Wim held his breath for 135 seconds.
The time he held his breath can also be written as
`1 1/2\ text(minutes)`  `2 1/4\ text(minutes)`  `2 1/2\ text(minutes)`  `2 3/4\ text(minutes)` 




Aussie Maths Teachers: Save your time with SmarterMaths
Wim held his breath for 135 seconds.
The time he held his breath can also be written as
`1 1/2\ text(minutes)`  `2 1/4\ text(minutes)`  `2 1/2\ text(minutes)`  `2 3/4\ text(minutes)` 




`2 1/4\ text(minutes)`
`text(There are 60 seconds in 1 minute.)`
`=> 135\ text(seconds = 2 mins 15 seconds)`
`=>\ text(Wim held his breath for)\ 2 1/4\ text(minutes.)`
Archie is 5 years old.
His sister Ruby is exactly 18 months old.
How many months older than Ruby is Archie?
`32`  `36`  `42`  `56` 




`42\ text(months)`
`text(Age of Archie in months)`
`= 5 xx 12`
`= 60\ text(months)`
`:. 60  18 = 42\ text(months)`
Which of these has the same value as 3.57?

`300 + 50 + 7` 

`300 + 57/100` 

`3 + 5/100 + 7/10` 

`3 + 5/10 + 7/100` 
`3 + 5/10 + 7/100`
`3 + 5/10 + 7/100`
Jeremy earned $11 each time he walked his neighbour's dog.
He walks his neighbour's dog twice per week.
How much money will Jeremy earn over 4 weeks?
$ 
`$88`
`text(Total amount Jeremy earned)`
`= 4 xx 2 xx 11`
`= $88`
Ana wants to make some dumplings.
A batch of dumplings requires 4 eggs and 200 grams of flour.
If Ana uses 64 eggs to make a larger batch of dumplings, how much flour will she need?

3.2 kg 

4.0 kg 

6.2 kg 

8.0 kg 
`3.2 \ text{kg}`
`text(Flour : Eggs)\ = 200:4 = 50:1`
`text{Let} \ \ x =\ text{amount of flour needed}`
`frac{x}{64}`  `= frac{50}{1}` 
`x`  `= 50 xx 64` 
`=3200\ text(g)`  
`=3.2\ text(kg)` 
A chemist makes 70 millilitres of a compound by mixing 20 millilitres of Chemical A and 50 millilitres of Chemical B.
If 250 millilitres of Chemical B is used to make a larger batch of the compound, how much Chemical A is needed?

200 mL 

180 mL 

120 mL 

100 mL 
`100 \ text{mL}`
`text(Chemical A : Chemical B)\ = 20:50 = 2:5`
`text{Let} \ \ x =\ text{amount of Chemical A needed}`
`frac{x}{250}`  `= frac{2}{5}` 
`x`  `= frac{2 xx 250}{5}` 
`=100\ text(mL)` 
Three corners of a rectangle are shown below.
Which point represents the fourth corner of the rectangle?

(3, –1) 

(3, –2) 

(–2, 3) 

(1, 3) 
`(3, 2)`
`text(Consider the top left point on the graph (1, 1),)`
`text(The point below is 3 grid lines down.)`
`text{Consider the top right point on the graph (3, 1),}`
`text{The point (3, 2) is 3 grid lines down.}`
Hilary wants to buy second hand furniture for her new flat.
She went to a charity store that sold furniture with the pricing listed in the table below.
She decided to buy one of each furniture item listed.
Which of these gives the correct range of the total cost of the furniture that she bought?

$475 – $500 

$500 – $525 

$525 – $550 

$550 – $575 
`$550  $575`
`text(Estimate the price of each furniture:)`
`$69.20 ≈ $70`
`$298.75 ≈ $300`
`$79.50 ≈ $80`
`$112.30 ≈ $110`
`text(Total cost of furniture)`  `= 70 + 300 + 80 + 110` 
`= $560` 
`:.\ text(The range of the total cost is around $550 – $575.)`
Nicolas wants to build his own desktop gaming setup.
The shop’s prices for different gaming components are as follows:
Nicolas bought all 4 components from the shop.
Which of these gives the correct range of the total cost of his purchase?

$450 – $475 

$475 – $500 

$500 – $525 

$525 – $550 
`$475 – $500`
`text(Estimate the prices of the components)`
`$54.30 ≈ $ 55`
`$23.50 ≈ $25`
`$248.60 ≈ $250`
`$158.25 ≈ $160`
`text(Total estimated price)`  `= 55 + 25 + 250 + 160` 
`= $490` 
`:.\ text(The range of the total cost is around $475 – $500)`
Some beverages are for sale in a convenience store.
The table below shows the different prices of beverages being sold.
Which of the following beverages is the most expensive per litre?

Water 

Soft drinks 

Milkshake 

Tea 
`text(Milkshake)`
`text(Conversion: 1000 millilitres = 1 litre)`
`text(Check each option:)`
`text(Water: $1 per 1 litre)`
`text(Soft drinks: $0.65 per 500 millilitres = 2 x 0.65 = $1.30 per litre)`
`text(Milkshake: $0.45 per 250 millilitres = 4 x 0.45 = $1.80 per litre)`
`text(Tea: $0.30 per 200 millilitres = 5 x 0.30 = $1.50 per litre)`
`:.\ text(Milkshake is the most expensive per litre.)`
Brock decided to cut out a small rectangle a piece of rectangular paper.
The rectangle cut out has a length of 60 mm and a height of 40 mm.
Which of the following expressions gives the area of Brock’s paper that was left after cutting out the smaller rectangle?

`(120 xx 200)  (60 xx 160)` 

`60 xx 160` 

`(120 xx 200) + (40 xx 60)` 

`(120 xx 200)  (60 xx 40)` 
`(120 xx 200)  (60 xx 40)`
`text(Area)`  `= text(Area of large rectangle)  text(Area of small rectangle)` 
`= (120 xx 200)  (60 xx 40)` 
Trisha cuts out a triangular shape from a piece of rectangular piece of cardboard.
The triangle has a height of 2 cm and base of 8 cm.
Which of the following expression gives the area of Trisha’s cardboard after cutting out the triangle?

`(32 xx 60)  (8 xx 2)` 

`(52 xx 30)` 

`(32 xx 60)  (1/2 xx 8 xx 2)` 

`(60 xx 32)  (1/2 + 8 + 2)` 
`(32 xx 60)  (1/2 xx 8 xx 2)`
`text(Area)`  `= text(Area of rectangle)  text(Area of triangle)` 
`= (32 xx 60)  (1/2 xx 8 xx 2)` 
The table below shows the prices of different kinds of fruit sold at a supermarket.
Which type of fruit is the most expensive per kilogram?

Banana 

Apple 

Orange 

Melon 
`text(Orange)`
`text(Conversion: 1000 grams = 1 kilogram)`
`text(Check each option:)`
`text(Banana: $2.50 for 500 g = 2 x 2.50 = $5 per kilogram)`
`text(Apple: $1.3 for 250 g = 4 x 1.30 = $5.20 per kilogram)`
`text(Orange: $1.15 for 200 g = 5 x 1.15 = $5.75 per kilogram)`
`text(Melon: $5.25 for 1 kilogram = $5.25 per kilogram)`
`:\.text(Oranges are the most expensive per kilogram.)`
Two circles have radii of different lengths.
The larger circle’s radius is 3.5 times the radius of the smaller circle.
Which of the following is the circumference of the larger circle?

`56pi\ text(cm)` 

`42pi\ text(cm)` 

`40pi\ text(cm)` 

`36pi\ text(cm)` 
`42 pi \ text{cm}`
`text{Large radius}`  `= 6 xx 3.5` 
`= 21 \ text{cm}` 
`text{C}_text(large)`  `= 2 xx R xx pi` 
`= 2 xx 21 xx pi`  
`= 42 pi \ text{cm}` 
Derrick has a backyard in the shape of a rectangle.
The longer side is `1 1/3` times longer than the shorter side.
What is the perimeter of Derick’s backyard?

82 m 

98 m 

115.5 m 

133.5 m 
`98 \ text{m}`
`text{Longer side}`  `= 21 xx 1 1/3` 
`= 28 \ text{m}` 
`:.\ text{Perimeter}`  `= (2 xx 21) + (2 xx 28)` 
`= 42 + 56`  
`= 98 \ text{m}` 
A box of fruit contains 12 apples, 16 oranges, and 13 pears.
About what percentage of the fruit in the box are apples?

29% 

32% 

37% 

41% 
`29text(%)`
`text(Percentage of apples)`  `= text(number of apples)/text(total pieces of fruit)`  
`=12/(12+16+13)`  
`=0.292`  
`=29text(%)` 
In a classroom there are 24 boys and 36 girls.
About what percentage of the students in the classroom are girls?

48% 

57% 

60% 

64% 
`60text(%)`
`text(Percentage of girls)`  `= text(number of girls)/text(total students)`  
`=36/(24+36)`  
`=0.6`  
`=60text(%)` 
A father and his son attended a video game convention, arriving at 9:15 am.
They left the convention at 2:05 pm.
How long did they spend at the convention?

2 hours and 50 minutes 

3 hours and 10 minutes 

4 hour and 10 minutes 

4 hours and 50 minutes 
`text(4 hours and 50 minutes)`
`text(9:15 am to 10:00 am → 45 minutes)`
`text(10:00 am to 2:00 pm → 4 hours)`
`text(2:00 pm to 2:05 pm → 5 minutes)`
`:.\ text(Time at convention = 4 hours and 50 minutes.)`
Ashley attended a seminar about marketing which started at 8:30 am.
The seminar ended at 12:10 pm.
How long was the was the seminar held?

2 hours and 10 minutes 

3 hours and 10 minutes 

3 hours and 40 minutes 

4 hours and 40 minutes 
`text(3 hours and 40 minutes)`
`text(8:30 am to 9:00 am → 30 minutes)`
`text(9:00 am to 12:00 am → 3 hours)`
`text(12:00 pm to 12:10 pm → 10 minutes)`
`:.\ text(Duration of seminar = 3 hours and 40 minutes.)`
The parallelogram shown below has width (`W`) and length (`L`).
Which expression can be used as a perimeter of this figure?

`L xx W` 

`2L xx 2W` 

`2W + L` 

`2 (L + W)` 
`2 (L + W)`
`text{Perimeter of parallelogram}`
`= L + L + W + W`
`= 2 (L + W)`
Charlie wants to determine the number of students enrolled in both Mathematics and Physics.
Which shaded region of the following Venn diagrams shows the information that is needed by Charlie?







`text{This diagram shows the intersection of students enrolled in both Math and Physics.}`
In a deck of 52 playing cards, Ian draws one without looking.
Which card is most likely to be drawn?

A king 

A number four or five 

A black suit 

A diamond suit 
`text{A black suit card}`
`text{Check each option:}`
`Ptext{(King)} = frac{4}{52} = 1/13`
`Ptext{(Number 4 or 5)} = frac{8}{52} = 2/13`
`Ptext{(Black suit)} = frac{26}{52} = 1/2`
`Ptext{(Diamond)} = frac{13}{52} = 1/4`
`:. therefore \ text{A black suit card is most likely.}`
Two fair dice were rolled and the numbers on each die were added up.
Which resulting sum is most likely to occur?

2 

9 

11 

12 
`9`
`text{Check each option:}`
`text{Sum of 2  (1, 1)}`
`text{Sum of 9  (3, 6), (6, 3), (4, 5), (5, 4)}`
`text{Sum of 11  (5, 6), (6, 5)}`
`text{Sum of 12  (6, 6)}`
`:. \ text{Sum of 9 is most likely.}`
The table shown below represents a rule of changing each into a .
Which rule is used?

`=`  `xx 4  1`  

`=`  `xx 2 2`  

`=`  `xx 3 2`  

`=`  `xx 5  6` 
` = \ \ `  ` xx 4  1 ` 
`text{Consider option 1:}`
`5 xx 4  1 = 19\ text{(Correct)}`
`7 xx 4  1 = 27\ text{(Correct)}`
`9 xx 4  1 = 3 \ text{(Correct)}`
` = \ \ `  ` xx 4  1 ` 
The table below shows the results of a rule that changes each into a .
Which rule is used?

`=`  `xx 4  4`  

`=`  `xx 2 2`  

`=`  `xx 3  2`  

`=`  `xx 5  6` 
` = \ \ `  ` xx 3  2 ` 
`text{Check each option:}`
`2 xx 4  4 = 4 \ text{(Correct)}`
`4 xx 4  4 = 12 \ text{(Incorrect)}`
`2 xx 2 + 2 = 6 \ text{(Incorrect)}`
`2 xx 3  2 = 4\ text{(Correct)}`
`4 xx 3  2 = 10\ text{(Correct)}`
`6 xx 3  2 = 16 \ text{(Correct)}`
`2 xx 5  6 = 4\ text{(Correct)}`
`4 xx 10  6 = 34 \ text{(Incorrect)}`
` = \ \ `  ` xx 3  2 ` 
What is the value of `16^2`?

8 

18 

32 

128 

256 
`256`
`16^2`  `= 16 xx 16`  
`=256` 
What is the value of `24^2`?

26 

48 

96 

576 

784 
`216`
`24^2`  `= 24 xx 24`  
`=576` 
Anthony is driving southeast along Sterling road and turns left 90° turn into Faraday road.
In which direction is Anthony driving along Faraday road?

Northeast 

Southeast 

Southwest 

Northwest 
`text{Northeast}`
Cesar was driving northeast along Leo street.
In which direction is Cesar travelling if he turns right 90° into Grove street?

Northwest 

Southeast 

Southwest 

Northeast 
`text{Southeast}`
`therefore \ text{Cesar was heading in the SouthEast direction.}`
The regular hexagon below has a side length of `a`.
Which expression cannot be used to calculate the perimeter?

`6 xx a` 

`3 xx (a+ a)` 

`2 xx (a + 4a)` 

`(a + a + a) xx 2` 
`2 xx (a + 3a)`
`text{Perimeter of the regular hexagon} = 6a`
`text{Check each option:}`
`6 xx a = 6a \ \ text{(Correct)}`
`3 xx (a + a) = 3 xx 2a = 6a \ \ text{(Correct)}`
`2 xx (a + 4a) = 2 xx 5a = 10a \ \ text{(Incorrect)}`
`(a + a + a) xx 2 = 3a xx 2 = 6a \ \ text{(Correct)}`
A partial deck of cards consists of 8 diamonds, 9 clubs, 4 spades and 3 hearts.
Patrick draws a card from the deck without looking.
What is the probability that he draws a spade?

`1/4` 

`4/21` 

`1/3` 

`1/6` 
`1/4`
`P(text(Spade))`  `= text(Total Number of spades)/text(Total cards)` 
`= 4/(8 + 9 + 4 + 3)`  
`= 4/24`  
`= 1/6` 
A bag of coloured balls contains 12 blue balls, 10 white balls, 6 black balls, 2 red balls, and 8 orange balls.
Kimberly grabs a ball from the bag without looking what is inside.
What is the probability that she grabs an orange ball?

`3/5` 

`5/17` 

`8/21` 

`4/19` 
`4/19`
`P(text(Orange ball))`  `= text(Total orange balls)/text(Total balls)` 
`= 8/(12 + 10 + 6 + 2 + 8)`  
`= 8/38`  
`= 4/19` 
Andrew produced a pattern of small stars and diamonds.
If this pattern continues how many diamonds will the 9th figure contain?

21 

19 

17 

15 
`17`
`text(Each succeeding figure adds 2 diamonds)`
`text(Number of diamonds)`
`text(Figure 4 = 7 diamonds)`
`text(Figure 5 = 9 diamonds)`
`vdots`
`text(Figure 8 = 15 diamonds)`
`:.\ text(Figure 9 contains 17 diamonds.)`
Rica produced a pattern of small circles and trapeziums.
If this pattern continues how many small circles will be in the 10th figure?

10 

11 

19 

21 
`19`
`text{Each succeeding figure adds 2 circles}.`
`text{Number of small circles}`
`text{Figure 4: 7 circles}.`
`text{Figure 5: 9 circles}.`
`vdots`
`:.\ text(Figure 10 contains 19 circles.)`
Jason creates the following figures using toothpicks.
How many toothpicks will figure 9 have?

36 

38 

41 

46 
`46`
`text(Each succeeding figure adds 5 extra toothpicks.)`
`text(Figure 4: 21 toothpicks)`
`text(Figure 5: 26 toothpicks)`
`text(Figure 6: 31 toothpicks)`
`text(Figure 7: 36 toothpicks)`
`text(Figure 8: 41 toothpicks)`
`:.\ text(Figure 9 will have 46 toothpicks)`
`15`
`text(Each succeeding figure adds 2 extra sticks.)`
`text(Figure 4: 9 sticks)`
`text(Figure 5: 11 sticks)`
`text(Figure 6: 13 sticks)`
`:.\ text(Figure 7 will have 15 sticks)`
The image below is a plan of a commercial garden.
The total planted area is 48 square metres.
What is the total unplanted area?

60 m² 

64 m² 

78 m² 

81 m² 
`text(64 m)^2`
`text(6 planted areas = 48 m)^2`
`text(1 hexagon grid) = 48 ÷ 6 = 8\ text(m)^2`
`text(Number of unplanted areas: 8)`
`:.\ text(Total unplanted area)`  `=8 xx 8`  
`=64\ text(m²)` 
The image below shows a layout of a village.
The total area of the occupied lots is 60 m².
What is the total area of the unoccupied lots in the village?

36 m² 

42 m² 

50 m² 

54 m² 
`50\ text(m)^2`
`text(12 occupied lots = 60 m)^2`
`text(1 lot = 60 ÷ 12 = 5 m)^2`
`text(Number of unoccupied lots = 10)`
`:.\ text(Area of unoccupied lots)`  `=10 xx 5`  
`=50\ text(m²)` 
A bookmaker's bag is filled with different types of notes.
The bag contains 16 tendollar notes, 11 twentydollar notes, 8 fiftydollar notes and 3 hundreddollar notes.
The bookmaker reaches in to the bag and randomly selects one note.
What is the chance that a fiftydollar note is selected?

`4/19` 

`8/29` 

`6/17` 

`4/17` 
`4/19`
`P(text($50 bill))`  `= text(Number of $50 bills)/text(Total number of bills)` 
`= 8/(16 + 11 + 8 + 3)`  
`= 8/38`  
`= 4/19` 
A bag contains different coloured balls.
It contains 4 red balls, 8 green balls, 3 pink balls, 6 grey balls and 11 yellow balls.
Nathalie picks a ball from the bag without looking.
What is the chance that she draws a grey ball?

`1/5` 

`3/16` 

`6/31` 

`4/13` 
`3/16`
`P(text(Grey ball))`  `= text(Number of grey balls)/text(Total number of balls)` 
`= 6/(4 + 8 + 3 + 6 + 11)`  
`= 6/32`  
`=3/16` 
Which dotted line is a line of symmetry?







`text(Option 3: the left side is the mirror reflection of the right side.)`
Which dotted line is a line of symmetry?







`text(Option 1: the top side is the mirror reflection of the bottom side.)`
A certain plane rises 2 metres for every 12 metres of its base length.
If it rises by 1.6 metres, what will be its base length?

12.4 m 

10.8 m 

9.6 m 

8.4 m 
`text(9.6 m)`
`text(Every 2 metres of height → 12 metres of base)`
`text(Every 1 metre of height → 6 metres of base)`
`:.\ text(Base length)`  `= 1.6 xx 6`  
`=9.6\ text(m)` 
A onemetre tall person casts a 4metres shadow on level ground.
If a 1.8 metre tall person stands at the same position, how long will the shadow be?

6.8 m 

7.2 m 

8.0 m 

8.6 m 
`text(7.2 m)`
`text(1 metre height → 4 metre shadow)`
`:.\ text(1.8 m height shadow)`  `= 1.8 xx 4`  
`=7.2/ text(m)` 
William has a St Bernard puppy that weighs 25 kilograms.
After 8 months the St Bernard weighs 12% more than its previous weight.
How much does the dog weighs now?

28 kg 

30 kg 

32 kg 

37 kg 
`text(28 kg)`
`text(Weight)`  `= 25 + (25 xx 12text(%))` 
`= 25 + 3`  
`= 28\ text(kg)` 
`:.\ text(The weight of the St Bernard after 8 months is 28 kilograms.)`
Paul’s height is 146 centimetres when he was 15 years old.
On his 18th birthday he was 10% taller than when he was at 15 years old.
How tall is Paul when he is 18?

160.6 cm 

150.8 cm 

168.2 cm 

180.3 cm 
`text(160.6 cm)`
`text(Pauls new height)`  `= 146 + (146 xx 10text(%))` 
`= 146 + 14.6`  
`= 160.6\ text(cm)` 
`:.\ text(Paul’s height on his 18th birthday is 160.6 centimetres.)`
Mr Squiggle bought 13 pencils.
He bought:
What is the mean price of the 13 pencils?
`$1.45`  `$1.50`  `$1.55`  `$1.88` 




`$1.55`
`text(Total cost)`  `= 14.50 + 5.65` 
`= $20.15`  
`:.\ text(Mean price)`  `= 20.15/13` 
`= $1.55` 
Malcolm uses a travel card to pay for his train trips.
At the beginning of the day, he has a balance of $20 on his travel card.
Malcolm makes 3 trips that day.
Each trip costs $2.40
Which sequence shows the balance on his card at different times on that day?

$17.60, $15.20, $12.80 

$17.60, $15.20, $13.80 

$18.60, $16.20, $13.80 

$18.60, $16.20, $14.80 
`$17.60, $15.20, $12.80`
`text(Balance after 1st trip) = $20  2.40 = $17.60`
`text(Balance after 2nd trip) = $17.60  2.40 = $15.20`
`text(Balance after 3rd trip) = $15.20  2.40 = $12.80`
`:.\ text(Sequence is): $17.60, $15.20, $12.80`
Craig is a town planner and needs to know the angles that streets make with each other.
He knows that Tombs Street and Horan Street are parallel.
What is the size of the shaded angle on the map?
`60^@`  `45^@`  `30^@`  `120^@` 




`60^@`
`text(Corresponding angles are equal.)`
`:.\ text(Shaded angle) = 60°`
Santana is buying a guitar string.
Some of the strings are on sale.
Select the string that will be cheapest.




`text(Sale: take 20% off)`
`text(C)text(ost of each option:)`
`$17`
`$35\ text(less 50%) = $17.50`
`text($20 less 20%) = 20  4 = $16`
`text($24 less 25%) = 24  6 = $18`
`:.\ text(Sale: take 20% off is the cheapest string.)`
The weather bureau publishes the weekday maximum temperatures in the table below.
How much warmer was it on Thursday than on Monday?

°C 
`3.7`
`text(Degrees warmer)`  `= 26.4  22.7` 
`= 3.7` 
Kransky has a photo which is 25 cm wide and 10 cm high
He wants to enlarge it to make a poster with a width of 50 cm.
What will be the height of the poster?
`text(20 cm)`  `text(25 cm)`  `text(75 cm)`  `text(125 cm)` 




`text(20 cm)`
`text(Ratio increase)`  `= text(new width)/text(old width)` 
`= 50/25`  
`= 2` 
`:.\ text(New height)`  `= 2 xx 10` 
`= 20\ text(cm)` 
A kayak can be hired for different numbers of hours, as shown in the table below.
Select the answer that shows how to calculate the cost of hiring a kayak.

number of hours multiplied by $30 

$10 for every hour plus an extra $30 

number of hours multiplied by $10 

$10 for every hour plus an extra $20 
`text($10 for every hour plus an extra $20)`
`text($10 for every hour plus $20)`
`text(Test):`
`2\ text(hours) = 2 xx 10 + 20 = $40` ✔
`5\ text(hours) = 5 xx 10 + 20 = $70` ✔
Santana is buying a guitar string.
Some of the strings are on sale.
Select the string that will be cheapest.




`text(Sale: take 20% off)`
`text(C)text(ost of each option:)`
`$17`
`$35\ text(less 50%) = $17.50`
`text($20 less 20%) = 20  4 = $16`
`text($24 less 25%) = 24  6 = $18`
`:.\ text(Sale: take 20% off is the cheapest string.)`