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Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, NAPX-J3-CA23

The running time of a documentary is 148 minutes.

Paul starts watching the documentary at 2:13 pm.

What time will the documentary end in 24-hour time?

12:30 15:61 16:01 16:31 16:41
 
 
 
 
 
Show Answers Only

`16:41`

Show Worked Solution
`text(Running time)` `= 148\ text(minutes)`
  `= 2\ text(hours 28 minutes`

 

`:.\ text(Finish time)` `= 2:13\ text(pm plus 2 hours 28 minutes)`
  `= 4:41\ text(pm)`
  `= 16:41`

Statistics and Probability, NAPX-J3-CA19, NAPX-J2-34

Ricky has a bag of marbles. His marbles are orange, white, blue and green.
 

 
Ricky picks one marble from his bag.

Which of the following could be the probability that the marble he picks is green.

`23/7` `1.07` `7` `7/23`
 
 
 
 
Show Answers Only

`7/23`

Show Worked Solution

`text(Any probability must be between 0 and 1.)`

`:.\ text(Only possibility is)\ 7/23.`

Number, NAPX-J3-CA18

Sergio's golf bag contains white, pink and yellow golf balls.

There are:

  • 6 more yellow balls than pink balls
  • 8 fewer pink balls than white balls
  • 13 white balls

How many golf balls, in total, are in Sergio's bag?

`17` `23` `27` `29` `37`
 
 
 
 
 
Show Answers Only

`29`

Show Worked Solution

`text{13 white balls (given)}`

`=> 13 – 8 = 5\ text(pink balls)`

`=> 5 + 6 = 11\ text(yellow balls)`

`:.\ text(Total balls)` `= 13 + 5 + 11`
  `= 29`

Statistics and Probability, NAPX-J3-CA17, NAPX-J2-31

The bottles in Leisa's fridge are pictured below.
 

 
Leisa decides to make a graph where each bar represents one type of bottle in her fridge.
 

 
Leisa makes an error when creating the graph.

What should Leisa do to correct the error?

 
 Change the 'Number of bottles' label to 'Volume of bottles'.
 
 Change the title to 'Number of bottles in the fridge by volume'.
 
 The thickness of each bar should vary, depending on the number of bottles.
 
 Remove the 'Water' category since tonic water and soda water are already shown.
Show Answers Only

`text(Remove the ‘Water’ category since tonic water and)`

`text(soda water are already shown.)`

Show Worked Solution

`text(Remove the ‘Water’ category since tonic water and)`

`text(soda water are already shown.)`

Number, NAPX-J3-CA14

Kami uses the number sentence  `9 xx 12 = 108`  to solve a problem.

Which of the following could be the problem?

 
 Kami buys 9 books that cost $12 each. How many books does she buy?
 
 Kami spends $9 on 12 books. How many books does she buy?
 
 Kami buys 12 books that cost $9 each. How much does she spend?
 
 Kami buys 9 books. How much does each book cost?
Show Answers Only

`text(Kami buys 12 books that cost $9 each.)`

`text(How much does she spend)`

Show Worked Solution

`text($9 per book × 12 books = $180)`

`:.\ text(Kami buys 12 books that cost $9 each.)`

`text(How much does she spend?)`

Number, NAPX-J3-CA09

Pamela is a teacher and buys pencils for her class.

She purchases the pencils in two different sized packets.
 

 
Pamela buys 6 packet A's and 4 packet B's.

She then divides all the pencils equally among her 6 students.

How many pencils does each student receive?

`6` `7` `8` `42` `48`
 
 
 
 
 
Show Answers Only

`8`

Show Worked Solution
`text(Total pencils)` `= (6 xx 6)+(4 xx3)`
  `= 48`

 

`:.\ text(Pencils per student)` `= 48 -: 6`
  `= 8`

Statistics and Probability, NAPX-J3-CA01

Four students recorded the number of times they participated in different sports in one week in the table below.
  

  
In total, which sport was participated in the most times?

AFL Soccer Tennis Netball
 
 
 
 
Show Answers Only

`text(Tennis)`

Show Worked Solution

`text(Times each sport was played:)`

`text(AFL – 9)`

`text(Soccer – 10)`

`text(Tennis – 12)`

`text(Netball – 6)`

`:.\ text(Tennis was participated in the most.)`

Measurement, NAPX-E4-NC26

Phoebe completed a double marathon on two consecutive days of a running carnival.

Her times are in the table below.
 

 
What was Phoebe's total time for the first two days of this event?

`25:53:21` `26:13:21` `25:113:81` `26:54:21`
 
 
 
 
Show Answers Only

`26:54:21`

Show Worked Solution

`12:58:46\ \ text(plus)\ \ 13:55:35`

`= 26:54:21`

`text{(Remember to convert more than 60 seconds into}`

`text{into minutes and seconds, and likewise convert}`

`text{more than 60 minutes into hours and minutes)}`

Number, NAPX-E4-NC24

A dog kennel has 300 dogs staying.

90 of the dogs are labradors.

What is the ratio of labradors to non-labradors?

`3:5` `3:7` `3:9` `3:10`
 
 
 
 
Show Answers Only

`3:7`

Show Worked Solution

`text(S)text(ince 90 are labradors,)`

`300 – 90 = 210\ text(are non-labradors.)`

`text(Labradors)` `:\ text(Non-labradors)`
`90` `: 210`
`3` `: 7`

Algebra, NAPX-E4-NC23

A positive number `x` is multiplied by 6, then 12 is added.

Which of the following operations give the same result?

 
 Add 2 to `x`, then multiply by 12.
 
 Add 2 to `x`, then multiply by 6.
 
 Add 6 to `x`, then multiply by 2.
 
 Add 12 to `x`, then multiply by 6.
Show Answers Only

`text(Add 2 to)\  x, \ text(then multiply by 6.)`

Show Worked Solution

`text(Number) = 6x + 12`

 

`text(Consider each option:)`

`(x + 2) xx 12` `= 12x + 24`  
`(x + 2) xx 6` `= 6x + 12`
`(x + 6) xx 2` `= 2x + 12`  
`(x + 12) xx 6` `= 6x + 72`  

 

`:.\ text(Add 2 to)\  x, \ text(then multiply by 6.)`

Measurement, NAPX-E4-NC15

Snowphish is hunting seals.

He leaves his igloo at 5:25 am.

If he returns at 8:15 am, how long has he been away?

 
 `text(2 hours and 10 minutes)`
 
 `text(2 hours and 50 minutes)`
 
 `text(3 hours and 10 minutes)`
 
 `text(3 hours and 50 minutes)`
Show Answers Only

`text(2 hours and 50 minutes)`

Show Worked Solution

`text(5:25 am plus 2 hours and 50 minutes)`

`= 8: 15\ text(am)`

Number, NAPX-E4-NC14, NAPX-E3-NC18

Keenak is making a fruit cake.

The recipe says he needs 1 cup of sultanas for every 4 cups of flour.

If 7 cups of flour are used, how many cups of sultanas are needed?

`1 3/4\ text(cups)` `2 1/2\ text(cups)` `3\ text(cups)` `28\ text(cups)`
 
 
 
 
Show Answers Only

`1 3/4\ text(cups)`

Show Worked Solution
`text(If 4 cups of flour)` `=> 1\ text(cup sultanas)`
`text(1 cup of flour)` `=> 1/4\ text(cup sultanas)`
`:. 7\ text(cups of flour)` `= 7 xx 1/4`
  `= 1 3/4\ text(cups of sultanas)`

Number, NAPX-E4-NC13

Columbo had a full bucket of water.
 

 

 
He put two holes in the bottom and the water leaked out.

After a few minutes, Columbo closed off one of the holes in the bucket and the water poured out more slowly.

Which graph below best shows the depth of water in the bucket against time?

 

   
 
 
 
 
Show Answers Only

Show Worked Solution

`text(The depth decreases quickly at the start)`

`text{(steep decline) and then slows down when}`

`text{one hole is closed (less steep decline).}`

Statistics and Probability, NAPX-E4-NC12

Quincy rolls one standard six-sided dice.

Which of the following events has a probability of less than  0.5?

 
 rolling an even number
 
 rolling a number greater than 5
 
 rolling a number greater than or equal to 2
 
 rolling a number less than or equal to 6
Show Answers Only

`text(rolling a number greater than 5)`

Show Worked Solution

`text{Pr (rolling number greater than 5)}`

`=\ text{Pr (rolling a 6)}`

`= 1/6\ \ …\ text{(which is less than 0.5)}`

Algebra, NAPX-E4-NC11

Coral bought 8 bags of mandarins from the market.

Each bag had the same number of mandarins and a total of 56 mandarins were purchased.

Which equation shows the average number of mandarins,  `x`,  in each bag?

 
 `x = 56 - 8`
 
 `x = 56 xx 8`
 
 `x xx 8 = 56`
 
 `x ÷ 8 = 56`
Show Answers Only

`x xx 8 = 56`

Show Worked Solution
`text(Mandarins per bag) ` `= text(total mandarins)/text(number of bags)`
` x` `= 56 ÷ 8`
`:. x xx 8` `= 56`

Algebra, NAPX-E4-NC10, NAPX-E3-NC12

The table below shows the results of a rule that changes each    into a  .
 

 
Which rule below was used?

 
      `=`        `xx 3 - 1`
 
      `=`        `xx 3 + 1`
 
      `=`        `xx 2 + 1`
 
      `=`        `xx 5 - 5`
Show Answers Only
     `=`        `xx 5 – 5`
Show Worked Solution

`text(Consider the final option:)`

`5` `= 2 xx 5 – 5`
`10` `= 3 xx 5 – 5`
`25` `= 6 xx 5 – 5`

Statistics and Probability, NAPX-E4-NC08

This graph shows the price per tonne of resources in a country.
 

 
The price of coal was less than the price of iron ore for a number of quarters, as shown by the graph.

In one of those quarters, the price of aluminium scrap metal fell below $50 per tonne.

Which quarter was this?

`text(2010 Q1)` `text(2010 Q4)` `text(2011 Q4)` `text(2013 Q3)`
 
 
 
 
Show Answers Only

`text(2011 Q4)`

Show Worked Solution

`text(In 2011 Q4, the aluminium scrap price was below)`

`text($50 and coal was cheaper than iron ore.)`

Algebra, NAPX-E4-NC07

Which expression is equal to  `4r^3`?

 
 `7 xx r`
 
 `12 xx r`
 
 `4 xx r xx 4 xx r xx 4 xx r`
 
 `4 + 4 + 4 + r + r + r`
 
 `4 xx r xx r xx r`
Show Answers Only

`4 xx r xx r xx r`

Show Worked Solution

`4r^3 = 4 xx r xx r xx r`

Number, NAPX-E4-NC04

Ash bought 7 candy canes and 2 chocolate bars from the shop.

The candy cost 25 cents each and the chocolate bars cost $1.20 each.

How much did Ash pay?

`$1.45` `$2.65` `$3.90` `$4.15` `$8.90`
 
 
 
 
 
Show Answers Only

`$4.15`

Show Worked Solution
`text(Total Cost)` `= (7 xx 0.25) + (2 xx 1.20)`
  `= 1.75 + 2.40`
  `= $4.15`

Number, NAPX-E4-NC03

Cinder grows large pumpkins in her garden.

One pumpkin she picks weighs 2.4 kg.

Cinder cuts 400 grams off the pumpkin to cook with.

What fraction was used for cooking?

`1/6` `1/5` `1/4` `1/3`
 
 
 
 
Show Answers Only

`1/6`

Show Worked Solution
`text(Fraction)` `= 400/2400`
  `= 1/6`

Measurement, NAPX-E4-CA26

A builder is placing tiles on a floor that is 240 cm wide and 360 cm long.

She uses the triangular floor tile that is drawn below.
 

 
She uses all of her tiles and has no gaps between them.

How many tiles does she need?

`900` `1500` `1800` `3600`
 
 
 
 
Show Answers Only

`3600`

Show Worked Solution

`text(2 tiles form a 4 × 12 cm rectangle.`

`text(Fitting tiles into floor plan:)`

`text(Width) = 240/4 = 60\ text(rectangles)`

`text(Length) = 360/12 = 30\ text(rectangles)`

 

`:.\ text(Total tiles)`

`= 2 xx (30 xx 60)`

`= 3600`

Geometry, NAPX-E4-CA22

Kramer walks around his local park.

He starts at point `J` and walks east.

If he walks `1/3` of the distance around the park to what direction is he heading?
 

 
Penelope walks around the park, starting at point A and walking south.

When she is  `1/3`  of the distance around, what direction is she heading?

`text(east)` `text(north-east)` `text(north)` `text(north-west)`
 
 
 
  
Show Answers Only

`text(North)`

Show Worked Solution

`text(One third around the park will be)`

`text(between)\ 1/4 and 3/8.`

`:.\ text(Kramer is heading North.)`

Algebra, NAPX-E4-CA20

`300 = 3000 - b/9`

What is the value of  `b`?

`300` `366` `2700` `24\ 300` `29\ 700`
 
 
 
 
 
Show Answers Only

`24\ 300`

Show Worked Solution
`b/9` `= 3000 – 300`
`b` `= 9 xx 2700`
  `= 24\ 300`

Algebra, NAPX-E4-CA19, NAPX-E3-CA23

Clinton designs a line of tiles that repeats 6 different tiles in the same order, as shown below.
 

 Each tile costs $7.50 and Clinton uses $240 worth of tiles.

Which of these is the last tile in his line of tiles?
 

 
 
 
 
 
 
Show Answers Only

Show Worked Solution

`text(Total number of tiles used)`

`= 240/7.50= 32`

 

`:.\ text{Five full patterns of 6 tiles plus 2 (i.e. the last tile is the}`

`text{is the second in the pattern.)}`

 

Statistics and Probability, NAPX-E4-CA18

Brock collected some data from his 8 cousins.

The data was used to draw the graph below although no labels were used.
 

 
What kind of data could Brock be showing on his graph?

  Horizontal axis Vertical axis
 
 Gender Favourite Sport
 
 Height Hair Colour
 
 Age Shoe Size
 
 Favourite Sport Hair Colour
Show Answers Only

`text(Age and Shoe Size.)`

Show Worked Solution

`text(Age and Shoe Size.)`

`text(Each data category needs to have a number of)`

`text(possibilities and the chosen pair need a general)`

`text(relationship where one moves higher at the same )`

`text(time as the other. Age and Shoe Size is the most likely.)`

Number, NAPX-E4-CA17

Vanessa has a basket of fruit that has plums, oranges and peaches.

`1/3` of the basket of fruit are oranges and `1/5`  are peaches.

What fraction of the fruit are plums?

`3/8` `7/10` `7/15` `8/10` `8/15`
 
 
 
 
 
Show Answers Only

`7/15`

Show Worked Solution
`text(Plums)` `= 1 – (1/3 + 1/5)`
  `= 1 – (5/15 + 3/15)`
  `= 7/15`

Number, NAPX-E4-CA16

Jeff walks across a football field. It takes him 48 strides to walk across.

His stride length is 80 centimetres long.

Jeff's daughter, Deloris, has a stride length of 60 centimetres.

How many strides does it take Deloris to walk across the same football field?

`42` `48` `64` `80` `100`
 
 
 
 
 
Show Answers Only

`64`

Show Worked Solution

`text{Distance Jeff walks}`

`= 48 xx 0.80 = 38.4\ text(m)`

 

`:.\ text(Number of Deloris’ steps)`

`= 38.4/0.6 = 64` 

Algebra, NAPX-E4-CA15

`b`  is a positive whole number.

Which of the equations below is not true?

 
 `2b + b + 2b = 5b`
 
 `b xx b xx b xx 3 = 3b`
 
 `b = -b  xx -1`
 
 `b/b = 1`
Show Answers Only

`b xx b xx b xx 3 = 3b`

Show Worked Solution
`b xx b xx b xx 3` `= 3b^3`
  `!= 3b`

Algebra, NAPX-E4-CA14

Alex has a job selling bikes. Her weekly salary, `C` dollars, is calculated using the rule below:

`C = 400 + 0.06 W`

where `W` is the total value in dollars of the bikes she sells that week.

Alex sold $24 000 worth of bikes in a given week.

What was Alex's salary in the week?

`$1040` `$1840` `$14\ 400` `$14\ 800`
 
 
 
 
Show Answers Only

`$1840`

Show Worked Solution
`C` `= 400 + (0.06 xx 24\ 000)`
  `= 400 + 1440`
  `= $1840`

Statistics and Probability, NAPX-E4-CA12, NAPX-E3-CA17

Billy has a sewing bag full of buttons. 65% of his buttons are red.

Billy takes a black button from his bag and sews it onto his shirt.

Billy then randomly takes a button from his sewing bag without looking.

What are the chances it is red?

 
 greater than 65%
 
 equal to 65%
 
 less than 65%
Show Answers Only

`text(greater than 65%)`

Show Worked Solution

`text(After taking a black button, the sewing bag has same)`

`text(number of red and less non-red coloured buttons.)`

`:.\ text(Chances of a red are now greater than 65%.)`

Measurement, NAPX-E4-CA11, NAPX-E3-CA15

Big Matt's Pie shop is open 10 am to 4 pm from Monday to Friday and 10 am to 1 pm on Sunday.

What is the total number of hours his shop is open in 1 week?

`23` `30` `33` `36`
 
 
 
 
Show Answers Only

`33\ text(hours)`

Show Worked Solution
`text(Total hours)` `=\ text{(6 hours/day × 5 days)} + 3\ text(hours)`
  `= 30 + 3`
  `= 33\ text(hours)`

Algebra, NAPX-E4-CA10, NAPX-E3-CA12

The rules of a number game are shown in the flowchart below.
 

 
The output number is 28.

What are two possible values for the input number?

`7 and 22` `7 and 34` `22 and 34` `34 and 112`
 
 
 
 
Show Answers Only

`7 and 34`

Show Worked Solution

`text(By trial and error:)`

`7\ text(is odd) => 7 xx 4 = 28`

`34\ text(is even) => 34 – 6 = 28`

`:. 7 and 34\ text(are the possible values.)`

Number, NAPX-E4-CA06

Barry lives 30 kilometres from the library.

On Tuesday, he drove to the library and averaged 90 kilometres per hour.

On Thursday, he took the train which averaged 30 kilometres per hour.

What was the extra time of the train journey, in minutes, compared to when he drove on Tuesday?

`20` `30` `40` `60`
 
 
 
 
Show Answers Only

`40\ text(minutes)`

Show Worked Solution
`text(Driving time)` `= text(distance)/text(speed)`
  `= 30-:90`
  `= 1/3\ text(hour)`
  `= 20\ text(minutes)`

 

`text(Train time)` `= 60\ text(minutes)`

 

`:.\ text(The extra time taking the train)`

`= 60 – 20`

`= 40\ text(minutes)`

Number, NAPX-E4-CA05

Jacob has 4 dogs.

Each dog eats 7 biscuits a week.

Jacob has no biscuits when he goes to the shop.

The shop sells its biscuits in packets of 6.

How many packets does Jacob need to buy for 1 week?

`4`  `5` `6` `7`
 
 
 
 
Show Answers Only

`5\ text(packets)`

Show Worked Solution

`text(Biscuits eaten in 1 week)`

`= 4 xx 7`

`= 28`

 

`:.\ text(Packets required)` `= 28 ÷ 6`
  `= 4\ text(remainder)\ 4`
  `= 5\ text(full packets)`

Geometry, NAPX-E4-CA04, NAPX-E3-CA08

A sculpture is pictured from 3 different angles below:
 

 
The sculpture is in the shape of

 
 a trapezium and a rectangle.
 
 a trapezium and a cylinder.
 
 a sphere and a prism.
 
 a cylinder and a prism.
Show Answers Only

`text(a cylinder and a prism)`

Show Worked Solution

`text{The bottom shape is a trapezoidal prism (not a trapezium).}`

`:.\ text(The sculpture is a cylinder and a prism.)`

Statistics and Probability, NAPX-E4-CA03, NAPX-E3-CA04

Joseph asked children in his class what their favourite sport is.

Their answers were used to draw the pie chart below.
 

 
Around a quarter of the students preferred which sport?

`text(Basketball)` `text(Soccer)` `text(Cricket)` `text(Rugby)`
 
 
 
 
Show Answers Only

`text(Soccer)`

Show Worked Solution

`text(Soccer represents one quarter of the graph.)`

Number, NAPX-E4-CA01, NAPX-E3-CA01

A coal mine buys 7 new conveyor belts to move coal for $787.5 million.

Each conveyor belt costs the same amount.

What is the cost of one conveyor belt?

 
 `$112.5\ text(million)`
 
 `$393.75\ text(million)`
 
 `$780.5\ text(million)`
 
 `$5512.5\ text(million)`
Show Answers Only

`$112.5\ text(million)`

Show Worked Solution
`text(C) text(ost per belt)` `= 787.5/7`
  `= 112.5\ text(million)`

Measurement, NAPX-F4-NC29

A wheelchair ramp is pictured below.
  

 
The ramp is in the shape of a triangular prism?

What is the volume of the ramp?

`2.8\ text(m³)` `5.6\ text(m³)` `0.28\ text(m³)` `0.56\ text(m³)`
 
 
 
 
Show Answers Only

`2.8\ text(m³)`

Show Worked Solution
`text(Volume)` `= Ah`
  `= (1/2 xx 7 xx 0.4) xx 2`
  `= 1.4 xx 2`
  `= 2.8\ text(m³)`

Number, NAPX-F4-NC27

The graph below can be used to approximately convert kilograms to pounds.

Using the graph, a mass of 2 kilograms is closest to

 
 `3.2\ text(pounds)`
 
 `3.5\ text(pounds)`
 
 `4.2\ text(pounds)`
 
 `4.4\ text(pounds)`
Show Answers Only

`4.4\ text(pounds)`

Show Worked Solution
`text(S) text(ince 5 kg)` `= 11\ text(pounds)`
`text(1 kg)` `= 11/5 = 2.2\ text(pounds)`

 

`:. 2\ text(kg)` `= 2 xx 2.2`
  `= 4.4\ text(pounds.)`