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Number, NAPX-K2-30 SA

Candice buys art supplies for her art studio.

She rounds each price to the nearest dollar to estimate the total cost of the supplies.
 

 
How much is Candice's estimate?

$  
Show Answers Only

`$33`

Show Worked Solution

`text(Rounding each item to the nearest dollar:)`

`text(paint = $7)`

`text(pencil = $2)`

`text(canvas = $13)`

`text(chalk = $7)`

`text(glue = $4)`
 

`text(Candice’s Estimate)` `= 7 + 2 + 13 + 7 + 4`
  `= $33`

Measurement, NAPX-K2-27 SA

What is the difference between the temperatures in Sydney and Melbourne?
 

  `\ text(°C)`
Show Answers Only

`18\ text(°C)`

Show Worked Solution

`text(Each mark is worth 2°C)`

`text(Temperature in Sydney is 36°C)`

`text(Temperature in Melbourne is 18°C)`
 

`:.\ text(Difference)` `= 36 – 18`
  `= 18\ text(°C)`

Statistics, NAPX-p122921v02

The picture graph shows how many tonnes of concrete are needed for 4 jobs.
 

 
How many more tonnes of concrete does Job 1 need than Job 3?

  tonnes
Show Answers Only

`2\ text(tonnes)`

Show Worked Solution

`text(Job 1 needs 9 tonnes)`

`text(Job 2 needs 7 tonnes)`
 

`:.\ text(Extra tonnes)` `= 9 – 7`
  `= 2\ text(tonnes)`

Statistics, NAPX-p122921v01

The picture graph shows how many tonnes of fertiliser are needed for 4 gardens.
 

 
How many more tonnes of fertiliser does Garden 4 need than Garden 3?

  tonnes
Show Answers Only

`7\ text(tonnes)`

Show Worked Solution

`text(Garden 4 needs 12 tonnes)`

`text(Garden 3 needs 5 tonnes)`
 

`:.\ text(Extra tonnes)` `= 12 – 5`
  `= 7\ text(tonnes)`

Statistics, NAPX-K2-23 SA

The picture graph shows how many tonnes of fertiliser are needed for 4 gardens.

   

How many more tonnes of fertiliser does Garden 2 need than Garden 3?

  tonnes
Show Answers Only

`5\ text(tonnes)`

Show Worked Solution

`text(Garden 2 needs 10 tonnes)`

`text(Garden 3 needs 5 tonnes)`
 

`:.\ text(Extra tonnes)` `= 10 – 5`
  `= 5\ text(tonnes)`

Algebra, NAPX-H2-39 SA

Soda cans are sold in three different ways at the supermarket.
  


 

What is the cheapest price that someone can buy 14 cans for?
Show Answers Only

`$15.80`

Show Worked Solution

`text(Two six packs and two cans:)`

`= (2 xx 7.00) + (2 xx 1.20)`

`= 14 + 2.40`

`= $16.80`
 

`text(One ten pack and 4 single cans:)`

`= 11 + (4 xx 1.20)`

`= 11 + 4.80`

`= $15.80`

 
`:.\ text(Cheapest price = $15.80)`

Algebra, NAPX-H2-35 SA

William spent $15.30 on pencils for the new school year.

Each pencil cost 30 cents.

How many pencils did he buy?

 
Show Answers Only

`51`

Show Worked Solution

`text(Strategy 1)`

`=> 10\ text(pencils cost $3.00)`

 `=> 50\ text(pencils cost $15.00)`

`:. 51\ text(pencils cost $15.30)`

 

`text(Strategy 2)`

`$15.30 = 1530\ text(cents)`

`text(Using long division:)`

`1530-:30 = 51`

Algebra, NAPX-H2-34 SA

Bonnie and Clyde ate 57 cashew nuts.

Bonnie ate 13 less cashew nuts than Clyde.

How many cashew nuts did Bonnie eat?

 
Show Answers Only

`22`

Show Worked Solution

`text(Strategy 1)`

`text(Consider the possible splits -)`

`28 – 29:`  `text(Bonnie eats 1 less)`
`27 – 30:`  `text(Bonnie eats 3 less)`
`vdots`  
`22 – 35:`  `text(Bonnie eats 13 less)`

 
`:.\ text(Bonnie eats 22 cashew nuts)`

 

`text{Strategy 2 (Algebra)}`

`text(Let)\ c =\ text(number of cashews Bonnie eats)`

`c + c + 13` `= 57`
`2c` `= 44`
`c` `= 44 ÷ 2`
  `= 22`

Measurement, NAPX-H2-33 SA

Usain and Merv are the first two runners in a cross country relay team.

Usain runs 1 lap of the course and passes a baton to Merv for the second lap.

Their results are in the table below.
 

 
How long after Usain started, in seconds, did Merv finish his lap?

    seconds
Show Answers Only

`text(350 seconds)`

Show Worked Solution
`text(Total time)` `= 2:17 + 3:33`
  `= 5\ text(minutes and 50 seconds)`
  `= (5 xx 60) + 50`
  `= 300 + 50`
  `= 350\ \ text(seconds)`

Algebra, NAPX-K2-05 SA

In a squash competition Michelle won 9 games and lost the other 7 games.

Finish the subtraction sentence below to show the number of games Michelle played.

`\ - 9 = 7`
Show Answers Only

`16`

Show Worked Solution
 
 `\ – 9` `= 7`
 
 `= 7 + 9`
    `= 16`

Number, NAPX-H2-28 SA

 

What number is the arrow pointing to on this number line?
Show Answers Only

`75`

Show Worked Solution

`text(Each interval on the number line is worth 15.)`

`:.\ text(Number the arrow points to)`

`= 60 + 15`

`= 75`

Statistics, NAPX-p120830v01

The goals scored by 4 players in a season of soccer were recorded in the graph below.
 

 
Simon scored 6 goals in the season.

Gigi scored 3 goals.

How many more goals did Henry score than Fiona?

 
Show Answers Only

`5`

Show Worked Solution

`text(S)text(ince Simon scored 6 goals)`

 `text(= 2 goals)`

`=>\ text(Henry scored 8 goals)`

`=>\ text(Gigi scored 1 goal)`

`:.\ text(Henry scored 7 more goals than Fiona.)`

Statistics, NAPX-H2-26 SA

The goals scored by 4 players in a season of soccer were recorded in the graph below.
 

 
Fiona scored 8 goals in the season.

Simon scored 5 goals.

How many more goals did Henry score than Gigi?

 
Show Answers Only

`5`

Show Worked Solution

`text(S)text(ince Fiona scored 8 goals)`

 `text(= 2 goals)`

`=>\ text(Henry scored 10)`

`=>\ text(Gigi scored 5)`

`:.\ text(Henry scored 5 more than Gigi.)`

Algebra, NAPX-I2-40 SA

There are 56 students in year 7 at a school.

Every student is either right-handed or left-handed.

There are 6 times more right-handers than left-handers.

How many left handers are there in Year 7?

 
Show Answers Only

`8`

Show Worked Solution

`text(S) text(ince there are 6 times more right-handers,)`

`=>\ text(1 out of 7 are left-handers.)`
 

`:.\ text(Number of left-handers)`

`= 1/7 xx 56`

`= 8`

Algebra, NAPX-I2-36 SA

A group of 8 friends are planning a trip to Leyland Brothers World.

Lunch will cost $7 per person.

Entry will cost $13 per person.

Hiring a bus for transport will cost $180 for the whole group.

What is the expected total cost of the trip for the whole group?

$  
Show Answers Only

`$340`

Show Worked Solution
`text(Lunch cost)` `= 8 xx 7 = $56`
`text(Entry cost)` `= 8 xx 13=$104`
`text(Bus hire)` ` = $180`

 

`:.\ text(Total cost)` `= 56 + 104 + 180`
  `= $340`

Statistics, NAPX-p116609v01

Zyler recorded the number of times he was swooped by magpies over a three month period.

The results were recorded in the table below.

     

How many times Zyler has been swooped?
Show Answers Only

`29`

Show Worked Solution

`text(Number of times swooped)`

`= 8 + 19 + 2`

`= 29`

Statistics, NAPX-I2-02 SA

Cher recorded the colour of all cars that drove past her school during one hour for a class project.

The results were recorded in the table below.
 

 
How many cars drove past Cher's school in the hour?
Show Answers Only

`43`

Show Worked Solution

`text(Number of cars)`

`= 7 + 17 + 13 + 6`

`= 43`

Geometry, NAPX-G3-NC31 SA, NAPX-G2-40

The pictures show the front, side and top views of an object made of cubes.
 


 

How many cubes are needed to make the object?
Show Answers Only

`11`

Show Worked Solution

`text(Using the top view)`

`=>\ text(7 cubes on base.)`
 

`text(Using the front view)`

`=>\ text(Stacked cubes only along the middle row.)`
 

`text(Using the side view)`

`=>\ text(4 cubes in total are stacked)`

`text(higher than the base level.)`
 

`:.\ text(Total cubes in the object = 11.)`

Number, NAPX-F3-CA31 SA

Shinji used 8 litres of paint to paint a wall.

The wall was a square with sides 4 metres long.

How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 10 metres wide?

   litres
Show Answers Only

`15`

Show Worked Solution

`text(Area of smaller wall)`

`= 4 xx 4`

`= 16\ text(m²)`
 

`text(Area of larger wall)`

`= 3 xx 10`

`= 30\ text(m²)`
 

`:.\ text(Paint needed for larger wall)`

`= 30/16 xx 8`

`= 15\ text(litres)`

Number, NAPX-F3-CA30 SA

A farmers market sells potatoes in four different sizes.
 


 
What is the lowest price a customer can pay for 8 kg of potatoes?

$   
Show Answers Only

`$12.20`

Show Worked Solution

`text(Calculate the cost per kg for each size:)`

`text(1 kg: $3.40 per kg)`

`text(2 kg: $6.10 ÷ 2 = $3.05 per kg)`

`text(3 kg: $9.35 ÷ 3 ≈ $3.12 per kg)`

`text(5 kg: $15.75 ÷ 5 = $3.15 per kg)`
 

 `:.\ text(Cheapest price to buy 8 kg)`

`= 4 xx 3.05`

`= $12.20`

Number, NAPX-F3-CA26 SA

Bill buys a new computer.

The disk in its hard drive makes 110 full turns every second.

How many minutes will it take for the disk to make 363 000 full turns?

   minutes 
Show Answers Only

`55\ text(minutes)`

Show Worked Solution

`text(Turns in 1 minute)`

`= 60 xx 110`

`= 6600`
 

`:.\ text(Minutes needed)`

`= 363\ 000 -: 6600`

`= 55\ text(minutes)`

Number, NAPX-F3-CA25 SA

The mass of a 50-cent coin is about 13.3 grams.

The mass of a 10-cent coin is about 5.65 grams.

Tom has 226.1 grams of 50-cent coins.

Jerry has 129.95 grams of 10-cent coins.

How much more are Tom's coins worth than Jerry's coins, in cents?

   cents
Show Answers Only

`620\ text(cents)`

Show Worked Solution

`text(Value of Tom’s coins)`

`= 226.1/13.3 xx 0.50`

`= 17 xx 0.50`

`= $8.50`

 

`text(Value of Jerry’s coins)`

`= 129.95/5.65 xx 0.10`

`= 23 xx 0.10`

`= $2.30`

 

`:.\ text(Extra worth of Tom’s coins)`

`= 850 – 230`

`= 620\ text(cents)`

Number, NAPX-F3-CA24 SA

A piece of wood is leaning against four stacks of bricks.
 

 
There are 31 bricks in total.

How many bricks are in the tallest stack?
Show Answers Only

`10\ text(bricks)`

Show Worked Solution

`text(15 bricks can be seen above the wood.)`

`=>\ text(16 bricks cannot be seen)`

`=>\ text(4 stacks of 4 bricks cannot be seen)`

 

`:.\ text(Height of tallest stack)`

`= 6 + 4`

`= 10`

Measurement, NAPX-G3-NC29 SA

The length of this rectangle is one and a half times its height.
 

 
The perimeter of the rectangle is 50 centimetres.

What is the area of the rectangle?

  square centimetres
Show Answers Only

`150\ text(cm²)`

Show Worked Solution
`text(Let)\ x` `=\ text(height)`
`3/2 x` `=\ text(length)`
`2 xx (x + 3/2 x)` `= 50`
`5x` `= 50`
`x` `= 10`

 

`:.\ text(Area)` `= 10 xx 15`
  `= 150\ text(cm²)`

Algebra, NAPX-G3-NC26 SA

Grace and Angie are dog breeders.

The total number of dogs they currently own is 23.

Grace owns 9 more dogs than Angie.

How many dogs does Grace own?
Show Answers Only

`16`

Show Worked Solution

`text{Solution 1 (Trial and error)}`

`text(If Grace owns 14)`

`=>\ text{Angie owns 9 (5 difference)}`

 `text(If Grace owns 16)`

`=>\ text{Angie owns 7 (9 difference)}`

`:.\ text(Grace owns 16 dogs.)`

 

`text{Solution 2 (Algebra)}`

`text(Let)\ n = text(number of dogs Angie owns)`

`=>\ n + 9 = text(Grace’s dogs)`

`n + n + 9` `= 23`
`2n` `= 14`
`n` `= 7`
`n + 9` `= 16`

Number, NAPX-G3-NC23 SA

Health insurance for his family costs Rex $90 per week.

How much does it cost him over 52 weeks?

$  
Show Answers Only

`$4680`

Show Worked Solution

`text{One strategy (mental arithmetic)}`

`52 xx 90` `= 52 xx 100 – 52 xx 10`
  `= 5200 – 520`
  `= $4680`

Number, NAPX-G3-NC21 SA

Yuna used 300 grams of sugar to make 15 cookies.

How many grams of sugar will she need to make 25 cookies?

 grams
Show Answers Only

`text(500 grams)`

Show Worked Solution

`text(Sugar to make 1 cookie) = 300/15 = 20\ text(grams)`

`:.\ text(Sugar to make 25 cookies)`

`= 25 xx 20`

`= 500\ text(grams)`

Number, NAPX-G3-CA31 SA

One litre of cordial contains 25 grams of sugar.

How many millilitres of cordial contain 0.5 grams of sugar?

   millilitres
Show Answers Only

`20\ text(mL)`

Show Worked Solution

`text(1 litre = 1000 mL)`

`text(1000 mL contains 25 grams)`
 

`:.\ text(Volume that contains 0.5 grams)`

`= 0.5/25 xx 1000`

`= 20\ text(mL)`