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Aussie Maths & Science Teachers: Save your time with SmarterEd

Number, NAPX-G3-CA28 SA

Fargo is doing an intensive swim program over the summer holidays.

In his first session, he swims 50 laps.

In his second session, he swims 10% more laps than his first session.

In his third session, he swims 20% more laps than his second session.

How many laps does Fargo swim at his third practice?
Show Answers Only

`66\ text(laps)`

Show Worked Solution

`text(1st session) = 50\ text(laps)`

`text(2nd session)` `= 50 + (10text(%) xx 50)`
  `= 50 + 5`
  `= 55`

 

`text(3rd session)` `= 55 + (20text(%) xx 55)`
  `= 55 + 11`
  `= 66\ text(laps)`

Statistics and Probability, NAPX-G3-CA27 SA

Suzie asked all the students in her primary school how many brothers and sisters they have.

She used the results to create the bar chart below but left off some labels.
 

 
Suzie's primary school has 100 students.

How many students have over 4 brothers and sisters?
Show Answers Only

`22`

Show Worked Solution

`text(S) text(ince there are 100 students and 5 columns, the)`

`text(average number of students per column is 20.)`

`=>\ text(Each horizontal interval = 4 students)`
 

`:.\ text(Students with more than 4)`

`= 5.5 xx 4`

`= 22`

Number, NAPX-G3-CA25 SA

Vishnu's mobile plan costs $11 per month for calls only.

His mobile provider offers him a special monthly rate to add 12GB of mobile broadband data to his plan.

The total cost of his mobile plan and the extra broadband data is $336 for 12 months.

What is the extra monthly cost of the broadband data?

$   
Show Answers Only

`$17\ text(per month)`

Show Worked Solution

`text(Total cost of extra broadband)`

`= 336 – (12 xx 11)`

`= $204`
  

`:.\ text(Monthly cost of broadband)`

`= 204 ÷ 12`

`= $17`

Number, NAPX-H3-NC32 SA

Tamaki owns a Japanese garden.

Her garden pond has twice as many carp as bream, and four times as many bream as frogs.

The pond has 24 more bream than frogs.

How many carp does Tamaki's garden pond have?
Show Answers Only

`64`

Show Worked Solution

`text(Expressing the information as equations:)`

`text(Let)\ \ c = text(carps)`

`text(Let)\ \ b = text(bream)`

`text(Let)\ \ f = text(frogs)`
 

`c = 2b` `\ …\ (1)`
`b = 4f` `\ …\ (2)`
`24 = b – f` `\ …\ (3)`

 
`text(Substitute)\ \ b = 4f\ \ text{into (3)}`

`24` `= 4f – f`
`3f` `= 24`
`f` `= 8`
`=> b` `= 32`
`:. c` `= 64`

Geometry, NAPX-H3-NC31 SA

Manuel cuts a triangular prism to make two smaller prisms.

What is the highest number of total faces that the two smaller prisms could have combined?

 
Show Answers Only

`11`

Show Worked Solution

`text(Most faces occur when the cut produces a triangular and a )`

`text{quadrilateral prism (i.e. not 2 triangular prisms),}`

`text(Consider the top view of the triangular prism:)`

`:.\ text{Total faces (max)}` `= 5 + 6`
  `= 11`

Number, NAPX-H3-NC28 SA

Two odd numbers, both greater than 1, have a product of 133?

What is the sum of the two numbers?

  
Show Answers Only

`26`

Show Worked Solution

`text(By trial and error:)`

`133 ÷ 3` `= 44.33`
`133 ÷ 5` `= 26.6`
`133 ÷ 7` `= 19`

 

`:.\ text(Sum of products)` `= 7 + 19`
  `= 26`

Number, NAPX-H3-NC27 SA, NAPX-H2-40 SA

Dianne was making a scale drawing of a pipeline on grid paper.

The full length of the pipeline is drawn to scale on the grid below. It consists of 6 identical sections joined together (not shown on the diagram).
  

 
What is the length of each section of pipeline?

  metres
Show Answers Only

`45`

Show Worked Solution

`text(Length of 1 section)`

`= text(total length)/text(number of sections)`

`= (9 xx 30)/6`

`= 45\ text(metres)`

Number, NAPX-H3-NC25 SA

Nico spent $54 at the post office.

He bought a large box of envelopes for $17.

With the remaining money he bought 10 stamps at $1.30 each and some more stamps at 80 cents each.

How many 80-cent stamps did Nico buy?
Show Answers Only

`30`

Show Worked Solution

`text(Calculate money left for stamps:)`

`$54 – $17 = $37`

`$37 – (10 xx 1.30) = $24`

 

`:.\ text(Number of stamps)`

`= 24 ÷ 0.8`

`=24 -: 4/5`

`=24 xx 5/4`

`= 30`

Number, NAPX-H3-NC23 SA

Rory has 25 lollies that he shares with 3 other friends.

He gave Steve 2 more than he kept for himself.

He gave Delilah 3 less that lollies of Steve.

Kelly has twice as many as Steve.

How many lollies did Rory keep for himself?
Show Answers Only

`4`

Show Worked Solution

`text(By trial and error:)`

`=>\ text(If)\ \ \ \ ` `R = 1, S = 3, D = 0, K = 6` `\ \ (text(10 total))`
  `R = 2, S = 4, D = 1, K = 8` `\ \ (text(15 total))`
  `R = 3, S = 5, D = 2, K = 10` `\ \ (text(20 total))`
  `R = 4, S = 6, D = 3, K = 12` `\ \ (text(25 total))`

 
`:.\ text(Rory kept 4 lollies.)`

Number, NAPX-H3-NC08 SA

A netball game had a crowd of 2000 fans.

One quarter of the fans supported the home team.

How many fans did not support the home team?
Show Answers Only

`1500`

Show Worked Solution

`text(Fans not supporting the home team)`

`= 3/4 xx 2000`

`= 1500`

Algebra, NAPX-H3-CA29 SA

Ember is six years younger than Keenak.

Starla is thirteen years older than twice Keenak's age.

The sum of all three ages is 63.

How old is Starla?
Show Answers Only

`41`

Show Worked Solution

`text(Strategy one:)`

`text(Try some educated guesses,)`

`text(If Ember is 7,)`

`text(Total of ages)\ = 7 + 13 + 39 = 59`

`text(If Ember is 8,)`

`text(Total of ages)\ = 8 + 14 + 41 = 63`

 

`text{Strategy two (using algebra):}`

`text(Express the information into 3 equations,)`

`E` `= K – 6\ \ …\ (1)`
`S` `= 2K + 13\ \ … (2)`
`E + K + S` `= 63\ \ …\ (3)`

 

`text{Substitute (1) and (2) into (3)}`

`K – 6 + K + 2K + 13` `= 63`
`4K` `= 56`
`K` `= 14`

 

`:.\ text(Starla’s age)` `= 2 xx 14 + 13`
  `= 41`

Number, NAPX-H3-CA21 SA

Mr Lantry has more than 20 students in his class.

When he divides the class into groups of 6, there are 3 students left over.

When he divides the class into groups of 5, there are 2 students left over.

What is the least number of students that could be in Mr Lantry's class?
Show Answers Only

`27`

Show Worked Solution

`text(S)text(ince the class has more than 20 students)`

`text(and 3 left over when divided by 6;)`

`=>\ text(Possible numbers are:  21, 27, 33, …)`

 

`text(If he divides by 5, 2 students left over.)`

`=>\ text(Possible numbers are:  22, 27, 32, …)`

`:.\ text(Mr Lantry has 27 in his class.)`

Geometry, NAPX-I3-NC32 SA

A regular piece of wood is cut out of the prism below.
 

 
The rectangular piece creates an opening at the front and back of the prism.

How many edges does the original piece of wood have after the rectangular prism is removed?
Show Answers Only

`48`

Show Worked Solution

`text(Edges on front face = 16)`

`text(Edges on back face = 16)`

`text{Edges on side (including the hole)}`

`= 16`
 

`:.\ text(Total edges)` `= 16 + 16 + 16`
  `= 48`

Number, NAPX-I3-NC31 SA

Daisy is in high school and her age this year is both a prime number and a factor of 51.

In two years' time, Daisy's age will again be a prime number.

What is Daisy's age this year?
Show Answers Only

`17`

Show Worked Solution

`text(Consider the factors of 51:)`

`3 xx 17 = 51`

`3\ text(is too young for high school, but 17 is not.)`

`text(In two years’ time,)`

`17 -> 19\ text{(both prime)}`

 
`:.\ text(Daisy is 17 this year.)`

Number, NAPX-I3-NC29 SA

Bananas cost $5 per kilogram.

Magilla buys 5.45 kilograms of bananas.

How much does Magilla pay for the bananas? 

$  
Show Answers Only

`$27.25` 

Show Worked Solution

`text(C)text(ost of 5 kg) = 5 xx $5 = $25`

`text(C)text(ost of 0.1 kg) = 0.1 xx $5 = text(50 cents)`

`=>\ text(C)text(ost of 0.45 kg)` `= 4.5 × 50\ text(cents)`
  `= $2.25`

  

`:.\ text(C)text(ost of 5.45 kg)` `= 25 + 2.25`
  `= $27.25` 

Number, NAPX-I3-NC27 SA, NAPX-I2-39

A tube of tennis balls normally cost $11.50.

During a sale, the sports store took 10% off the regular price of the balls.

What is the new sale price of the tube of tennis balls?

$  
Show Answers Only

`$10.35` 

Show Worked Solution
`text(10% discount)` `= 11.50/10`
  `= $1.15`

 

`:.\ text(Sale price)` `= 11.50 – 1.15`
  `= $10.35`

Statistics and Probability, NAPX-I3-NC24 SA

Bryant rolled a standard dice 70 times.

He recorded if an odd or even number was rolled, each time, and wrote the results in the table below.

What is the difference between the expected number of even rolls and the actual number recorded?
Show Answers Only

`4`

Show Worked Solution

`text(Probability of even number) = 3/6 = 50text(%)`

 
`=>\ text(Expected even number rolls)`

`= 50text(%) xx 70`

`= 35`

`:.\ text(Difference)` `= 39 – 35`
  `= 4`

Algebra, NAPX-I3-NC23 SA, NAPX-I2-35 SA

Tyler counts the number of possums in a habitat every 2 months.

She records the results in the table below.

 

If this pattern continues, how many possums will be in the environment after 8 months?
Show Answers Only

`324`

Show Worked Solution

`text(The pattern shows that each number is 3 times)`

`text(the previous number.)`

`:.\ text(Number of possums after 8 months)`

`= 3 xx 108`

`= 324`

Number, NAPX-I3-NC13 SA

Nick bought 6 tennis balls for $42.60.

What was the cost of 1 tennis ball.

$  
Show Answers Only

`$7.10`

Show Worked Solution

`text{One strategy (mental arithmetic):}`

`text(C)text(ost of 1 ball)` `= 42.60/6`
  `= 42-:6 + 0.6-:6`
  `=$7.10`

Measurement, NAPX-I3-CA32 SA

Michael designs an outdoor table that is in the shape of a trapezium.

The dimensions of the table top are shown in the picture below.
 

 

 
What is the area of Michael's table top?

   cm²
Show Answers Only

`3600\ text(cm²)`

Show Worked Solution
`text(Area)` `=\ text(Area of rectangle + 2 × Area of triangle)`
  `= (45 xx 65) + 2 xx (1/2 xx 15 xx 45)`
  `=2925 + 675`
  `= 3600\ text(cm²)`

Number, NAPX-I3-CA30 SA

Caleb is travelling from Brisbane to Toowoomba. The journey is 135 kilometres.

His car uses 9.45 litres of fuel per 100 kilometres.

How much fuel will Caleb need to make the journey?

Round your answer to the nearest litre.

   litres
Show Answers Only

`13\ text{litres  (nearest whole)}`

Show Worked Solution
`text(Fuel needed)` `= 135/100 xx 9.45`
  `= 12.75…`
  `= 13\ text{litres  (nearest whole)}`

Algebra, NAPX-I3-CA27 SA

David is going on a golfing trip.

He wants to purchase balls before the trip, which are sold in boxes of a dozen balls.

The more boxes of balls that David buys, the less it costs per box, as shown in the table below.
 

 
If this price pattern continues, how much will it cost for 6 boxes of balls?

$   
Show Answers Only

`$67.50`

Show Worked Solution

`text(The boxes reduce in cost by 50 cents)`

`text(for each extra box.)`

`=>\ text(5th box costs $10.50)`

`=>\ text(6th box costs $10.00)`

 

`:.\ text(C)text(ost of 6 boxes)` `= 47.00 + 10.50 + 10.00`
  `= $67.50`

Geometry, NAPX-I3-CA26 SA

Rob creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
 

 
What is the size of angle `x° ?`

   degrees
Show Answers Only

`120°`

Show Worked Solution

`text(Base angles of isosceles triangle) = 30^@`

`text(S)text(ince)\ 180^@\ text(in a straight line:)`

`a^@` `= 180 – (90 + 30)`
  `= 60^@`

 

`:.x` `= 180 – 60`
  `= 120^@`

Number, NAPX-I3-CA14 SA

A gardener spreads 23.5 kg of grass seeds on his lawn each day.

Seeds costs $1.44 per kilogram.

How much does the gardener pay for seed each day?

$   
Show Answers Only

`$33.84`

Show Worked Solution
`text(C) text(ost per day)` `= $1.44 xx 23.5`
  `= $33.84` 

Number, NAPX-I3-CA04 SA

A botanical garden has 27 different types of orchids.

It has a total of 513 orchids.

The garden has the same number of each type of orchid.

How many orchids of each type does the garden have?

   orchids
Show Answers Only

`19`

Show Worked Solution

`text(Number of each orchid type)`

`= 513/27`

`= 19` 

Number, NAPX-J3-NC04 SA

Joel and Clive throw a cricket ball from the boundary of the cricket oval to the wicket-keeper.

It takes Joel's throw 3.52 seconds to reach the wicket-keeper.

It takes Clive's throw 2.79 seconds.

What is the difference in the time taken to reach the wicket-keeper between the two throws?

  seconds
Show Answers Only

`0.73\ text(seconds)`

Show Worked Solution

`text{One strategy (mental arithmetic):}`

`text(Time Difference)` `= 3.52 – 2.79`
  `= 3.52 – (3 – 0.21)`
  `= 0.52 + 0.21`
  `= 0.73\ text(seconds)`

Statistics and Probability, NAPX-J3-CA40 SA

A random sample of people were surveyed on what is their favourite winter sport.

The table below recorded the results.
 

 
Using the data from the survey, predict how many people would choose Aussie Rules if 2000 people were surveyed.
Show Answers Only

`750`

Show Worked Solution

`text(Total people surveyed)`

`= 56 + 69 + 42 + 17`

`= 184`
 

`:.\ text(Predicted number to choose Aussie Rules)`

`= 69/184 xx 2000`

`= 750`

Measurement, NAPX-J3-CA39 SA

Two identical solid cubes are placed at the bottom of a fish tank.

The fish tank is then completely filled, as shown below.

What is the volume of the water that surrounds the cubes?

Give your answer in cubic centimetres.

  cm3
Show Answers Only

`220\ 544\ text(cm)^3`

Show Worked Solution
`text(Volume of tank)` `= 70 xx 40 xx 80`
  `= 224\ 000\ text(cm)^3`

 

`text(Volume of cubes)` `= 2 xx 12 xx 12 xx 12`
  `= 3456\ text(cm)^3`

 

`:.\ text(Volume of water)` `= 224\ 000 – 3456`
  `= 220\ 544\ text(cm)^3`

Number, NAPX-J3-CA38 SA

Laurel and Hardy own a shed business.

They charge $4150 to build a shed.

They pay 5 workers $44 per hour for 7 hours each to construct the shed.

The materials used for the shed cost $985.

The remaining money is divided equally between Laurel and Hardy.

How much will they each receive?

`$` 
Show Answers Only

`$812.50`

Show Worked Solution

`text(Shed sale price = $4150)`

`text(Labour cost)` `= 5 xx 44 xx 7`
  `= $1540`

 

`text(Materials cost = $985)`

`text(Remaining money)` `= 4150 – (1540 + 985)`
  `= $1625`

 

`:.\ text(Each receives $812.50)`

Number, NAPX-J3-CA35 SA

A class of 48 students is surveyed. 36 students said they owned a mobile phone.

What percentage of the students surveyed do not own a mobile phone?

  %
Show Answers Only

`25text(%)`

Show Worked Solution

`text(Number of students who don’t own mobile)`

`= 48 – 36`

`= 12`

`:.\ text(Percentage)` `= 12/48 xx 100`
  `= 25text(%)`

Number, NAPX-J3-NC08 SA, NAPX-J2-42 SA

Kyle and Jackie are standing in a line, waiting to go into their classroom.

There are:

  • 7 people between Kyle and Jackie.
  • 15 people behind Jackie including Kyle.
  • 12 people in front of Kyle including Jackie.

In total, how many people are in the line?
Show Answers Only

`20`

Show Worked Solution

`text(The line-up will be:)`

`text(7 people → Kyle → 7 people → Jackie → 4 people)`

`:.\ text(Total people in line)`

`= 7 + 1 + 7 + 1 + 4`

`= 20`

Number, NAPX-J3-NC05 SA, NAPX-J2-35 SA

Jan is selling tickets for a raffle.

Each ticket costs $1.25.

Jan sells a total of 40 tickets.

How much money does Jan collect for selling the tickets?

$ 
Show Answers Only

`$50`

Show Worked Solution
`text(Money collected)` `= 40 xx 1.25`
  `= (40 xx 1) + (40 xx 0.25)`
  `= 40 + 10`
  `= $50`

Number, NAPX-J3-CA33 SA

Brett has three 6-litre cans of paint.

He divides the paint up equally between his 24 art students.

How much paint will each student receive?

Write you answer as a decimal.

  litres
Show Answers Only

`0.75`

Show Worked Solution
`text(Total paint)` `= 3 xx 6`
  `= 18\ text(litres)`

 

`:.\ text(Paint per student)` `= 18/24`
  `=3/4`
  `= 0.75\ text(litres)`

Measurement, NAPX-J3-CA32

A block is in the shape of a prism.

Its surface is covered in triangles.

 

 
How many triangles cover the entire surface of the block?

    triangles
Show Answers Only

`48`

Show Worked Solution

`text(Triangles on 1 end = 6)`

`text(Triangles on 1 side = 6)`

`text(Total triangles)` `= (6 xx 2) + (6 xx 6)`
  `= 12 + 36`
  `= 48`

Number, NAPX-J3-CA30 SA

Jahangir buys a squash racquet, originally marked $40, that is discounted by 20%.

He also has a loyalty card that gives him another 25% off the sale price.

What is the final cost of the squash racquet?

$  
Show Answers Only

`$24`

Show Worked Solution

`text(Solution 1)`

`text(Sale price)` `= 40 – (20text(%) xx 40)`
  `= $32`

 

`:.\ text(Final cost)` `= 32 – (25text(%) xx 32)`
  `= $24`

 

`text{Solution 2 (advanced)}`

`text(Final cost)` `= 40 xx 0.80 xx 0.75 `
  `= $24`

Number, NAPX-J3-CA22 SA

Paris buys 18 kilograms of dog food for her wolf hound that costs $114.30.

The dog food can be purchased in 1 kilogram bags.

How much does 11 kilograms of the same dog food cost?

$  
Show Answers Only

`$69.85`

Show Worked Solution

`text(Price of 1 kilogram)`

`= 114.30-:18`

`= $6.35`
 

`:.\ text(C)text(ost of 11 kilograms)`

`= 11 xx 6.35`

`= $69.85`

Number, NAPX-J3-CA06 SA

There are 28 Year 7 students at a small high school.

Each student is asked if they have a trampoline at home or not and the results are recorded.

`3/4` of the students answered yes.

How many Year 7 students at the school have a trampoline at home?
Show Answers Only

`21`

Show Worked Solution

`text(Students who have a trampoline)`

`= 3/4 xx 28`

`= 21`

Algebra, NAPX-J3-CA04 SA, NAPX-J2-11 SA

A school teacher allocates pieces of cardboard to class groups depending on the number of students in each group.

The table below is used.
 

  
Using the pattern in the table, how many pieces of cardboard should a group of 6 students receive?
Show Answers Only

`18`

Show Worked Solution

`text(The pattern shows that each student receives)`

`text(3 pieces of cardboard.)`

`:.\ text(A group of 6 will be given 18 pieces.)`

Measurement, NAPX-E4-NC32 SA

Two circles have the same centre, `O`, as shown in the diagram below.
 

 
The radius of the small circle is  `3/4`  the radius of the large circle.

Arc `CD` is `24` mm and the angle between the lines `AC` and `BD` is `30^@`.

What is the length of the arc `RS` in millimetres?

  mm
Show Answers Only

`90 text(mm)`

Show Worked Solution
`text(Arc)\ ST` `= 3/4 xx text(arc)\ CD`
  `= 3/4 xx 24`
  `= 18\ text(mm)`

 

`angleSOR` `= 180-30`
  `= 150^@`
  `= 5 xx angleSOT`

 

`:. text(Arc)\ RS` `= 5 xx 18`
  `= 90\ text(mm)`

Measurement, NAPX-E4-NC31 SA

Shaz uses a rectangular prism pictured below as a basic building block.
  

 

 
She stacks the blocks and makes a solid cube.

What is the smallest number of blocks needed to make a cube?
Show Answers Only

`225`

Show Worked Solution

`text(The smallest cube will have the)`

`text(smallest base:)`

 

`text(Base will have 15 blocks.)`

`text(Cube will have 15 stacked levels.)`

 

`:.\ text(Blocks needed for the smallest cube)`

`= 15 xx 15`

`= 225`

Geometry, NAPX-E4-NC30 SA

Thorfinn was designing a viking shield using 9 identical isosceles triangles, as shown in the diagram below.
 

 
How many degrees in the angle marked `x`?

  degrees
Show Answers Only

`72^@`

Show Worked Solution

`text(Angles at centre of circle)`

`= 360/9`

`= 40^@`

 

`text(S)text(ince triangles are isosceles,)`

`180` `= 40 + 2x`
`2x` `= 140`
`x` `= 70^@`

Measurement, NAPX-E4-NC29 SA

The octagon below is divided into identical squares and identical triangles.
  

 
The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 112 cm².

What is the side length of each square?

  cm
Show Answers Only

`4\ text(cm)`

Show Worked Solution

`text(Area of octagon in squares)`

`= 7\ text(squares)`

`=>\ text(Area of 1 square)`

`= 112-:7`

`= 16\ text(cm²)`

 

`:.\ text(Side length of each square)`

`= sqrt16`

`= 4\ text(cm)`

Number, NAPX-E4-NC28 SA

Write the answer to this division in the box.

`24.36 ÷ 0.12 =`  
Show Answers Only

`203`

Show Worked Solution

`text(One strategy:)`

`text(Splitting the number into an integer and a decimal,)`

`24/0.12` `= (2 xx 12)/0.12`
  `= 2 xx 100`
  `=200`
   
`0.36/0.12` `= 3`

 

`:. 24.36 ÷ 0.12 = 203`

Number, NAPX-E4-NC27 SA, NAPX-E3-NC28 SA

Xavier bought 2 identical tubs of liquid chlorine for his swimming pool.

After he used  `3/4`  of one tub in the pool, he had a total of 30 litres of chlorine left.

How many litres of chlorine were in one full tub?

  litres
Show Answers Only

`24\ text(litres)`

Show Worked Solution

`text(Let)\ \ V=\ text(volume of 1 tub)`

`1/4V + V` `= 30`
`5/4V` `= 30`
`:. V` `= (30 xx 4)/5`
  `= 24\ text(litres)`

Number, NAPX-E4-NC25 SA, NAPX-E3-NC27 SA

Wayne is from Canada and makes maple syrup.

300 millilitres of Wayne's maple syrup has a mass of 400 grams.

How many litres is 2.4 kilograms of Wayne's maple syrup?

  litres
Show Answers Only

`1.8\ text(litres)`

Show Worked Solution
`2.4\ text(kg)` `= 2400\ text(grams)`
  `=6 xx 400\ text(grams)`

 
`text(S)text(ince every 400 grams is contained in 300 millilitres,)`

`:.\ text(Volume)` `= 6 xx 300`
  `= 1800\ text(mL)`
  `= 1.8\ text(litres)`

Algebra, NAPX-E4-NC22 SA

Rex is a lettuce grower and the cost of fertilising different crop areas is shown in the table below.
 

 
Complete the rule that agrees with the values in the table.

cost of fertilising crop =     × area of crop
Show Answers Only

`90`

Show Worked Solution

`text(Taking the values in the 1st column:)`

`text(C)text(ost of fertilising)` `=\ text(cost of 1 m² × area of crop)`
  `= 1800/20 xx text(area of crop)`
  `= 90 xx text(area of crop)`

Statistics and Probability, NAPX-E4-NC19 SA, NAPX-E3-NC25 SA

Misty made 21 shakes at her friend's birthday party. Some were kale and some were spinach.

All the shakes were served in an aluminium cup and looked the same.

Barry took one shake and had a 1 in 7 chance of taking a kale shake.

How many spinach shake did Misty make?
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`18`

Show Worked Solution

`text(Number of kale shakes)`

`= 1/7 xx 21`

`= 3`
 

`:.\ text(Number of spinach shakes)`

`= 21 – 3`

`= 18`

Measurement, NAPX-E4-CA32 SA

Two views of a trapezoidal prism are shown below.
 

 
Each square on this grid has an area of one square centimetre.

The vertical edges of the prism are 5 centimetres.

What is the volume of the prism in cubic centimetres?

   cubic centimetres
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`100\ text(cm³)`

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`text(The area of the base)`

`= 14\ text(squares) + 8\ text(triangles)\ (1 xx 1) + 1\ text(triangle)\ (1 xx 4)`

`= 14 + (8 xx 1/2) + 2`

`= 20\ text(cm²)`

 

`:.\ text(Volume)` `= 20 xx 5`
  `= 100\ text(cm³)`

Measurement, NAPX-E4-CA31 SA

A cube has a total surface area of 294 square centimetres.

What is the volume of the cube? 

   cubic centimetres
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`343\ text(cm³)`

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`text(Cube has 6 faces.)`

`text(Area of 1 face)` `= 294-:6`
  `= 49\ text(cm²)`
`text(Side length)` `= sqrt 49`
  `= 7\ text(cm)`

 

`:.\ text(Volume)` `= 7^3`
  `= 343\ text(cm³)`

Algebra, NAPX-E4-CA30 SA

A teacher is choosing two students from a group of 3 to ring the school bell.

There are a total of 3 different combinations that are possible.

The formula below gives the total number of combinations `C` if the teacher is choosing from `S` students.
 

`C = 0.5 S (S - 1)`
 

What is the value of `S` if the total possible combinations `C` is 153? 
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`18`

Show Worked Solution

`text(Strategy 1)`

`text(By trial and error:)`

`text(If)\ \ S=12, C=0.5xx12xx11=66`

`text(If)\ \ S=16, C=0.5xx16xx15=120`

`text(If)\ \ S=18, C=0.5xx18xx17=153`

 

`text{Strategy 2 (advanced)}`

`C` `= 0.5 S (S – 1)`
`153` `= 0.5 S^2 – 0.5 S`
`S^2 – S – 306` `= 0`
`(S – 18)(S + 17)` `= 0`

 

`:. S = 18,\ \ S > 0`

Geometry, NAPX-E4-CA28 SA, NAPX-E3-CA31 SA

Darrell put 4 points on a grid and labelled them `V` to `Y`, as shown on the diagram below.
 

 
Point `V` is 56 millimetres from point `X.`

Darrell adds a fifth point, `Z` so that the arrangement of points has one line of symmetry.

How far is point `Z` from point `Y`?

   millimetres 
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`28\ text(mm)`

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`V\ text(to)\ X = 8\ text(grid widths)`

`=> 1\ text(width) = 56/8 = 7\ text(mm)`

`:.\ text(Distance of)\ Z\ text(to)\ Y`

`= 4 xx 7`

`= 28\ text(mm)`

Number, NAPX-E4-CA27 SA

A biologist records the number of eggs laid by 3 komodo dragons.

They record the number laid and the number hatched.

What percentage of the eggs from all 3 lizards hatched?

   % 
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`text(36%)`

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`text(Total hatched)`

`= 40 xx 0.3 + 58 xx 0.5 + 52 xx 0.25`

`= 12 + 29 + 13`

`= 54`

 

`:.\ text(Percentage of total hatched)`

`=\ text(number of eggs hatched)/text(total eggs) xx 100`

`= 54/((40 + 58 + 52)) xx 100`

`= 54/150 xx 100`

`= 36 text(%)`

Algebra, NAPX-E4-CA24 SA

Jim and Andy each bought a large order of plums from the farmers' market.

Jim bought three-quarters of the quantity that Andy bought.

The total cost of Jim and Andy's plums was $158.55.

What was the cost of Andy's plums?

$ 
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`$90.60`

Show Worked Solution
`text(Let)\ \ \ a` `=\ text(cost of Andy’s plums)`
`3/4 a` `=\ text(cost of Jim’s plums)`

 

`a + 3/4 a` `= 158.55`
`7/4 a` `= 158.55`
`a` `= 158.55 ÷ 7/4`
  `= $90.60`

Algebra, NAPX-E4-CA23 SA

Jeremy uses the formula below to estimate the population of Amazonian River Dolphins in three years.
 

`text(Year 1) = 2000`

`text(Year 2) = text(Year 1) + text(Year 1)/20`

`text(Year 3) = text(Year 2) + text(Year 2)/20`

 
Estimate the population of Amazonian River Dolphins in Year 3?
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`2205`

Show Worked Solution

`text(Year 1) = 2000`

`text(Year 2) = 2000 + 2000/20 = 2100`

`text(Year 3) = 2100 + 2100/20 = 2205`

Measurement, NAPX-F4-NC32 SA

Triangles `ABC` and `ADE` are similar.
 

 
What is the distance from `A` to `D`?

  metres
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`8\ text(m)`

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`text(Triangles)\ ABC and ADE\ text(are similar)`

`=>\ text(Corresponding sides are in the same ratio)`

`(AD)/(AE)` `= (AB)/(AC)`
`(AD)/6` `= 12/9`
`:. AD` `= (12 xx 6)/9`
  `= 8\ text(metres)`