What is the value of `(29.4 + 78.24)/(5.2 xx 1.8)`
`3.7`  `8.9`  `11.5`  `22.7` 



Aussie Maths Teachers: Save your time with SmarterMaths
What is the value of `(29.4 + 78.24)/(5.2 xx 1.8)`
`3.7`  `8.9`  `11.5`  `22.7` 



`11.5`
`(29.4 + 78.24)/(5.2 xx 1.8)`  `= 107.64/9.36` 
`= 11.5` 
This calculation gives the population of quokkas on Rottnest Island in April 2021.
`(74.219  7.019)/0.08`
What was the population in April 2021?
quokkas 
`840`
`(74.219  7.019)/0.08`  `= 67.2/0.08` 
`= 840\ text(quokkas)` 
Dilbert and Smacka were playing a game where they both started with zero points.
Dilbert's final score was 165 points and Smacka's final score was − 90.
How many more points did Dilbert have than Smacka?
`−255`  `−75`  `75`  `255` 




`255`
`text(Difference)`  `= 165  (−90)` 
`= 255` 
Jet created a new world record by running 5982 kilometres in a month.
Randall ran 4976 kilometres in the same time.
How many more kilometres did Jet run than Randall?
`10\ 961`  `1016`  `1004`  `1006` 




`1006`
`5982  4976 = 1006`
Which of these numbers is a multiple of both 3 and 11?
`616`  `666`  `3113`  `3333` 




`3333`
`text(Test if each option is divisible by both 3 and 11.)`
`3333/4 = 1111`
`3333/11 = 303`
`:. 3333\ text(is divisible by 4 and 11.)`
Which one of these numbers is a factor of 65?
`3`  `6`  `13`  `130` 




`13`
`text(Test each option:)`
`65 : 3 = 21\ text(remainder 2)`
`65 : 6 = 10\ text(remainder 5)`
`65 : 13 = 5`
`:. 13\ text(is a factor of 65)`
Which number is seven thousand and sixtythree?
`7036`  `7630`  `7603`  `7063` 




`7063`
`7063`
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` 
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
Con packs oranges into boxes for the market.
Each box holds 20 oranges.
Con fills 3 boxes and has 6 oranges left over.
How many oranges does Con have altogether?
`46`  `60`  `66`  `78` 




`66`
`text(One full box holds 20 oranges.)`
`:.\ text(Total oranges)`  `= 3 xx 20` 
`= 60 + 6`  
`= 66` 
Hendrix is driving from Bundaberg to Caloundra, a distance of 306 kilometres.
When Hendrix gets to the Sunshine Coast, he has 36 kilometres left.
What distance has Hendrix travelled when he gets to the Sunshine Coast?
kilometres 
`270`
`text(Distance travelled)`  `= 306  36` 
`= 270\ text(kilometres)` 
Lucretia writes 1197 as the product of its prime factors correctly.
Which expression does Lucretia write?

`3 xx 21 xx 19` 

`3^2 xx 133` 

`3 xx 7 xx 57` 

`3^2 xx 7 xx 19` 
`3^2 xx 7 xx 19`
`text(Prime factors require all factors to be)`
`text(prime numbers:)`
`:. 3^2 xx 7 xx 19,\ \ text{(can also be written as}\ \ 3xx3xx7xx19)`
A biscuit factory produces 72 000 packets of biscuits in a year.
Production is expected to increase by 1500 packets each year.
Which of these will give the best estimate of the production of the biscuit factory in 3 years' time?

`72\ 000 + 1500 xx 3` 

`(72\ 000 + 1500) xx 3` 

`72\ 000 + 1500 + 3` 

`(72\ 000 + 3) xx 1500` 
`72\ 000 + 1500 xx 3`
`text(Estimate)`  `= 72\ 000+ 1500 + 1500 + 1500` 
`= 72\ 000 + 1500 xx 3` 
Murray lives in Bundaberg where the temperature on a particular day was 39°C.
Murray's son lives in Salt Lake City, USA, and on the same day the temperature there was −15°C.
What was the temperature difference between the two towns on this day?
°C 
`54°text(C)`
`text(Temperature difference)`  `= 39  (15)` 
`= 54°text(C)` 
What is the missing number?
`3 xx `  `= 6 xx 4` 
`8`
`3 xx ` 

`= 6 xx 4` 

`= (6 xx 4)/3`  

`= 8` 
Another way of writing `5^2` is
`5 xx 2`  `5 xx 5`  `5 + 5`  `2 xx 2 xx 2 xx 2 xx 2`  




`5 xx 5`
`5 xx 5`
Which expression is equal to `6^3 xx 36^2`?

`6 xx 3 xx 36 xx 2` 

`6 xx 6 xx 6 xx 6 xx 6` 

`6 xx 6 xx 6 xx 36 xx 6` 

`6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6` 
`6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`
`6^3 xx 36^2`  `= (6xx6xx6) xx (6xx6)^2` 
`= (6xx6xx6) xx (6xx6) xx (6 xx6)`  
`=6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6` 
`sqrt (190)` is between
`9 and 12`  `12 and 14`  `14 and 20`  `40 and 50` 




`12 and 14`
`12^2`  `= 144` 
`13^2`  `= 169` 
`14^2`  `= 196` 
`:.sqrt190\ text(is between 12 and 14.)`
Which is the best estimate for `26 xx 14 + 77  32`?

`20 xx 10 + 70  30` 

`20 xx 10 + 80  30` 

`30 xx 10 + 80  30` 

`30 xx 20 + 80  40` 
`30 xx 10 + 80  30`
`text(Round 26 up to 30)`
`=>\ text(round 14 down to 10)`
`text(Round 77 up to 80)`
`text(Round 32 down to 30)`
`:.\ text(Best estimate is)\ \ 30 xx 10 + 80  30`
`8 + (17  5 xx 3 + 2) =` 
?

What number does 
?

represent? 
`62`  `46`  `12`  `0` 




`12`
`8 + (17  5 xx 3 + 2)`  `=` 
?

`8 + (1715+2)`  `=` 
?

`8 + 4`  `=` 
?

`12`  `=` 
?

Locky got a new car and recorded how many litres of petrol he put into the car over 4 weeks.
Week 1: 62.35 litres
Week 2: 58.65 litres
Week 3: 44.95 litres
Week 4: 53.75 litres
To estimate how many litres of petrol he put into his car over the 4 weeks, Locky rounded the weekly amounts to the nearest 10 litres and added them.
How much was Locky's estimate?
`240\ text(litres)`  `230\ text(litres)`  `210\ text(litres)`  `200\ text(litres)` 




`210\ text(litres)`
`text{Estimate (after rounding)}`  `= 60 + 60 + 40 + 50` 
`= 210\ text(litres)` 
Death Valley is the lowest point in the United States at −85 metres, which is below sea level.
King's Peak, also in the United States, is 4128 metres above sea level.
What is the difference, in metres, between Death Valley and King's Peak?
4213 metres  4203 metres  4045 metres  4043 metres 




`4213\ text(metres)`
`text(Difference)`  `= 4128  ( 85)` 
`= 4213\ text(metres)` 
Warwick needs to calculate `13 xx 6 + 13 × 4`.
Which expression will give Warwick the same answer?

`13 xx (6 + 4)` 

`13 xx (6 + 13)` 

`(13 xx 2) + (6 xx 4)` 

`(13 xx 2) + (6 + 4)` 
`13 xx (6 + 4)`
`13 xx 6 + 13 xx 4`
`= 13 xx (6 + 4)`
Madison uses the number sentence 15 × 12 = 180 to solve a problem.
Which of the following could be the problem?

Madison buys 15 showbags. How much does each showbag cost? 

Madison spends $15 on 180 showbags. How much does she spend? 

Madison buys 15 showbags that cost $12 each. How many showbags does she buy? 

Madison buys 12 showbags that cost $15 each. How much does she spend? 
`text(Madison buys 12 showbags that cost $15 each.)`
`text(How much does she spend?)`
`text($15 per showbag × 12 showbags = $180)`
`:.\ text(Madison buys 12 showbags that cost $15 each.)`
`text(How much does she spend?)`
Milly purchases 48 batteries.
The batteries come in packets of 8.
Which number sentence shows the number of packets of batteries Milly buys?
`48 ÷ 8 = 6`  `48 + 8 = 56`  `48  8 = 40`  `48 xx 8 = 384` 




`48 ÷ 8 = 6`
`48 ÷ 8 = 6`
1102 is a trisquare number because
`1^2 + 1^2 + 0^2 = 2`
The next trisquare number after 1102 is
`1104`  `1113`  `1209`  `1126` 




`1113`
`1^2 + 1^2 + 1^2`  `= 1 + 1 + 1` 
`= 3` 
`:. 1113\ text(is the next trisquare number.)`
The distance between the Earth and the moon is 384 712 303 metres.
How far is that to the nearest million?

`380\ 000\ 000` 

`385\ 000\ 000` 

`384\ 700\ 000` 

`384\ 710\ 000` 
`385\ 000\ 000`
`385\ 000\ 000`
The temperature at the summit of a large mountain is − 6°C.
The temperature at the base of the mountain is 32°C warmer than at the summit.
What is the temperature at the base of the mountain?
°C 
`26^@text(C)`
`text(Temperature at the base of the mountain)`
`=  6 + 32`
`=26^@ text(C)`
This calculation gives the average speed (kilometres per hour) of a satellite over a small time interval.
`(86.365  5.125)/0.06`
What is the average speed of the satellite?
kilometres per hour 
`1354\ text(kph)`
`(86.365  5.125)/0.06`  `= 81.24/0.06` 
`= 1354\ text(kph)` 
`5 xx` 

`\ + 15 = 95` 
What value would make this number sentence correct?
`10`  `14`  `16`  `20` 




`16`
`text(Let)\ \ x=\ text(required number)`
`5 xx x +15`  `=95` 
`5 xx x`  `=80` 
`:. x`  `=80/5` 
`=16` 
Michelle is tiling a walkway that is 5.6 metres long.
She is using cement tiles that are 0.08 metres wide.
There are no gaps between the tiles.
How should Michelle calculate how many cement tiles she will need?

`5.6 ÷ 0.08` 

`0.08 ÷ 5.6` 

`5.6 xx 0.08` 

`5.6  0.08` 
`5.6 ÷ 0.08`
`5.6 ÷ 0.08`
The area of New South Wales is 1 896 790 square kilometres.
What is the area rounded to the nearest thousand square kilometres?
`1\ 000\ 000`  `1\ 800\ 000`  `1\ 896\ 000`  `1\ 897\ 000` 




`1\ 897\ 000`
`1\ 897\ 000`
In 1788, Captain Cook first landed on Australian soil. In 1996, Australia issued a collector's coin with his picture on it.
How many years separated Captain Cook's landing and the issuance of the collector's coin?
`108`  `118`  `208`  `218` 




`208`
`1996  1788 = 208`
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.)` 
`text(2 million people.)`
`33.21  31.16 = 2.05`
`:.\ text(The number increased by about 2 million people.)`
Which of these numbers is not a prime number?
`7`  `17`  `27`  `37` 




`27`
`9 xx 3 = 27`
`:.\ text(27 is not prime.)`
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 
`text(−5m, −3m, 0m, 2m)`
`text(−5 m, −3 m, 0 m, 2 m)`
`17 xx (68  13)` has the same value as

`(17 xx 68)  13` 

`(17 xx 68)  (13 xx 68)` 

`17 xx (68  17 xx 13)` 

`(17 xx 68)  (17 xx 13)` 
`(17 xx 68)  (17 xx 13)`
`text(Expanding the brackets:)`
`17 xx (68  13) = (17 xx 68)  (17 xx 13)`
The number 27 982 can be rounded in different ways.
Which two ways of rounding give the same answer?

rounding to the nearest ten and nearest hundred 

rounding to the nearest ten and nearest thousand 

rounding to the nearest hundred and nearest thousand 

rounding to the nearest thousand and nearest ten thousand 
`text(rounding to the nearest hundred and nearest thousand)`
`27\ 982 = 28\ 000\ \ text{(rounding to nearest 100)}`
`27\ 982 = 28\ 000\ \ text{(rounding to nearest 1000)}`
`:.\ text(Rounding to the nearest hundred and nearest)`
`text(thousand give the same answer.)`
The airforce buys 8 new fighter jets for $882.0 million.
Each jet costs the same amount.
What is the cost of 1 fighter jet?
`$110.25\ text(million)`  `$441.0\ text(million)`  `$874.0\ text(million)`  `$7056\ text(million)` 




`$110.25\ text(million)`
`{$882.0\ text(million)}/ 8 = $110.25\ text(million)`
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` 




`$9`
`$72 ÷ 8 = $9`
`text($9 is the only amount that can be evenly)`
`text(divided into $72 with no remainder.)`
Patrick paid $3552 for some cattle.
He paid the same amount of money for each animal.
The cost of each animal was a whole number of dollars.
Which of the following could be the number of cattle Patrick bought?
`33`  `36`  `37`  `38` 




`37`
`text(Consider the individual price of the cattle for each option:)`
`text(Option 1:)\ \ 3552/33`  `= 107.64…` 
`text(Option 2:)\ \ 3552/36`  `= 98.67…` 
`text(Option 3:)\ \ 3552/37`  `= 96` 
`text(Option 4:)\ \ 3552/38`  `= 93.47…` 
`:.\ text(S)text(ince only option 3 produces a whole number,)`
`text(there are 37 cattle.)`
Waleed tried to write down all the prime numbers below 20.
His list was: 3, 5, 7, 11, 13, 19
Which number below is one of the prime numbers Waleed missed?
`2`  `9`  `15`  `23` 




`2`
`2`
Which number sentence is correct when 7 is placed in the box?
`17 + ` 

`= 10` 

` 8 = 1`  `10 ` 

`= 3`  `12 + 5 =` 





`10  7 = 3`
`10  7 = 3`
What is the value of `25^2?`
`5`  `27`  `50`  `525`  `625` 





`625`
`25^2`  `= 25 xx 25` 
`=625` 
Which of these has the same value as `98 xx 2 + 5`?
`200 + 1`  `98 + 103`  `100 xx 2 + 9`  `98 xx 7` 




`200 + 1`
`98 xx 2 + 5`  `=(98 xx2) + (2 xx 2) + 5  (2 xx2)` 
`=(100 xx 2) + 54`  
`=200 + 1` 
Manou placed an apple pie into his oven.
The 1st measurement of the apple pie's temperature was − 4°C.
Twenty minutes later, a second temperature reading was taken, which measured 21°C.
What was the change in temperature between the two measurements?
decrease of 25°C  decrease of 17°C  increase of 25°C  increase of 17°C 




`text(increase of)\ 22^@text(C)`
`text(Change in temperature)`  `=21(4)` 
`=25^@ text(C)` 
`:.\ text(An increase of 25°C.)`
Which value of `A` is closest to the missing number in this equation?
`(A + 89.29) ÷ 5.12 = 48.4`
`− 80`  `80`  `130`  `160`  `250` 





`160`
`(A + 89.29) ÷ 5.12`  `= 48.4` 
`(A + 89.29)`  `= 48.4 xx 5.12` 
`~~50 xx 5\ \ \ text{(using approximation)}`  
`~~ 250` 
`:. A`  `~~ 250  89.29` 
`~~250  90`  
`~~ 160` 
Which of these values below makes this number sentence true?
`4 xx` 

`> 28` 
`5`  `6`  `7`  `8` 




`8`
`text(By trial and error:)`
`4 xx 5 =20 < 28`
`4 xx 6 = 24 < 28`
`4 xx 7 = 28`
`4 xx 8 =32 > 28`
`:.\ text(8 makes the number sentence correct.)`
Zoe collects 100 eggs from her chicken shed.
She puts the eggs in cartons that hold 12 eggs.
How many full cartons can she fill?
`6`  `8`  `9`  `12` 




`8`
`text(Cartons required)`
`=100/12`
`= 8 4/12`
`:.\ text(Zoe can pack 8 full cartons.)`
What is the whole number closest in value to `6.2^2?`
`12`  `13`  `38`  `39`  `49` 





`38`
`6.2 xx 6.2 = 38.44`
Which list contains only prime numbers?
`2, 4, 5, 7`  `2, 5, 9, 13`  `2, 7, 11, 13`  `7, 13, 17, 21` 




`2, 7, 11, 13`
`2, 7, 11, 13`