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Aussie Maths & Science Teachers: Save your time with SmarterEd

Number, NAPX-Z3-CA11 v2

Comet Hale-Bopp travels through space at a speed of 142 kilometres per second.

What is the speed of the comet in kilometres per minute?

 
 
    1.42
 
 
    2.37
 
 
    8 520
 
 
   14 200
Show Answers Only

8 520

Show Worked Solution

`text{60 seconds in 1 minute}`

`therefore \ text{Speed in kilometres per minute}`

`= 142 xx 60`

`= 8\ 520`

Number, NAPX-Z3-CA11 v1

A RAAF fighter jet can travel at a speed of 1230 meters per second.

What is the speed of the fighter jet in metres per minute?

 
 
   12.3
 
 
   20.5
 
 
   73 800
 
 
   123 000
Show Answers Only

73 800

Show Worked Solution

`text{60 seconds in 1 minute}`

`therefore \ text{Speed in metres per minute}`

`= 1230 xx 60`

`= 73 \ 800`

Probability, NAPX-Z3-CA10 v1

An AFL coach gave a press conference where she stated it was likely that her star player would return from injury for the next game.

Which probability below best describes the chance of the star player returning from injury?

 
 
   `0.3`
 
 
   `1/2`
 
 
    `7/10`
 
 
   `9.5`
Show Answers Only

`7/10`

Show Worked Solution

`text{Probability of  “likely” is between 0.5 and 1.}`

`text{(probability cannot be > 1)}`

`therefore \ frac{7}{10}`

Algebra, NAPX-Z3-CA09 v1

Sophie makes a pattern using sticks as shown below.

The number of sticks in the first 3 figures are 3, 9, and 18.
  


 

What is the number of sticks needed for figure 4?

 
 
   24
 
 
   27
 
 
   30
 
 
   36
Show Answers Only

30

Show Worked Solution

`text{Figure 1}\ = 3`

`text{Figure 2} \ = 3 + 2 xx 3 = 9`

`text{Figure 3} \ = 9 + 3 xx 3 = 18`

`text{Figure 4} \ = 18 + 4 xx 3 = 30`

Number, NAPX-Z3-CA06 v1

What number is exactly halfway between `4 frac{1}{4}` and `6 frac{3}{4}`

 
 
   `4 frac{3}{4}`
 
 
   `5`
 
 
   `5 frac{1}{4}`
 
 
   `5 frac{1}{2}`
Show Answers Only

`5 frac{1}{2}`

Show Worked Solution
  `text{Halfway}` `= (4 frac{1}{4} + 6 frac{3}{4}) \ div 2`
    `= 11/2`
    `= 5 frac{1}{2}`

Number, NAPX-Z3-CA05 v1

The number of emperor penguins nesting in 3 Antarctic regions is counted for a research project and recorded in the table below.

   

What is the total number of penguins nesting in the 3 regions, rounded to the nearest thousand.

 
 
   100 000
 
 
   104 000
 
 
   105 000
 
 
   110 000
Show Answers Only

105 000

Show Worked Solution

`24 \ 822 + 38 \ 317 + 41 \ 445`

`= 104 \ 584`

`= 105 \ 000 \ text{(to the nearest 1000)}`

Statistics, NAPX-Z3-CA03 v1

A group of students collected insects for a science experiment.

The number of insects collected by each student is as follows:

22, 29, 18, 28, 26, 24, 24, 25, 28

Select the dot plot that correctly displays this data.

 
 
  

 
 
  

 
 
  

Show Answers Only

Show Worked Solution

Number, NAPX-Z4-CA40 v2

Alisi is 3 times older than Elenoa.

If the sum of their ages is 60 years, how old is Alisi?

`15` `20` `40` `45`
 
 
 
 
Show Answers Only

`45` 

Show Worked Solution

`text(Strategy 1)`

`text(Ratio)`

`text{Alisi : Elenoa = 3 : 1  (4 parts)}`

`text(1 part) = 60-:4=15`

`:.\ text(Alisi’s age = 3 × 15 = 45 years old)`

 

`text(Strategy 2)`

`text(Let)\ \ x = text(Elenoa’s age)`

`3x + x` `= 60`
`x` `= 15`

 

`:.\ text(Alisi is 45 yeqars old.)`

Number, NAPX-Z4-CA40 v1

Kate saved twice as much money as Patrick.

If they saved a total of $42 between them, how much did Kate save?

`$14` `$24` `$28` `$126`
 
 
 
 
Show Answers Only

`$28` 

Show Worked Solution

`text(Strategy 1)`

`text(Ratio)`

`text{Kate : Patrick = 2 : 1  (3 parts)}`

`text(1 part) = $42-:3=$14`

`:.\ text(Kate’s savings = 2 × $14 = $28)`

 

`text(Strategy 2)`

`text(Let)\ \ $x = text(Amount Patrick saved)`

`2x + x` `= 42`
`x` `= $14`

 

`:.\ text(Kate saved $28.)`

Statistics, NAPX-Z4-CA37 v2

A survey asked people what kind of washing up detergent they use at home.

The results were recorded in the pie chart below.

Which brand of detergent was preferred by around one-third of the population?

`text(Brand A)` `text(Brand B)` `text(Brand C)` `text(Brand D)`
 
 
 
 
Show Answers Only

`text(Brand D)`

Show Worked Solution

`text(A third of the people surveyed will represent a sector that)`

`text(is the size of one-third of the circle.)`

`:.\ text(Brand D)`

Probability, NAPX-Z4-CA36 v2

A bag contains 10 coloured balls.

William took 4 balls out of the bag at the same time.
 

 
Which of the following results is impossible?

 
 2 striped balls, one purple and one green ball.
 
 2 striped balls, one purple and one black ball.
 
 2 black balls and 2 striped balls.
 
 2 red balls and 2 black balls.
Show Answers Only

`text(2 blue balls and 2 black balls.)`

Show Worked Solution

`text(2 red balls and 2 black balls since there is only one red ball)`

`text{in the bag.}`

Probability, NAPX-Z4-CA36 v1

A bag contains 10 coloured marbles.

Sarah picks 3 marbles out of the bag at the same time.
 

 
Which of the following results is impossible?

 
 3 pink marbles.
 
 2 red marbles and 1 green marble.
 
 2 blue marbles and 1 green marble.
 
 3 red marbles.
Show Answers Only

`text(3 red marbles.)`

Show Worked Solution

`text(3 red marbles since there is only 2 red marbles)`

`text{in the bag}`

Number, NAPX-Z4-CA34 v2

Ronald has $8.00.

A burger cost $2.50.

What is the highest number of burgers that Ronald can buy?

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

`3`

Show Worked Solution
`2 xx $2.50` `= $5.00`
`3 xx $2.50` `= $7.50`
`4xx $2.50` `= $10.00`

 

`:.\ text(Ronald can buy 3.)`

Measurement, NAPX-Z4-CA32 v5

A shape, pictured below, is made up of 6 equilateral triangles.
 

 
What is the perimeter of the shape?

12 cm 20 cm 24 cm 36 cm
 
 
 
 
Show Answers Only

`24\ text(cm)`

Show Worked Solution

`text(S)text(ince all sides of an equilateral triangle are equal,)`

 `text(Perimeter)\ = 6 xx 4 = 24\ text(cm)`

Number, NAPX-Z4-CA31 v2

Eric has 6 cups of sesame seeds to use for baking 2 loaves of sesame bread.

He used  `1 3/4`  cups of sesame seeds in the first loaf and another  `1 3/4`  cups in the second loaf.

How many cups of sesame seeds did Eric have left?

`2 1/4` `2 1/2`  `3 1/4`  `9 1/2`
 
 
 
 
Show Answers Only

`2 1/2`

Show Worked Solution

`text(Cups of sesame seeds left)`

`=6 – (1 3/4 + 1 3/4)`

`= 6 – 3 1/2`

`= 2 1/2`

Number, NAPX-Z4-CA30 v1

Mark wants to make 5 apple pies, where each apple pie needs 3 apples.

He goes to a shop to buy the required apples.

The shop sells apples in bags of 6.

How many bags does Mark need to buy?

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

`3`

Show Worked Solution

`text(Number of apples needed)`

`= 5 xx 3`

`= 15`
 

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

`= 15 ÷ 6`

`= 2\ text(remainder 3)`

`= 3`

Statistics, NAPX-Z4-CA26 v2

Geraldine is taking an inventory of her goods for sale at the market.

How did Geraldine order her data?

`text(by price)` `text(by product)` `text(by quantity)` `text(by total cost)`
 
 
 
 
Show Answers Only

`text(Data is ordered by total cost.)`

Show Worked Solution

`text(The data on total cost is arranged from highest to lowest.)`

`:.\ text(Data is ordered by total cost.)`

Statistics, NAPX-Z4-CA26 v1

Andy Collected data on 4 of his friends and recorded the results in the table below.

 

How did Andy order his data?

`text(by age)` `text(by weight)` `text(name)` `text(by height)`
 
 
 
 
Show Answers Only

`text(Data is ordered by height.)`

Show Worked Solution

`text(The data on height is arranged from shortest to tallest.)`

`:.\ text(Data is ordered by height.)`

Number, NAPX-Z4-CA26 v2

Jake decided to re-heat pizza that was in the fridge.

The pizza’s initial temperature was  –2°C.

After reheating for two minutes, the pizza’s final temperature was 20°C.

What was the change in temperature of the pizza?

increase of 10°C increase of 18°C increase of 22°C decrease of 18°C
 
 
 
 
Show Answers Only

`text(increase of)\  22^@text(C)`

Show Worked Solution
`text(Change in temperature)` `= 20 – (-2)`
  `= 22 text{°C   (increase)}`

Measurement, NAPX-Z4-CA22 v2

Jenna is designing a stage in the shape of a rectangle.

She wants the stage to be at least 18 square metres.

She has made two sides of the stage each 6.5 metres in length.

What is the smallest possible length of each of the other two sides, rounded to one decimal place?

2.6 metres 2.8 metres 3 metres 3.2 metres
 
 
 
 
Show Answers Only

`text(2.8 metres)`

Show Worked Solution

`text(Let)\ \ d =\ text(length of other side)`

`6.5 xx d` `>= 18`
`d` `>= 18/6.5`
`d` `>= 2.76…\ text(m)`

 

`:.\ text{Smallest length is 2.8 m (to 1 d.p.)}`

Measurement, NAPX-Z4-CA22 v1

Martin is designing a rectangular pool.

He wants the pool surface to be at least 48 square metres.

He has dug out two sides each 8.3 metres in length.

What is the smallest possible length of each of the other two sides, rounded to one decimal place?

6 metres 5.8 metres 5.5 metres 5 metres
 
 
 
 
Show Answers Only

`text(5.8 metres)`

Show Worked Solution

`text(Let)\ \ d =\ text(length of other side)`

`8.3 xx d` `>= 48`
`d` `>= 48/8.3`
`d` `>= 5.78…\ text(m)`

 

`:.\ text{Smallest length is 5.8 m (to 1 d.p.)}`

Algebra, NAPX-Z4-CA40 v2

A stack of 6 cups is 300 mm tall.

A stack of 9 cups is 420 mm tall.
 

  
Which rule can be used to work out the height, in millimetres, of a stack of `n` cups?

`60n +60` `40n - 20` `40n + 60` `60n - 60`
 
 
 
 
Show Answers Only

`40n + 60`

Show Worked Solution

`text(6 cups = 300 mm)`

`text(9 cups = 420 mm)`

`=> 3\ text(extra cups add 120 mm)`

`=> 1\ text(extra cup adds 40 mm)`
 

`:. 40n + 60\ text(is the rule.)`

Number, NAPX-Z4-CA38 v2

Ana and Ralph were given similar tasks and began working on them without a break.

Ana took 1 hour and 22 minutes to finish the task while Ralph took 20% longer to complete it.

Approximately how long did Ralph take to finish the task?

84 minutes 98 minutes 126 minutes 146 minutes
 
 
 
 
Show Answers Only

`98\ text(minutes)`

Show Worked Solution

`text(Ralph’s completion time)`

`= text{(1 hour and 22 seconds)} xx\ text(120%)`

`= 82 xx 1.2`

`= 98.4\ text(minutes)`
 

`:.\ text(98 minutes is the closest to Ralph’s completion time.)`

Number, NAPX-Z4-CA38 v1

Logan and Thea competed a 400 metre running race.

It took Logan 1 minute 12 seconds to finish the race, while Thea took 30% longer.

Approximately how long did Thea take to finish the race?

74 seconds 82 seconds 94 seconds 146 seconds
 
 
 
 
Show Answers Only

`94\ text(seconds)`

Show Worked Solution

`text(Thea’s time)`

`= text{(1 minute and 12 seconds)} xx\ text(130%)`

`= 72 xx 1.3`

`= 93.6\ text(seconds)`
 

`:.\ text(94 seconds is the closest time.)`

Statistics, NAPX-Z4-CA37 v2

In four 100-metre sprint races, Usain recorded times of 13.5, 14.0, 12.5, and 15 seconds.

In his 5th race, his time was 13.5 seconds.

Which of the following will not change after Usain’s 5th sprint race?

 
 his median sprint time
 
 his mean sprint time
 
 his total time sprinting
 
 the range of his sprint times
Show Answers Only

`text(the range of his sprint times)`

Show Worked Solution

`text(After 4 games:)`

`text(Range)` `= (15.0 – 12.5) = 2.5`

 
`text(After 5 games:)`

`text(Range)` `= (15.0 – 12.5) = 2.5`

 
`:.\ text(The range of his sprint times will not change.)`

Statistics, NAPX-Z4-CA37 v1

In 4 games of basketball, Jason scored 12, 21, 10, and 12 points.

In the 5th game, he scored a season high 25 points.

Which of the following will not change after Jason’s 5th game?

 
 his total points score
 
 the mean of his point scores
 
 the range of his point scores
 
 the median of his point scores
Show Answers Only

`text(the median of his point scores)`

Show Worked Solution

`text(After 4 games,)`

`text(Median)` `= (12 + 12)/2 = 12`

 

`text(After 5 games,)`

`text(Median)` `=\ text(3rd highest score)`
  `=\ 12`

 

`:.\ text(The median will not change.)`

Probability, NAPX-Z4-CA36 v2

A dice in the shape of a rectangular prism has 6 faces numbered 1 to 6.

Jevin throws the dice 100 times and and records the outcomes.
 

 What is the probability of throwing a 2 with this dice?

`12/31` `11/50` `3/8` `9/17`
 
 
 
 
Show Answers Only

`11/50`

Show Worked Solution
`P(2)` `=22/100`
  `=11/50`

Probability, NAPX-Z4-CA36 v1

A rectangular prism die has 6 faces with faces numbered with 1 to 6 dots.

Dave throws the die 100 times and records the outcomes.

 What is the probability of throwing a 5 with this die?

`1/4` `2/7` `3/25` `15/26`
 
 
 
 
Show Answers Only

`3/25`

Show Worked Solution
`P(5)` `=12/100`
  `=3/25`

Number, NAPX-Z4-CA35 v2

The distance from `B` to `C` is four times longer than the distance from `A` to `B`.

The distance from `A` to `C` is 340 metres.

What is the distance from `B` to `C` in metres?

120 metres 190 metres 245 metres 272 metres
 
 
 
 
Show Answers Only

`272\ text(metres)`

Show Worked Solution

`AB : BC = 1 : 4`

`text(Ratio has 5 parts) \ => \ 1\ text(part) = 340/5 = 68`

`:. BC` `= 4 xx 68`  
  `=272\ text(m)`  

Number, NAPX-Z4-CA34 v2

Trish and Karl decided to sell some of their books at the market.

Their amount each of them has made is listed in the table below.

If Trish makes $35 more, she would have made three times as much money as Karl.

How much money do Karl and Trish currently have?
 

  Karl Trish
 
 $35 $60
 
 $40 $45
 
 $20 $25
 
 $50 $85
Show Answers Only

`text(Karl $20, Trish $25)`

Show Worked Solution

`text(Consider the 3rd option:)`

`text(Trish)\ + $35` `= 3 xx text(Karl)`
`$25 + $35` `= 3 xx $20`
`$60` `= $60\ \ \text{(correct)}`

 

`:.\ text(Karl $20, Trish $25)`

Number, NAPX-Z4-CA34 v1

Alex and Paolo both have part-time jobs to earn money to travel overseas.

If Paolo earned $120 more, he would have twice as much money as Alex.

How much money does each of them have?

  Alex Paolo
 
 $90 $60
 
 $45 $20
 
 $70 $60
 
 $85 $40
Show Answers Only

`text(Alex $90, Paolo $60)`

Show Worked Solution

`text(Consider the 1st option:)`

`text(Paolo)\ + $120` `= 2 xx text(Alex)`
`$60 + $120` `= 2 xx $90`
`$180` `= $180\ \ \text{(correct)}`

 

`:.\ text(Alex $90, Paolo $60)`

Geometry, NAPX-Z4-CA33 v4

Helene was jogging in an easterly direction and made a 45° turn to her left.

What direction is Helene heading in now?

South-East South-West North-East North-West
 
 
 
 
Show Answers Only

`text(North-East)`

Show Worked Solution

`text(North-East)`

Measurement, NAPX-Z4-CA32 v3

A square has a perimeter of 84 cm.

A rectangle has the same perimeter as the square and has a width of 15cm.

What is the length of the rectangle in centimetres?

`10` `20` `27` `42`
 
 
 
 
Show Answers Only

`27\ text(cm)`

Show Worked Solution

`text(Perimeter of square) = 84\ text(cm)`

`:.\ text(Length of rectangle)` `= (84 – (2 xx 15))/2`
  `= 54/2`
  `=27\ text(cm)`

Measurement, NAPX-Z4-CA32 v1

A rectangle has width of 12 cm and a length of 26 cm

A square has the same perimeter as the rectangle

What is the length of each side of the square in centimetres?

`14` `19` `20` `28`
 
 
 
 
Show Answers Only

`19\ text(cm)`

Show Worked Solution
`text(Perimeter of rectangle)` `= (2 xx 12) + (2 xx 26)`
  `=76\ text(cm)`

 

`:.\ text(Side length of square)` `=76/4`
  `=19\ text(cm)`

Number, NAPX-Z4-CA31 v3

Miya made lemonade by mixing 1.5 litres of water and 6 table spoons of lemonade powder.

How many table spoons of lemonade powder is needed if there is 9 litres of water?

24  30 32 36
 
 
 
 
Show Answers Only

`text(36 table spoons)`

Show Worked Solution

`text(Let)\ \ x =\ text(table spoons needed)`

`1.5/6` `= 9/x`
`1.5x` `= 6 xx 9`
`:. x` `= 54/1.5`
  `= 36\ text(table spoons)`

Number, NAPX-Z4-CA31 v2

The colour cyan is made by mixing 7 litres of green paint and 4 litres of blue paint.

If 63 litres of green paint are used for the mixture, how much blue paint is needed?

28 litres 32 litres 36 litres 42 litres
 
 
 
 
Show Answers Only

`text(36 litres)`

Show Worked Solution

`text(Let)\ \ x =\ text(litres of blue paint needed)`

`x/63` `= 4/7`
`:.x` `= (4 xx 63)/7`
  `= 36\ text(litres)`

Number, NAPX-Z4-CA30 v2

John’s receipt from Eat & Treat was torn.

He knew the following:

  • each hamburger he ordered cost just below $15.
  • each serve of fries cost just under $6.

His credit card statement showed that he spent $83.75.

About how much did the Iced Tea cost?

`$3` `$6` `$10` `$12`
 
 
 
 
Show Answers Only

`$6`

Show Worked Solution

`text(C) text(ost of hamburgers and fries)`

`~~ (4 xx 15) + (3 xx 6)`

`~~ 60 + 18`

`~~ $78\ \ text{(just under)}`

 

`:.\ text(Iced Tea cost)` `~~ 83.75 – 78`
  `~~ $5.75`
  `~~ $6`

Statistics, NAPX-Z4-CA28 v2

A survey was conducted in a high school where the students were asked if they enjoy each of the subjects Mathematics, English and Science.

A Venn diagram is shown to represent the number of students that like each subject.

How many of the people surveyed like both Mathematics and Science?

`23` `40` `43` `49` `93`
 
 
 
 
 
Show Answers Only

`23`

Show Worked Solution

`text(People in the overlapping circles of Maths and Science)`

`=18+5`

`=23`

Statistics, NAPX-Z4-CA28 v1

A survey is held where people are asked if they like soft drinks, milkshakes or lemonade.

The results are summarised in the Venn diagram below.
 

 
How many of the people surveyed like at least two of the three drinks?

`36` `38` `40` `46` `89`
 
 
 
 
 
Show Answers Only

`46`

Show Worked Solution

`text(Any people in overlapping circles like 2 or 3)`

`text(of the drinks.)`
 

`:.\ text(Number of people)` `= 18 + 12 + 10 + 6`
  `= 46`

Algebra, NAPX-Z4-CA26 v2

A certain stall sells donuts for $2 each and beverages for $3 each.

Sam wrote an equation  `2d + 3b = 40`  to calculate the number of donuts and beverages he could buy for exactly $40.

How many donuts and beverages could he buy?

 
 12 donuts and 10 beverages
 
 8 donuts and 8 beverages
 
 10 donuts and 11 beverages
 
 9 donuts and 10 beverages
Show Answers Only

`text(8 donuts and 8 beverages)`

Show Worked Solution

`text(By trial and error:)`

`text(C) text(ost of 8 donuts and 8 beverages)`

`= (8 xx $2) + (8 xx $3)`

`= $40`
 

`:.\ text(8 donuts and 8 beverages.)`

Algebra, NAPX-Z4-CA19 v2

Which expression equals `b^3`?

`2b xx b` `b + 2b` `(b^2 + b^2)/b` `frac{b^6}{b^3}`
 
 
 
 
Show Answers Only

`frac{b^6}{b^3}`

Show Worked Solution
`frac{b^6}{b^3}` `=(b xx b xx b xx b xx b xx b)/(b xx b xx b)`  
  `= b xx b xx b`  
  `=b^3`  

Number, NAPX-Z4-CA17 v2

Mandy sells 40 apple pies at the market. Each pie costs her $2.50 to make.

She sells 36 pies for $5.00 each.

In the last hour of the market, she sells the last 4 pies for $1.50 each.

What is the total profit or loss of the 40 apple pies?

`– $65` `– $57` `$74` `$86`
 
 
 
 
Show Answers Only

`$86`

Show Worked Solution

`text{Total profit/loss}`

`= text{sales revenue} \ – \ text{cost}`

`= (36 xx 5) + (4 xx 1.5) – (40 xx 2.5)`

`= 186 – 100`

`= $86`

Statistics, NAPX-Z4-CA16 v2

A fundraiser was conducted by a primary school.

The graph below shows the amount of money raised by each grade.
  

 
How much money was raised by students below 5th grade?

`$300` `$1300` `$1500` `$1900` `$2200`
 
 
 
 
 
Show Answers Only

`$1900`

Show Worked Solution

`text{Amount of money raised:}`

`= 700 + 400 +800`

`= $1900`