A ticket to Leyland Brothers World for two adults costs $42 in total.
A ticket to Leyland Brothers World for one child is one third the cost of an adult ticket.
What is the cost of a ticket for one child?
$ 
Aussie Maths Teachers: Save your time with SmarterMaths
A ticket to Leyland Brothers World for two adults costs $42 in total.
A ticket to Leyland Brothers World for one child is one third the cost of an adult ticket.
What is the cost of a ticket for one child?
$ 
`$7`
`text(C)text(ost of 1 adult ticket)`
`= 42 : 2`
`= $21`
`:.\ text(C)text(ost of 1 child ticket)`
`= 1/3 xx 21`
`= $7`
A broadband provider offers 3 types of broadband plans: Standard, High Speed and Fibre To The Door.
The Standard plan costs $50.40 less than the High Speed plan.
The Standard plan costs $72.60 less than the Fibre To The Door plan.
Which of these equations correctly states the cost of the High Speed plan?

Cost of High Speed plan = Cost of Fibre To The Door plan – $72.60 

Cost of High Speed plan = Cost of Fibre To The Door plan – $50.40 

Cost of High Speed plan = Cost of Fibre To The Door plan – $32.80 

Cost of High Speed plan = Cost of Fibre To The Door plan – $22.20 
`text{C}text{ost of High Speed plan = Cost of Fibre To The Door plan − $22.20}`
`text{Fibre To The Door plan cost over High Speed plan}`
`= 72.60  50.40`
`= $22.20`
`:.\ text{C}text{ost of High Speed plan = Cost of Fibre To The Door plan − $22.20}`
A food delivery company provides 3 levels of service: Regular, Moderate and Premium.
Regular service costs $15.50 less than Moderate service.
Regular service costs $45.80 less than Premium service.
Which of these equations correctly represents the cost of Moderate service?

Cost of Moderate Service = Cost of Premium service – $15.50 

Cost of Moderate Service = Cost of Premium service – $30.30 

Cost of Moderate Service = Cost of Premium service – $20.70 

Cost of Moderate Service = Cost of Premium service – $45.80 
`text{C}text{ost of Moderate Service = Premium service – $30.30}`
`text{Extra cost of Premium service over Moderate service}`
`= 45.80  15.50`
`= $30.30`
`:.\ text{C}text{ost of Moderate Service = Premium service – $30.30}`
Ashley makes $152 for every 19 beauty kits she sells online.
Which expression shows how much Ashley would earn if she sells `k` beauty kits?

`(19 × 152) ÷ k` 

`(152 ÷ 19) × k` 

`(19 ÷ 152) × k` 

`(152 + 19) ÷ k` 
`(152 ÷ 19) xx k`
`152\ → 19\ text(kits)`
`152 : 19 → \ text(1 kit)`
`:. (152 ÷ 19) xx k\ → \ k\ text(kits)`
A salesman earns $84 for every 7 litres of paint he sells.
Which expression shows how much would he would earn for selling `x` litres?

`(84 × 7) ÷ x` 

`(84 ÷ 7) ÷ x` 

`(84 ÷ 7) × x` 

`(84  7) × x` 
`(84 ÷ 7) xx x`
`84\ → 7\ text(litres)`
`84 : 7 → \ text(1 litre)`
`:. (84 ÷ 7) xx x\ → \ x\ text(litres)`
In the diagram below, line XYZ is a straight line.
What is the measurement of angle XYS?

31° 

36° 

47° 

103° 
`31^@`
`text{Sum of angles in triangle} = 180^@`
`angle ZYT`  `= 180  102  42` 
`= 36^@` 
`angle XYZ\ text{(straight line)} = 180^@`
`angle XYS`  `= 180  113  36` 
`= 31^@` 
`therefore angle XYS = 31^@`
From the diagram shown below, Line ABC is a straight line.
What is the size of angle DBC?

63° 

93° 

117° 

297° 
`117^@`
`text{Sum of angles in triangle} = 180^@`
`angle DBA`  `= 180  53  64` 
`= 63^@` 
`angle ABC\ text{(straight line)} = 180^@`
`angle DBC`  `= 180  63` 
`= 117^@` 
The graph below represents data gathered from 9 professional workers.
What kind of data could be represented in the graph shown above?
Vertical Axis  Horizontal Axis  

Age  Salary 

Kind of Job  Salary 

Name of Company  Age 

Favourite food  Years of Experience 
`text{Vertical Axis: Age}`
`text{Horizontal Axis: Salary}`
`text(Age and Salary.)`
`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 slary is the most likely.)`
`text{The graph represents varying numerical values. }`
Cyrene collected some data from 10 of her friends.
The graph represents the data gathered by Cyrene but no labels are used
What kind of data could Cyrene be showing in her graph?
Vertical Axis  Horizontal Axis  

Age  Name 

Gender  Weight 

Height  Favourite food 

Height  Weight 
`text{Vertical Axis: Height}`
`text{Horizontal Axis: Weight}`
`text(Height and Weight.)`
`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.)`
`text(Height and weight is the most likely.)`
A quadrilateral FGHI is moved to a new position labelled LMJK.
Which of these processes resulted in the new position of the quadrilateral?

Rotate quadrilateral FGHI 180° counterclockwise about the origin. 

Reflect quadrilateral in the `y`axis and then translate 8 units downward. 

Rotate quadrilateral FGHI 90° clockwise about the origin. 

Reflect quadrilateral FGHI in the `x`axis and then translate 9 units to the left. 
`text{Reflect triangle ABC in the}\ y text{axis and then translate 5 units downward}`
`text{Reflection in the}\ x text{axis}`
`FGHI \ rightarrow \ F′G′H′I′`
`text{Translate the triangle 9 units to the left}`
`F′G′H′I′\ rightarrow \ KJML`
The triangle ABC is moved to the new position labelled XYZ.
Which of these processes resulted in the new position of the triangle?

Rotate triangle ABC 180° counterclockwise about the origin. 

Reflect triangle ABC in the `y`axis and then translate 5 units downward 

Reflect triangle ABC in the `x`axis and then translate 9 units to the right 

Rotate triangle ABC 270° clockwise about the origin. 
`text{Reflect triangle ABC in the}\ y text{axis and then translate 5 units downward.}`
`text{Reflection in the}\ y text{axis:}`
`A B C \ rightarrow \ A′ B′ C′`
`text{Translate the triangle 5 units downward:}`
`A′ B′ C′ \ rightarrow \ X Y Z`
On a given day, the RSPCA had 87 lost dogs and cats in its care.
If there was 11 more dogs than cats, how many dogs were there?

38 

49 

53 

76 
`49`
`text(Strategy 1)`
`text{There are 11 more dogs than cats.}`
`text{Let} \ D \ = \ text{number of dogs}`
`D+ (D  11)`  `= 87` 
`2D`  `= 98` 
`:. D`  `= 49` 
`text(Strategy 2)`
`text{Check each option:}`
`38 + (38  11) = 65 \ text{(Incorrect)}`
`49+ (4911) = 87 \ text{(Correct)}`
`53 + (53  11) = 95 \ text{(Incorrect)}`
`76 + (76  11) = 141 \ text{(Incorrect)}`
A college marching band is made up of 102 people.
There are 24 more men than women.
How many women are there?

30 

39 

65 

78 
`39`
`text(Strategy 1)`
`text{There are 24 more men than women.}`
`text{Let}\ \ W \ = \ text{number of women}`
`W + (W + 24)`  `= 102` 
`2W`  `= 78` 
`:. W`  `= 39` 
`text(Strategy 2)`
`text{Check each option:}`
`30 + (30 + 24) = 84 \ text{(Incorrect)}`
`39 + (39 + 24) = 102 \ text{(Correct)}`
`65 + (65 + 24) = 154 \ text{(Incorrect)}`
`78 + (78 + 24) = 180 \ text{(Incorrect)}`
Select a number line which correctly represents the following values: 0.255, 0.65, 0.45 and 0.85.







Select a number line which correctly represents the following values: 0.09, 0.755, and 0.85.







`text{The line graph shows the smallest number from left to right.}`
Shawn has a bag that holds one blue ball, one red ball and one green ball.
Shawn picks one ball without looking, records its colour and puts it back in the bag.
He repeated this process 60 times and summarises the results in the table below.
What is the difference between the expected and actual number of red balls picked?
`3`
`text(Probability of grabbing a red ball) = 1/3`
`text(Expected number of red balls)`  `= 1/3 xx 60` 
`= 20` 
`:.\ text(Difference)`  `= 23  20` 
`= 3` 
Elaine rolled a regular die 100 times.
She recorded if an even or odd number appeared each time.
The table below represents the recorded data.
What is the difference between the expected number of odd rolls to the actual odd rolls recorded?
`8`
`text(Probability of odd number) = 3/6 = 50text(%)`
`text(Expected number of odd rolls)`
`= 50text(%) xx 100`
`= 50`
`:.\ text(Difference)`  `= 50  42` 
`= 8` 
Which of these number has 7 in the thousandths place?

167.23 

12.537 

42.6667 

96.873 
`12.537`
`text{Digits in the decimal places are (in order):}`
`text(Tenths, hundredths, thousandths, …)`
`:. 12.537\ text(is correct.)`
Which of these number has 3 in the hundredths place?

12.35 

321.223 

0.253 

12.43 
`text(12.43)`
`text{Digits in the decimal places are (in order):}`
`text(Tenths, hundredths, thousandths, …)`
`text(Therefore, 12.43 is correct.)`
The corners of a certain parallelogram are shown below.
Which point in the graph represents the fourth point?

`(1, – 4)` 

`(3, – 4)` 

`(– 4, 1)` 

`(4, – 3)` 
`(1, – 4)`
Martin has a piece of wire that measures 1.32 metres.
He cuts off a 470 millimetre piece of it.
How long is the remaining wire in millimetres?
mm
`850\ text(mm)`
`text(Conversion: 1 metre = 1000 millimetres)`
`text(Length remaining)`  `= (1.320 xx 1000)  468` 
`= 1320  470`  
`= 850\ text(mm)` 
Henry is 175 centimetre tall.
He stands on top of a 425 millimetres chair.
How tall is Henry now in centimetres?
cm
`text(217.5 centimetres)`
`text(Conversion: 10 millimetres = 1 centimetre)`
`text(Total height)`  `= (425 ÷ 10) + 175` 
`= 42.5 + 175`  
`= 217.5\ text(cm)` 
Deirdre walks to work which is 6 km from her home.
She walks there at a constant speed of 5 kilometres per hour.
How many minutes does it take Deirdre to walk to work from her home?
`1 1/4`  `70`  `72`  `84` 




`72\ text(minutes)`
`text(Time)`  `= text(Distance)/(text(S)text(peed))` 
`= 6/5\ text(hours)`  
`= 6/5 xx 60\ text(minutes)`  
`= 72\ text(minutes)` 
Oggy's gym is 3 kilometres away from his apartment.
He jogs there at a constant speed of 10 kilometres per hour.
How many minutes does it take for Oggy to get to the gym from his apartment?
`1 2/3`  `18`  `24`  `36` 




`18\ text(minutes)`
`text(Time)`  `= text(Distance)/(text(S)text(peed))` 
`= 3/10\ text(hr)`  
`= 3/10 xx 60\ text(minutes)`  
`= 18\ text(minutes)` 
A man spins a wheel with 5 different coloured sections and records which colour it lands on each time.
He repeats the process multiple times.
The table below shows the results.
Using the table, what is the probability that the next spin will be yellow?

`6/31` 

`16/84` 

`1/7` 

`2/5` 
`1/7`
`P(text(Yellow))`  `= text(Number of yellow)/text(Total number of throws)` 
`= 24/(42 + 24 + 38 + 27 + 37)`  
`= 24/168`  
`=1/7` 
Andrei has a stack of cards that contains only Aces, Kings, Queens, Jacks and Jokers.
He picks one card without looking, records the card and puts it back again with the others.
He repeated this process 62 times.
Using the table, what are the chances of Andrei randomly selecting the Joker in his next pick?

`8/33` 

`6/31` 

`11/62` 

`6/25` 
`6/31`
`P(text(Joker))`  `= text(Number of Jokers)/text(Total number of draws)` 
`= 12/62`  
`= 6/31` 
Marie grabs a coloured ball from a bag and records the colour. She then puts the ball back to the bag and repeats this process 96 times.
The results are shown in the table below.
Using the table, what is the probability that the next ball picked up by Marie will be yellow?

`5/48` 

`6/25` 

`5/43` 

`7/36` 
`5/48`
`P(5)`  `= text(Number of yellow)/text(Total number)` 
`= 10/96`  
`= 5/48` 
A biased die has 6 faces numbered from 1 to 6.
Raven throws the die 50 times and recorded the results in the table below.
Using the table, what is the probability that Raven will be throwing a 5 on her next throw?

`6/44` 

`2/17` 

`11/25` 

`3/25` 
`3/25`
`P(5)`  `= text(Number of 5's)/text(Total number of throws)` 
`= 6/50`  
`= 3/25` 
In 100 grams of the alloy electrum, there are 87.5 grams of gold and 12.5 grams of other metals.
Of the other metals, 2.1 grams are silver.
Which of these fractions is the closest to the proportion of silver among the other metals?
`1/8`  `1/5`  `1/10`  `1/4` 




`1/5`
`text(Fraction)`  `= 2.1/12.5` 
`= 21/125`  
`~~ 1/5` 
A menu requires 600 grams of curry paste.
Three satchels are emptied that provide 120 grams of curry paste.
How many more satchels are required?

`12`
`text(Paste per satchel)`  `= 120/3 = 40\ text(grams)` 
`text(Total satchels required)`  `= 600/40` 
`= 15 ` 
`:.\ text(An extra 12 satchels are required.)`
Albert buys six donuts at a bakery.
He pays with a $5 note and gets 80 cents change.
How much does each donut cost?

cents 
`70`
`text(C)text(ost of donuts)= 5.00  0.80=$4.20`
`:.\ text(C)text(ost of 1 donut)`  `=420/6` 
`=70\ text(cents)` 
Earthquakes are measured using the Richter scale which calculates the amount of energy (in ergs) the earthquake releases.
An earthquake measuring 4 on the Richter scale releases `32^4` ergs of energy.
An earthquake measuring 8 on the Richter scale releases `32^8` ergs of energy.
An earthquake measuring 8 on the Richter scale releases how many times as much energy as an earthquake measuring 4?
`10^2`  `10^4`  `32^2`  `32^4` 




`32^4`
`text(Energy)\ (4) = 32 xx 32 xx 32 xx 32\ text(ergs)`
`text(Energy)\ (8) = 32 xx 32 xx 32 xx 32 xx 32 xx 32 xx 32 xx 32\ text(ergs)`
`:.\ text{Times of energy (8 ÷ 4)}`
`= 32^8/32^4`
`= 32^4`
Alan is fertilising his lawn over 2 days.
If Alan does no more work on the first day, what percentage of his lawn is fertilised after 1 day?
% 
`65 text(%)`
`text(Fraction fertilised)`  `= 2/5 + 1/4` 
`= (8 + 5)/20`  
`= 13/20` 
`:. 65 text(% is fertilised after Day 1.)`
Petrol costs 158.5 cents per litre.
How much does 12 litres of petrol cost?
$ 
`$19.02`
`text(1 litre costs $1.585)`
`:.\ text(12 litres cost)`  `= 12 xx 1.585` 
`= 19.02` 
Rogan has a square and a rectangle.
He cuts the rectangle along the dotted line as shown below.
Rogan then joins these 3 pieces to make a parallelogram.
Which of these calculations could Rogan use to find the area of the parallelogram?
`3\ text(cm) xx 6\ text(cm)`  `9\ text(cm) xx 6\ text(cm)`  `12\ text(cm) xx 6\ text(cm)`  `21\ text(cm) xx 3\ text(cm)` 




`9\ text(cm) xx 6\ text(cm)`
`text(Area)`  `= text(area of square) + text(area of rectangle)` 
`= 6 xx 6 + 3 xx 6`  
`= 9 xx 6\ text(cm)` 
A restaurant menu has the following different options available for a 3course meal.
How many different combinations of options are there for a 3course meal?
13  16  36  72 




`72`
`text(Combinations)`  `= 3 xx 6 xx 4` 
`= 72` 
The stemandleaf plot shows the number of koalas in a wildlife sanctuary each day during two weeks of bushfires.
On how many days were there at least 30 koalas in the sanctuary?
2  3  6  8  14 





`6`
`text(The plot shows 6 data points that)`
`text(are 30 or greater)`
`=> 6`
Nathan is on a hike from Nords Wharf to Burwood Beach.
The trail is 38 kilometres in length.
On the first day, Nathan walks 8300 metres to Little Pelican.
The next day, he walks 16 900 metres to Redhead Beach.
How many kilometres remain for Nathan to complete this trail?
Give your answer in kilometres, to one decimal place.
kilometres 
`12.8\ text(km)`
`text(Convert distances to km:)`
`8300\ text(m) > 8.3\ text(km)`
`16\ 900\ text(m) > 16.9\ text(km)`
`:.\ text(Distance remaining)`  `= 38  (8.3 + 16.9)` 
`= 12.8\ text(km)` 
This graph shows the number of people in Australia, in millions, in part time work, from 1998 to 2018.
Which of these statements about the graph is true?

More than three times as many people were in part time work in 2018 as in 1998. 

The number of people in part time work increased by more than 500 000 from 2003 to 2008 

The number of people in part time work increased more per year between 2008 and 2013 than at any other time. 
`text(The number of people in part time work increased by)`
`text(more than 500 000 from 2003 to 2008)`
`text(People in parttime work in 2003 ≈ 2.85 million)`
`text(People in parttime work in 2008 ≈ 3.5 million)`
`:.\ text(Increased by more than 500 000 between 2003 and 2008)`
A solar panel grid on a school roof produces an average of 8.6 kWh of energy per day.
How much energy will the grid produce for the school on average over 7 days?

kWh 
`60.2`
`text(One multiplication strategy:)`
`7xx8=56`
`7 xx 0.6 = 4.2`
`7 xx 8.6 = 56+4.2=60.2`
`:.\ text(It produces 60.2 kWh over 7 days.)`
Mount Kosciusko is 2228 metres high.
Mount Daligo is 1247 metres high.
How many metres higher is Mount Kosciusko than Mount Daligo?

metres 
`981`
`text(Metres higher)`  `= 2228  1247` 
`= 981` 
Year 7 students at a school collected aluminium cans to recycle.
In total, how much are the cans collected by all of Year 7 worth?

`$1200`
`text(Kilograms collected)`  `= 50 xx 30` 
`= 1500\ text(kg)` 
`text(Cans worth)`  `= 1.5 xx $800` 
`= $1200` 
Two sailing boats set sail from an island.
The direction that each boat sailed is shown in the diagram below.
The angle between the direction of the two boats has been shaded.
What is the size of the shaded angle?
° 
`69°`
`text(Shaded angle)`  `= 360  (229 + 62)` 
`= 360  291`  
`= 69°` 
Sapphire has 65 chocolates to pack into gift bags.
She puts 13 chocolates in each gift bag.
Which of the statements below are true?
Select three statements.

13 × 65 = (the number of gift bags Sapphire packs) 

13 × (the number of gift bags Sapphire packs) = 65 

65 ÷ 13 = (the number of gift bags Sapphire packs) 

65 ÷ (the number of gift bags Sapphire packs = 13 
13 × (the number of gift bags Sapphire packs) = 65
65 ÷ 13 = (the number of gift bags Sapphire packs)
65 ÷ (the number of gift bags Sapphire packs) = 13
`text(True statements are:)`
13 × (the number of gift bags Sapphire packs) = 65
65 ÷ 13 = (the number of gift bags Sapphire packs)
65 ÷ (the number of gift bags Sapphire packs) = 13
Rochelle drew a pattern which is pictured below.
Rochelle rotates the pattern.
How much does Rochelle to turn the pattern until it looks exactly the same?
`1/8\ text(turn)`  `1/4\ text(turn)`  `1/2\ text(turn)`  `text(1 turn)` 




`1/4\ text(turn)`
`text(Outer pattern looks the same every)\ \ 1/8\ \ text(turn).`
`text(Inner cross pattern looks the same every)\ \ 1/4\ \ text(turn).`
`:.\ text(Whole pattern looks the same every)\ \ 1/4\ \ text(turn).`
Stephan makes 14 loaves of bread to sell at his bakery.
Each loaf takes `1/4` cup of sugar.
After he makes each loaf, he counts how many cups of sugar he uses in total.
`1/4, \ 1/2, \ 3/4, \ 1, \ 1 1/4, \ 1 1/2, …`
Which is the last number he will count?
`4`  `3 3/4`  `3 1/2`  `3 1/4` 




`3 1/2`
`text(Last number)`  `= 14/4` 
`= 3 1/2` 
Stephan makes 14 loaves of bread to sell at his bakery.
Each loaf takes `1/4` cup of sugar.
After he makes each loaf, he counts how many cups of sugar he uses in total.
`1/4, \ 1/2, \ 3/4, \ 1, \ 1 1/4, \ 1 1/2, …`
Which is the last number he will count?
`4`  `3 3/4`  `3 1/2`  `3 1/4` 




`3 1/2`
`text(Last number)`  `= 14/4` 
`= 3 1/2` 
A water container has 5 litres of water in it.
Kate pours water into her dog's bowl.
She pours the water into the 250 cubic centimetre bowl until it is full.
How much water is left in the container.
250 millilitres  475 millilitres  4500 millilitres  4750 millilitres 




`text(4750 millilitres)`
`text(1 cm³ = 1 mL)`
`text(5 litres = 5000 mL)`
`:.\ text(Water left)`  `= 5000  250` 
`= 4750\ text(millilitres)` 
Patrick takes 25 minutes to walk to the beach for board training.
Last week he arrived at training at 4:15 pm, which was 20 minutes late.
At what time would Patrick leave home to arrive at board training on time?
pm 
`text(3:30 pm)`
`text(Start of training)`
`text(= 4:15 less 20 minutes)`
`text(= 3:55 pm)`
`:.\ text(Time to leave home)`
`text(= 3:55 less 25 minutes)`
`text(= 3:30 pm)`
Which of these numbers has a 3 in the thousandths place?
0.3244  2.8309  7.8231  23 082.8915 




`7.8231`
`text{The digits to the right of the decimal place are (in order):}`
`text(tenths, hundredths, thousandths, ...)`
`:.\ text(The correct number is 7.8231)`
Karen stands on a box and her new height is 1.8 metres.
Karen's actual height is twice that of the box.
What is the height of the box in centimetres?
centimetres 
`text(60 cm)`
`text(1.8 metres)`  `= 180\ text(centimetres)` 
`180 ÷ 3`  `= 60\ text(cm)` 
`:.\ text(The height of the box is 60 cm.)`
This graph shows the number of men and women that registered to vote before a council election on different days of the week.
On which day is the difference between the number of men and women registering closest to 50?
Monday  Tuesday  Wednesday  Thursday  Friday 





`text(Tuesday)`
`text(Each interval = 20 people)`
`text(Difference needs to be 2.5 intervals)`
`=>\ text(Tuesday is closest)`
Gian is writing a number pattern.
`13, 16, 19, 22, text(__, __, )` 
?

She continues this pattern until she has written 7 numbers.
Select all of the options that will give the 7th number in Gian's pattern.

` 22 + 4 + 4 + 4` 

`22 xx (3 + 3)` 

`22 + 3 + 3 + 3` 

`22 + (3 xx 3)` 
`22 + 3 + 3 + 3`
`22 + (3 xx 3)`
`text(Gian's 7th number) = 31`
`22 + 3 + 3 + 3 = 31`
`22 + (3 xx 3) = 31`
Ben needs to choose a shirt, a tie and a jacket to wear.
In his wardrobe, he owns the following clothes.
Which two of these show a way to calculate the number of different combinations that Ben can wear?
`3 + 2 xx 3`  `3 xx 2 xx 3`  `2 + 3 + 3`  `2 xx 3 xx 3` 




`3 xx 2 xx 3`
`2 xx 3 xx 3`
`text(Possible combinations:)`
`3 xx 2 xx 3`
`2 xx 3 xx 3`