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Algebra, NAP-I3-NC23 SA

Byron counts the number of guinea pigs in his breeding yard every 2 months.

He records the number in the table below.
 

 

 
If this pattern continues, how many guinea pigs will be in his breeding yard after 8 months?
Show Answers Only

`512`

Show Worked Solution

`text(The pattern shows that each number is 4 times)`

`text(the previous number.)`

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

`=128 xx 4`

`= 512`

Number, NAP-C3-NC30 SA

This is the label from a can of beans.
 

 

  
What is the mass of one serve of these beans?

  grams
Show Answers Only

`300`

Show Worked Solution

`text(Energy in 100g is 120kJ.)`

`text(Energy in one serve is 360kJ.)`

`:.\ text(One serve is 3 times larger)`

`=3 xx 100`

`= 300\ text(grams)`

Geometry, NAP-C3-NC27 SA

Elloise is taking a ride on a ferris wheel.

It takes her 5 minutes to complete a full lap.

What angle does the Ferris wheel turn through in 75 seconds?

  °
Show Answers Only

`90`

Show Worked Solution

`text(5 minutes = 300 seconds)`

`:.\ text(Angle turned through)` `=75/300 xx 360°`
  `=1/4 xx 360°`
  `=90°`

Number, NAP-C3-NC25

These are four number cards.
 

Use each number card once to make this number sentence true.
 

Show Answers Only

`702 xx 5 = 3510`

Show Worked Solution

`text(S)text(ince the last digit is 0, then the 4th card)`

`text(must be a 5.)`

`=> 702 xx 5 = 3510`

Algebra, NAP-E4-CA23 SA

Stewart uses the formulas below to estimate the population of koalas in a habitat over four years.

`text{Population (Year 1)} = 5000`

`text{Population (Year 2)} = text(Year 1) + text(Year 1)/10`

`text{Population (Year 3)} = text(Year 2) + text(Year 2)/10`

`text{Population (Year 4)} = text(Year 3) + text(Year 3)/10`  

What is the estimated population of koalas in year 4?
Show Answers Only

`6655\ text(koalas)`

Show Worked Solution

`text(Year 2) = 5000 + 5000/10 = 5500`

`text(Year 3) = 5500 + 5500/10 = 6050`

`text(Year 4) = 6050 + 6050/10 = 6655`

Geometry, NAP-E4-CA22

A pathway surrounds a park in the shape of an octagon, as shown in the diagram below.
 

 
Penelope walks around the park, starting at point A and walking south.

When she is  `1/3`  of the distance around, what direction is she heading?

`text(north-east)` `text(south)` `text(east)` `text(south-east)`
 
 
 
  
Show Answers Only

`text(east)`

Show Worked Solution

`text(east)`

Number, NAP-E4-CA17

Ali has a bag of marbles. The marbles are either blue, black or orange.

`1/6`  of her marbles are blue and  `1/4`  are black.

What fraction of her marbles are orange?

`2/3` `5/12` `3/10` `7/12` `7/10`
 
 
 
 
 
Show Answers Only

`7/12`

Show Worked Solution

`text(Orange marbles)`

`= 1 – (1/6 + 1/4)`

`= 1 – 5/12`

`= 7/12`

Number, NAP-E4-CA16

Paul has a paddock that takes him 56 steps to walk across.

One of his steps is 80 centimetres long.

His younger sister, Caroline, has a step length of 70 centimetres.

How many steps does it take Caroline to walk across the same paddock?

`49` `56` `64` `80` `100`
 
 
 
 
 
Show Answers Only

`64`

Show Worked Solution

`text(Paddock length)`

`= 56 xx 0.8`

`= 44.8\ text(m)`

 

`:.\ text(Number of Caroline’s steps)`

`= 44.8/0.7`

`= 64` 

Measurement, NAP-E4-NC26

Blair completed a double marathon on two consecutive days in an ultra distance running event.

His times are in the table below.
 

 
What was Blair's total time for the first two days of this event?

`21:10:40` `21:70:100` `22:11:00` `22:11:40`
 
 
 
 
Show Answers Only

`22:11:40`

Show Worked Solution

`11:18:48\ \ text(plus)\ \ 10:52:52`

`= 22:11:40`

`text{(Remember to convert more than 60 seconds}`

`text{into minutes and seconds, and likewise convert}`

`text{more than 60 minutes into hours and minutes)}`

Algebra, NAP-E4-NC23

A positive number `x` is multiplied by 3, then 15 is added.

Which of the following operations give the same result?

 
 Adding 15 to `x`, then multiply by 3.
 
 Adding 3 to `x`, then multiply by 15.
 
 Adding 3 to `x`, then multiply by 5.
 
 Adding 5 to `x`, then multiply by 3.
Show Answers Only

`(5 + x) xx 3`

Show Worked Solution

`text(Number) = 3x + 15`

 

`text(Consider each option:)`

`(15 + x) xx 3` `= 3x + 45`  
`(3 + x) xx 15` `= 15x + 45`  
`(3 + x) xx 5` `= 5x + 15`  
`(5 + x) xx 3` `= 3x + 15`

Algebra, NAP-E4-NC22 SA

Dan 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

`70`

Show Worked Solution
`text(C)text(ost of fertilising)` `=\ text(cost of 1 m² × area of crop)`
  `= 2100/30 xx text(area of crop)`
  `= 70 xx text(area of crop)`

Probability, NAP-E4-NC19 SA

Sharon made 24 milkshakes at her nephew's birthday party. Some were vanilla and some were chocolate.

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

Murray took one milkshake and had a 1 in 8 chance of taking a vanilla milkshake.

How many chocolate milkshakes did Sharon make?
Show Answers Only

`21`

Show Worked Solution

`text(Number of vanilla)`

`= 1/8 xx 24`

`= 3`
 

`:.\ text(Number of chocolate)`

`= 24 – 3`

`= 21`

Geometry, NAP-F4-CA25 SA

Towns  `A, B and C` are marked on the scale diagram below.

The distance from Town  `A`  to Town  `B`  is 9 km.

What is the distance from Town  `B`  to Town  `C?`

   kilometres
Show Answers Only

`3.6\ text(km)`

Show Worked Solution

`text(Let)\ \ d = text(distance of Town)\ B\ text(to Town)\ \ C`

`text(S)text(ince the diagram is to scale,)`

`d/9` `= 2/5`
`:. d` `= (9 xx 2)/5`
  `= 3.6\ text(km)`

Statistics, NAP-F4-CA23

A college basketball team has 10 players with the following heights.

   `182, \ 172, \ 165, \ 202, \ 190, \ 207, \ 195, \ 195, \ 188, \ 195`

What is the range of heights?

 
 `30\ text(centimetres)`
 
 `35\ text(centimetres)`
 
 `37\ text(centimetres)`
 
 `42\ text(centimetres)`
Show Answers Only

`42\ text(centimetres)`

Show Worked Solution
`text(Range)` `=  207 – 165`
  `= 42\ text(centimetres)`

Statistics, NAP-F4-CA22 SA

A school's drama class puts on a play over five nights.

The play is open to the public and the numbers of tickets sold are shown in the table below.
 

 
The cost of each ticket was $15.

What was the mean amount of money collected from ticket sales per night?

$ 
Show Answers Only

`$2850`

Show Worked Solution

`text(Mean number of tickets sold)`

`= (210 + 170 + 180 + 170 + 220)/5`

`=190`

 

`:.\ text(Mean tickets sales)` `= 190 xx 15`
  `= $2850`

Algebra, NAP-F4-CA20

Steph shoots a basketball from a height of 2 metres above the ground.

The graph below shows the height of the ball above ground level against the time after Steph releases the ball.
 

 
A basketball ring is 3 m above the ground.

How long is the ball at or above the height of the ring?

`text(1.4 sec)` `text(1.5 sec)` `text(1.7 sec)` `text(1.95 sec)`
 
 
 
 
Show Answers Only

`1.5\ text(sec)`

Show Worked Solution

`text(Ball initially hits 3 m at 0.2 seconds.)`

`text(Ball drops back to 3 m height at 1.7 seconds.)`

`:.\ text(The ball is at or above ring height for 1.5 seconds.)`

Number, NAP-F4-NC23 SA

John, Olivia and Louis are picking grapes to earn money.

Their pay is based on the number of tonnes of grapes they pick.
 

 

 
Their total pay is  $640.

How much does Olivia earn?

`$` 
Show Answers Only

`$240`

Show Worked Solution

`text(Payment per tonne)`

`= 640/8`

`= $80`
 

`:.\ text(Olivia earns)` `= 3 xx 80`
  `= $240`

Algebra, NAP-F4-NC21

Peter uses matchsticks to make a pattern of shapes, as shown in the table below.
 

 

 
The equation used to show the relationship between  `S`  and  `N`  is

`S = N + 5` `S = 5N` `S = 5N + 1` `S = 7N - 1`
 
 
 
 
Show Answers Only

`S = 5N + 1`

Show Worked Solution

`text(Shape 1:)\ \ S=5 xx 1 +1 =6`

`text(Shape 2:)\ \ S=5 xx 2 +1 =11`

`text(Shape 3:)\ \ S=5 xx 3 +1 =16`

`:. S = 5N + 1`

Number, NAP-F4-NC20 SA

It takes Kate 15 seconds to place a brochure in an envelope and seal it.

How many minutes will it take her to pack and seal 10 envelopes?

   minutes
Show Answers Only

`2.5`

Show Worked Solution
`text(Time)` `=10 xx 15`
  `=150\ text(seconds)`
  `=2.5\ text(minutes)`

Algebra, NAP-G4-NC27

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`
 
 
 
 
 
Show Answers Only

`160`

Show Worked Solution
`(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`

Geometry, NAP-G4-NC23

`PQRSTU` are vertices on the cube below.
 

 
What is the best description of  `DeltaPTR`?

isosceles equilateral right-angled scalene
 
 
 
 
Show Answers Only

`text(equilateral)`

Show Worked Solution

`PT, TR\ text(and)\ PR\ text(are all diagonals)`

`text(of the same sized square.)`

`:. PT = TR = PR`

`:. DeltaPTR\ text(is equilateral.)`

Number, NAP-G4-NC22

Alice has 5 guinea pigs.

They eat 200 grams of cabbage per day, in total.

How many grams of cabbage would 1 guinea pig eat in one week?

`40\ text(grams)` `280\ text(grams)` `1400\ text(grams)` `2800\ text(grams)`
 
 
 
 
Show Answers Only

`text(280 grams)`

Show Worked Solution

`text(Cabbage eaten by 1 guinea pig in 1 day)`

`=200/5`

`=40\ text(grams)`

`:.\ text(Cabbage eaten by 1 guniea pig in 1 week)`

`=7 xx 40`

`= 280\ text(grams)`

Number, NAP-G4-CA24

Scientists estimate that in 1 km² of swamp, 30 000 mosquito eggs are laid every minute.

Which value is the closest to the number of mosquito eggs that would be laid in one day?

`7.2 xx 10^4` `7.2 xx 10^5` `4.32 xx 10^5` `4.32 xx 10^7`
 
 
 
 
Show Answers Only

`4.32 xx 10^7`

Show Worked Solution

`text(Total eggs laid in one day)`

`= 30\ 000 xx 60 xx 24`

`=4.32 xx 10^7`

Measurement, NAP-G4-CA22 SA

Tom cut a tennis ball into two halves.
 

The following calculation gives the approximate volume of one half of the ball in cm³.
 

`text(Volume) = 1/2 xx 4/3 pi xx r^3`
 

What volume does the calculation give, to the nearest cm³, where `r` is the radius of the ball?

   cm³
Show Answers Only

 `90\ text(cm³)`

Show Worked Solution
`V` `= 1/2 xx 4/3 pi xx 3.5^3`
  `= 89.79…`
  `= 90\ text(cm³)`

Geometry, NAP-G4-CA21

Peter is standing 8 metres due west of Mary.

Bob is standing 8 metres due north of Mary.

Bob is facing north. He then turns anticlockwise so that he is facing Peter.

How many degrees does Bob turn through?

`45^@` `60^@` `90^@` `120^@` `135^@`
 
 
 
 
 
Show Answers Only

 `135^@`

Show Worked Solution

`text(Degrees Bob turns through)`

`= 90 + 45`

`= 135^@`

Number, NAP-G4-CA20 SA

The table below gives the lengths of two similar fleas.
 


 

One inch equals 25.4 millimetres.

What is the difference in millimetres between the length of a Cat Flea and a Pulex Flea?

Give your answer to three decimal places.

millimetres
Show Answers Only

 `0.825\ text(mm)`

Show Worked Solution

`1/8 xx 25.4 = 3.175`

`4 – 3.175 = 0.825\ text(mm)`

Number, NAP-H4-NC25

In a tap dancing class, the ratio of boys to girls is  5 : 7.

There are 6 more girls than boys in this group.

How many students are in this group altogether?

`12` `13` `18` `36`
 
 
 
 
Show Answers Only

`36`

Show Worked Solution

`5:7\ text(means that given 12 students,)`

`=> 5\ text(boys, 7 girls)`

`text(If 24 students,)`

`=> 10\ text(boys, 14 girls)`

`text(If 36 students,)`

`=> 15\ text(boys, 21 girls)`

 

`:.\ text(In a class of 36 students, there are 6 extra girls.)`

Geometry, NAP-H4-NC22

Pamela is using a computer graphics program to draw ellipses.

Three of her commands and the resulting shapes are drawn below:
 

`text(ellipse)\ (1,4,0)` `text(ellipse)\ (1,4,90)` `text(ellipse)\ (3,5,45)`

 
 
Which shape would be drawn by the command: `text(ellipse)\ (3,5,60)`?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Short axis = 3)`

`text(Long axis = 5)`

`text{Tilt: long axis at 60° to the vertical}`

`text{(this must be anti-clockwise as the clockwise tilt of}`

  `text{option 3 is only 30°)}`

Number, NAP-H4-NC19 SA

Paul stacks milk cartons into supermarket refrigerator shelves.

Each shelf is stacked with 6 full cream milk cartons, 4 lite milk cartons and 2 skim milk cartons.

Every hour Paul stacks 240 milk cartons in total.

How many lite milk cartons does he stack every hour?
Show Answers Only

`80`

Show Worked Solution

`text(Shelves stacked each hour)`

`= 240/12`

`= 20`

 

`:.\ text(Lite milk cartons stacked)`

`= 20 xx 4`

`= 80\ text(per hour.)`

Geometry, NAP-H4-NC18

Murphy draws and labels 3 points, on a Cartesian plane.
 

 

 
He wants to add another point so that all 4 points can be joined to make a parallelogram.

Which of these is a possible coordinate for the 4th point?

`(−1,2)` `(1,5)` `(2,−1)` `(5,1)`
 
  
  
  
Show Answers Only

`( – 1, 2)`

Show Worked Solution

`text(One Strategy:)`

`text{Consider the point (4, 4). The point below is 2 units down and)`

`text{2 units left. Apply this to the point (1, 4).}`

`:. ( – 1, 2)\ \ text(is the vertex of a parallelogram.)`

`text{Note that (5, 2) will also make a parallelogram but this point is}`

`text(is not given as an option.)`

Number, NAP-H4-CA23 SA

Harrison was saving his money to buy a cricket bat.

After 1 month, he had saved 45% of the bat's cost.

After 2 months, he had saved another $90 and now had 75% of the bat's cost.

How much does the bat cost?

$   
Show Answers Only

`$300`

Show Worked Solution
`text(75%)\ -\ text(45%)` `= $90`
`text(30%)` `= $90`
`:.\ text(1%)` `= $3`

 

`:.\ text(The bat cost)` `= 100 xx 3`
  `= $300`

Geometry, NAP-H4-CA21 SA

Jana drew a diagram of her tennis racquet.
 

 
The actual length of her racquet is 60 centimetres.

What is the actual width of her racquet head?

   centimetres
Show Answers Only

`26\ text(cm)`

Show Worked Solution

`text(Racquet is 30 grid intervals long.)`

`text(30 intervals)` `= 60\ text(cm)`
`:. 1\ text(grid interval)` `= 2\ text(cm)`

 

`text(Racquet head is 13 grid intervals high,)`

`:.\ text(Head width)` `= 13 xx 2`
  `= 26\ text(cm)`

Number, NAP-I4-NC24 SA

Murray picks a 2 digit number at random.

He can give the following clues about his number:

  • It is a square number.
  • It can be added to another square number to make 100.
  • It is not divisible by 9.

What is Murray's number?
Show Answers Only

`64`

Show Worked Solution
`8^2 + 6^2` `= 100`
`64 + 36` `= 100`

 

`=>\ text(64 is not divisible by 9.)`

Measurement, NAP-I4-NC22 SA

A plan of Zev's backyard is shown.
 

nap-169-nc022 

 
Zev wants to fertilise the lawn in his backyard and needs to know the total area.

What is the total area of Zev's lawn, in square metres?

 m²
Show Answers Only

`text(26 m²)`

Show Worked Solution

nap-169-nc022-answer

`text(Area)` `=\ text(square + triangle)`
  `= (4 xx 4) + (1/2 xx 4 xx 5)`
  `= 16 + 10`
  `= 26\ text(m²)`

Number, NAP-I4-CA24

A shop sells four sizes of chocolate bar.
 

 naplan-2016-24

 
Which packet costs the least per gram?

`text(Packet 1)` `text(Packet 2)` `text(Packet 3)` `text(Packet 4)`
 
 
 
 
Show Answers Only

`text(Packet 2)`

Show Worked Solution
`text(Packet 1)` `= 2.88/200 = 1.44\ text(c/g)`
`text(Packet 2)` `= 310/220 = 1.41\ text(c/g)`
`text(Packet 3)` `= 1.81/125 = 1.45\ text(c/g)`
`text(Packet 4)` `= 4.97/350 = 1.42\ text(c/g)`

 

`:.\ text(Packet 2 costs the least per gram.)`

Algebra, NAP-I4-CA26

A Cartesian plane is shown.
 

 naplan-2016-26

 
Select the correct statement below.

 
 `O` is located where `x = 0` and `y < 0.`
 
 `P` is located where `x < 0` and `y < 0.`
 
 `Q` is located where `x = 0` and `y > 0.`
 
 `R` is located where `x < 0` and `y < 0.` 
Show Answers Only

`x < 0 and y < 0`

Show Worked Solution

`R\ text(occurs when)`

`x < 0 and y < 0`

Number, NAP-I4-CA23 SA

An orchard has the following trees:

  • 5 lemon trees
  • 3 less apple trees than pear trees
  • 3 times as many pear trees as lemon trees
  • 2 nectarine trees and one plum tree
  • the number of pear trees is a quarter of the number of avocado trees.

How many trees are growing in the orchard?
Show Answers Only

`95\ text(trees)`

Show Worked Solution

`text(5 lemon trees)`

`text(15 pear trees)`

`text(12 apple trees)`

`text(2 nectarine)`

`text(1 plum)`

`text(60 avocado trees)`
 

`:.\ text(Total trees) = 95`

Number, NAP-I4-CA22 SA

There are 48 people in a meeting room.

The ratio of females to males in the room is 13 to 11.

How many females need to leave the room so that the ratio of females to males in the room is 1 to 1?
Show Answers Only

`4\ text(females)`

Show Worked Solution

`text(Females : Males) = 13 : 11`

`:.\ text(In the room, there are)`

`26\ text(females and 22 males.)`

 

`:. 4\ text(females need to leave for the)`

`text(ratio to become 1 : 1)`