Only

`text(Yoga)`

Show Worked Solution

`text(Rotate the second plan so that North points)`

`text(in the same direction.)`

`:.\ text(Yoga is closest to the corner of Bone and Depp Sts.)`

Number and Algebra, NAP-D2-20

A service station sells bottles of water for $2 each.

It also has a special of 3 bottles for $5.

What is the lowest cost of 8 bottles of water?

`$10.00` `$12.00` `$14.00` `$16.00`
 
 
 
 
Show Answers Only

`$14.00`

Show Worked Solution

`text(Lowest cost of 8 bottles)`

`= (2 xx $5) + (2 xx $2)`

`= $14`

Measurement, NAP-D2-18

 
How much more water is need to fill the jug to 2 litres?

`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-I2-25

Oliver's karate grading started at 9:15 am and went for  `3 1/4`  hours.

He then went straight home, which took him  `3/4`  hours.

What time did Oliver get home?

12:30 pm 1:00 am 1:00 pm 1:15 am 1:15 pm
 
 
 
 
 
Show Answers Only

`text(1:15 pm)`

Show Worked Solution

`text(Karate finishes at 9:15 plus 3 hours and 15)`

`text(minutes, which is 12:30 pm.)`

`text(12:30 plus 45 minutes means Oliver arrives)`

`text(home at 1:15 pm.)`

Statistics, NAP-I2-22

The number of students that could solve a Rubik's cube in less than 2 minutes were counted at 7 different primary schools.

The results were recorded in the graph below.
 

How many students, in total, could solve the cube in less than 2 minutes?

`3` `14` `15` `18`
 
 
 
 
Show Answers Only

`15`

Show Worked Solution

`text(Total students who can solve in 2 mins)`

`= 2+2+3+0+3+2+3`

`=15`

Number and Algebra, NAP-D2-15

Isla and Grace both bought a new towel and swimmers for summer.

They each spent the same amount of money.

Isla's towel cost $17.85 and her swimmers cost $22.15.

Grace's towel cost $20.90.

How much did Grace's swimmers cost?

`$19.00` `$19.10` `$20.90` `$22.15`
 
 
 
 
Show Answers Only

`$19.10`

Show Worked Solution
`text(Isla’s total cost)` `=17.85 + 22.15`
  `=$40.00`

 

`:.\ text(Grace’s swimmers)` `=40.00 – 20.90`
  `=20.00 – 0.90`
  `=$19.10`

Measurement, NAP-B3-CA10

A water jug has a capacity of 3.65 L.

How many millilitres does the water jug hold when it is full?

`365` `3065` `3650` `36\ 500`
 
 
 
 
Show Answers Only

`3650\ text(mL)`

Show Worked Solution

`text(1 litre = 1000 mL:)`

`:. 3.65\ text(L) xx 1000 = 8550\ text(mL)`

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.)`