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Statistics, NAP-E4-CA18

Brandon collected some data from his hockey team.

The data was used to draw the graph below although no labels were used.

What kind of data could Brandon be showing on his graph?

  Horizontal axis Vertical axis
 
 Type of pet Number of players
 
 Age Height
 
 Gender Height
 
 Years playing hockey Number of players
Show Answers Only

`text(Age and Height.)`

Show Worked Solution

`text(Age and Height.)`

`text(Each data category needs to have a number of)`

`text(possibilities and the chosen pair need a general)`

`text(correlation. Age and height is the most likely.)`

Number, NAP-E4-CA14

David has a job selling mobile phone plans. His weekly salary, `W` dollars, is calculated using the rule below:

`W = 300 + 0.05 P`

where `P` is the total value in dollars of the mobile phone plans he sells that week.

David sold $32 000 worth of mobile phone plans in a given week.

What was David's salary in the week?

`$640` `$1280` `$1900` `$3230` `$16\ 000`
 
 
 
 
 
Show Answers Only

`$1900`

Show Worked Solution
`W` `= 300 + 0.05 xx 32\ 000`
  `= 300 + 1600`
  `= 1900`

Probability, NAP-E4-CA12

Peter has a bag of marbles. 75% of his marbles are blue.

Peter takes a green marble from his bag and loses it in a game.

If he takes another marble from the bag without looking, what are the chances it is blue?

 
 less than 75%
 
 equal to 75%
 
 greater than 75%
Show Answers Only

`text(greater than 75%)`

Show Worked Solution

`text(There will be greater than 75% chance)`

`text(because there are the same amount of )`

`text(blue marbles to be chosen but 1 less)`

`text(in the bag.)`

Measurement, NAP-C3-NC22

Which of these is the longest distance?

`0.1309\ text(km)` `139\ text(m)` `1390\ text(cm)` `13090\ text(mm)`
 
 
 
 
Show Answers Only

`text(139 m)`

Show Worked Solution

`text(Converting all distances to metres:)`

`0.1309 xx 1000 = 130.9\ text(m)`

`139\ text(m)`

`1390/100 = 13.9\ text(m)`

`(13\ 090)/1000 = 13.09\ text(m)`

 

`:.\ text(139 m is the longest distance.)`

Measurement, NAP-C3-NC20

When it is 10 am in Sydney, it is 6 am in Perth on the same day. A plane leaves Sydney at 11:30 am Sydney time and flies to Perth.

The flight takes 4 hours and 40 minutes.

What is the time in Perth when the plane arrives?

`11:10\ text(am)` `12:10\ text(pm)` `1:10\ text(pm)` `2:10\ text(pm)`
 
 
 
 
Show Answers Only

`text(12:10 pm)`

Show Worked Solution

`text(11:30 am in Sydney is 7:30 am in Perth.)` 

`text(After 4 hours and 40 minutes flying time,)`

`text(it is 12:10 pm in Perth.)`

Number, NAP-E4-CA06

Fleur lives 15 kilometres from her work.

On Wednesday, she drove to work and averaged 60 kilometres per hour.

On Thursday, she took the bus which averaged 15 kilometres per hour.

What was the extra time of the bus journey, in minutes, compared to when she drove on Wednesday?

`15` `45` `60` `75`
 
 
 
 
Show Answers Only

`45\ text(minutes)`

Show Worked Solution
`text(Time on Wednesday)` `= 15/60`
  `= 0.25\ text(hour)`
  `= 15\ text(minutes)`

 

`text(Time on Thursday)` `= 15/15`
  `= 1\ text(hour)`
  `= 60\ text(minutes)`

 

`:.\ text(The extra time taking the bus)`

`=60 – 15`

`= 45\ text(minutes)`

Number, NAP-E4-NC17

Which of the following multiplications gives the greatest value?

`0.021 xx 100` `0.123 xx 10` `0.231 xx 0.1` `0.0003 xx 1000`
 
 
 
 
Show Answers Only

`0.021 xx 100`

Show Worked Solution

`0.021 xx 100 = 2.1`

 

`text(All others give lesser values:)`

`0.123 xx 10 = 1.23`

`0.231 xx 0.1 = 0.0231`

`0.0003 xx 1000 = 0.3`

Number, NAP-E4-NC14

Tony is making a fruit cake.

The recipe says he needs 3 cups of sultanas for every 5 cups of flour.

If 2.5 cups of flour are used, how many cups of sultanas are needed?

`0.5\ text(cups)` `1.5\ text(cups)` `2.5\ text(cups)` `4.5\ text(cups)`
 
 
 
 
Show Answers Only

`text(1.5 cups)`

Show Worked Solution

`text(Strategy 1:)`

`text(2.5 is half of 5 cups of flour, therefore half of)`

`text(3 cups of sultanas is required.)`

`=>\ text(1.5 cups of sultanas needed.)`

 

`text(Strategy 2:)`

`text(Let)\ \ n = text(cups of sultanas needed)`

`n/2.5` `=3/5`
`:.n` `=(3 xx 2.5)/5`
  `=1.5\ text(cups)`

Number, NAP-E4-NC13

Jack had a full bucket of water.

 

 

 

He put a hole in the bottom and the water leaked out.

After a few minutes, Jack put a second identical hole in the bucket and the water poured out more quickly.

Which graph below best shows the depth of water in the bucket against time?
 

 
 
 
  
 
 
 
  

Show Answers Only

Show Worked Solution

`text(The depth decreases slowly at first and once the)`

`text(second hole is made, it decreases at twice the rate.)`
 

Probability, NAP-E4-NC12

Shane rolls a standard six-sided dice.

Which of the following events has a probability of less than  0.5?

 
 rolling a number greater than 1
 
 rolling an odd number
 
 rolling a number less than 6
 
 rolling a number greater than or equal to 6
Show Answers Only

`text(rolling a number greater than or equal to 6)`

Show Worked Solution

`P(text(number) >= 6) = 1/6,`

`text(which is less than 0.5.)`

Measurement, NAP-F4-CA21

A cube has a side length of 6 cm.

Two smaller cubes of side length 3 cm are attached to the larger cube as shown in the diagram below.
  

What is the surface area of the new object?

`216\ text(cm²)` `243\ text(cm²)` `270\ text(cm²)` `288\ text(cm²)`
 
 
 
 
Show Answers Only

`270\ text(cm²)`

Show Worked Solution

`text(One strategy:)`

`text{Calculate the surface area (S.A.) of the 2 objects joined}`

`text(separately and deduct the area where they join.)`
 

`text{S.A. (large cube)} = 6 xx 6xx 6 = 216\ text(cm²)`

`text{S.A. (2 smaller cubes joined together)}`

`=2 xx (3 xx 3) + 4 xx (6 xx 3)`

`=90\ text(cm²)`

`text{S.A. to be deducted (where cubes are attached)}`

`= 2 xx (6 xx 3)`

`= 36\ text(cm²)`

 

`:.\ text{S.A. (new object)}` `= 216 + 90 – 36`
  `=270\ text(cm²)`

Number, NAP-F4-CA18

Ryan's tennis racquet is pictured below.
 

 

 
His handle is 19 cm in length.

Which of the following show the length of the handle as a percentage of the total length of the racquet?

`text(11%)` `text(18%)` `text(19%)` `text(33%)`
 
 
 
 
Show Answers Only

`text(18%)`

Show Worked Solution

`text(Length of the handle as a percentage)`

`=19/103.4 xx 100`

`=18.4…%`
 

`:.\ text(18% is the closest option.)`

Algebra, NAP-F4-CA17

Barry drives a barge that transports sand.

The table below shows the volume of sand, measured in cubic metres, of different sand masses, measured in tonnes.
 

 

Barry's barge has 84 cubic metres of sand loaded on it.

How many tonnes of sand are on his barge?

56 tonnes 58 tonnes 126 tonnes 136 tonnes`
 
 
 
 
Show Answers Only

`126\ text(tonnes)`

Show Worked Solution

`text(Tonnes in 1 cubic metre of sand)`

`=30/20`

`= 1.5`
 

`:.\ text(Tonnes in 84 cubic metres)`

`=84 xx 1.5`

`=126\ text(tonnes)` 

Geometry, NAP-F4-CA15

Brian enters a park at one of the entries shown below.

The map is drawn to scale but no scale is given.
 

 
He moves 60 metres in a north-east direction and then turns and walks 30 metres in a south-east direction.

Which point on the map shows where Brian ended up?

`A`   `B`  `C`  `D`
 
 
 
 
Show Answers Only

`text(Point B)`

Show Worked Solution

 `text(Point B)`

Number, NAP-F4-CA14

Lachlan drives his boat to an island 100 km away at an average speed of 80 km/h.

How long does the trip take?

`text(48 minutes)` `text(1 hour 15 minutes)` `text(1 hour 20 minutes)` `text(1 hour 30 minutes)`
 
 
 
 
Show Answers Only

`text(1 hour 15 minutes)`

Show Worked Solution
`text(Time)` `= text(Distance)/text(Speed)`
  `= 100/80`
  `= 1.25\ text(hours)`
  `=1\ text(hour 15 minutes)`

Algebra, NAP-F4-CA13

Charlie swam 250 lengths of a 50 metre pool in 5 days.

After the first day, he swam 5 more laps each day than the day before.

How many laps did he swim on the first day? 

`35` `40` `45` `50`
 
 
 
 
Show Answers Only

`40`

Show Worked Solution

`text(Average laps per day)`

`= 250/5`

`= 50`
 

`=>\ text(Laps swam each of the 5 days:)`

`text(40, 45, 50, 55, 60)`
 

`:.\ text(He swam 40 laps on the 1st day.)`

Algebra, NAP-F4-CA12

In a hockey club, there are 123 players.

There are 21 less women than men.

How many men are in the club? 

`51` `72` `81` `102`
 
 
 
 
Show Answers Only

`72`

Show Worked Solution

`text(Let)\ \ x = text(number of men players)`

`:. x + (x – 21)` `= 123`
`2x` `= 144`
`x` `= 72`

Geometry, NAP-C3-CA20

David visits his favourite coffee shop by travelling 6 km south then 4 km east.

He records his trip as 6S, 4E.
 

 
Which of these trips takes David home again?

 
 `text(3S, 2E, 3S, 2E)`
 
 `text(2S, 2E, 4S, 6E)`
 
 `text(3N, 2W, 3N, 4W)`
 
 `text(2N, 2E, 4N, 6W)`
Show Answers Only

 `text(2N, 2E, 4N, 6W)`

Show Worked Solution

`text(2N, 2E, 4N, 6W gets David back home.)`

Algebra, NAP-C3-CA19

Kate is 4 years older than Jess.

Sarah is 6 years older than Jess.

Which equation shows how Kate's age relates to Sarah's age?

 
 `text(Kate's age) = text(Sarah's age) + 2`
 
 `text(Kate's age) = text(Sarah's age) - 2`
 
 `text(Kate's age) = text(Sarah's age) + 10`
 
 `text(Kate's age) = text(Sarah's age) - 10`
Show Answers Only

 `text(Kate’s age) = text(Sarah’s age) – 2`

Show Worked Solution

`text(Kate is 2 years younger than Sarah,)`

`:.\ text(Kate’s age) = text(Sarah’s age) – 2`

Statistics, NAP-F4-NC17

Riley's basketball team has 5 players.

The height of each player is listed below (in cm):

   `155, \ 180, \ 160, \ 175, \ 180`

What is the median height of these players?

`160\ text(cm)` `170\ text(cm)` `175\ text(cm)` `180\ text(cm)`
 
 
 
 
Show Answers Only

`175\ text(cm)`

Show Worked Solution

`text{Heights from shortest to tallest are:}`

`155, 160, 175, 180, 180`

`text(Median)` `= 3text(rd height)`
  `= 175\ text(cm)`

Geometry, NAP-F4-NC16

Three corners of a parallelogram are drawn below.
 

 
Which point below is the fourth corner?

`(3,1)` `(1,4)` `(2,3)` `(1,3)`
 
 
 
 
Show Answers Only

`(1,3)`

Show Worked Solution

`text{Consider the far right point on the graph at (6,3),}`

`=>\ text(The point below is 3 grid lines down and two left.)`
 

`text{Consider the top point on the graph at (3,6),}`

`=>\ text{The point 3 grid lines down and two left is (1,3).}`

Number, NAP-F4-NC15

Brandon has a money jar that contains 50 cent, 20 cent, 10 cent and 5 cent pieces only.

If he buys a pie worth $2.65, what is the minimum amount of coins he can pay with?

`5` `7` `8` `9` `11`
 
 
 
 
 
Show Answers Only

`7`

Show Worked Solution

`text(Minimum number of coins would be:)`

`5 xx 50\ text(c)`

`1 xx 10\ text(c)`

`1 xx 5\ text(c)`

`:.\ text(A minimum of 7 coins is needed.)`

Geometry, NAP-F4-NC13

Which of the following triangle types is impossible to draw?

 
 a right-angled, isosceles triangle
 
 an acute-angled, isosceles triangle
 
 an obtuse-angled, scalene triangle
 
 a right-angled, equilateral triangle
Show Answers Only

`text(a right-angled, equilateral triangle)`

Show Worked Solution

`text(An equilateral triangle has all angles = 60°.)`

`:.\ text(A right-angled, equilateral triangle is impossible.)`

Measurement, NAP-F4-NC14

Mike takes 2 minutes 35 seconds to walk 1 lap of the running track.

Jordan runs 1 lap of the same track in 45 seconds.

If they start at the same time, how long after Jordan finishes will Mike finish his lap?

 
 `text(1 minute 50 seconds)`
 
 `text(2 minutes 10 seconds)`
 
 `text(2 minutes 50 seconds)`
 
 `text(3 minutes 20 seconds)`
Show Answers Only

`text(1 minute 50 seconds)`

Show Worked Solution

`text(2 minutes 35 seconds – 45 seconds)`

`=\ text(2 minutes – 10 seconds)`

`=\ text(1 minute 50 seconds)`

Geometry, NAP-G4-NC18

`AB` is the diameter of a circle, centre `O`.

There are 3 triangles drawn in the lower semi-circle and the angles at the centre are all equal to `x^@`.

The three triangles are best described as:

`text(isosceles)` `text(scalene)` `text(right-angled)` `text(equilateral)`
 
 
 
 
Show Answers Only

`text(equilateral)`

Show Worked Solution
`3x` `=180`
`:. x` `=60^@`

 
`AO=OC=OD=OB\ \ text{(radii of circle)}`

`=>\ text{Since angles opposite equal sides of a triangle are}`

`text(equal, all triangle angles can be found to equal 60°.)`

`:.\ text(The three triangles are equilateral.)`

Number, NAP-G4-CA18

Marty and Paul swam 3 km in an ocean swimming race.

Marty finished in a time of 1 hour and 10 minutes.

Paul took 25% longer than Marty.

Approximately how long did Paul take to finish the race?

`88\ text(minutes)` `95\ text(minutes)` `135\ text(minutes)` `138\ text(minutes)`
 
 
 
 
Show Answers Only

`88\ text(minutes)`

Show Worked Solution

`text(Paul’s time)`

`= (1\ text{hour and 10 minutes)} xx text(125%)`

`= 70 xx text(125%)`

`= 87.5\ text(minutes)`
 

`:.\ text(88 minutes is the closest choice.)`

Number, NAP-H4-NC16

Lily made a mobile phone call that lasted 39 minutes.

Her mobile phone provider charges her 19 cents per minute for calls.

Lily estimated that the total cost of the phone call was about $8.

Lily's estimate was

 
 less than the actual cost.
 
 equal to the actual cost.
 
 more than the actual cost.
Show Answers Only

`text(more than the actual cost.)`

Show Worked Solution

`text(An estimate of the cost could be just under:)`

`text(40 minutes × 20 cents = $8)`

`:.\ text($8 estimate is more than the actual cost.)`

Algebra, NAP-H4-NC15

Karen and Kim are sisters and share a bedroom.

They want their beds positioned the same distance from the centre of the room.
 

 

 
What is the distance  `x`  from the edge of each bed to the middle of the room?

`1.25\ text(m)` `2.25\ text(m)` `2.50\ text(m)` `2.75\ text(m)` `5.25\ text(m)`
 
 
 
 
 
Show Answers Only

`1.25`

Show Worked Solution

`text(Half the room is 4 m wide.)`

`:. x` `= 4 – (1 + 1.75)`
  `=4-2.75`
  `=1.25\ text(m)`

Algebra, NAP-G4-CA15

Alan earns $55 for making 11 deliveries.

Which expression shows how much he will earn for making `n` deliveries?

`(55 xx 11) xx n` `(55 ÷ 11) ÷ n` `(55 xx 11) ÷ n` `(55 ÷ 11) xx n`
 
 
 
 
Show Answers Only

`(55 ÷ 11) xx n`

Show Worked Solution

`55\ → 11\ text(deliveries)`

`55 -: 11 → \ text(1 delivery)`

`:. (55 ÷ 11) xx n\ → \ n\ text(deliveries)`

Geometry, NAP-H4-NC12

`PQRS` is a parallelogram.

Which of these must be a property of `PQRS`?

 
 Line `PS` is perpendicular to line `PQ`.
 
 Line `PQ` is parallel to line `PS`.
 
 Diagonals `PR` and `SQ` are perpendicular.
 
 Line `PS` is parallel to line `QR`.
Show Answers Only

`text(Line)\ PS\ text(is parallel to line)\ QR.`

Show Worked Solution

`text(Line)\ PS\ text(is parallel to line)\ QR.`

Number, NAP-H4-NC11

 

 
Which of the following situations best fits the distance/time graph above?

 
 Matt ran to the park, sat down on a bench, and then walked home.
 
 Matt walked to the park, sat down on a bench, and walked back home.
 
 Matt walked to the park, sat down on a bench and ran home.
 
 Matt walked to the park and back home without stopping. 
Show Answers Only

`text(Matt walked to the park, sat down on)`

`text(a bench and ran home.)`

Show Worked Solution

`text(Matt walked to the park, sat down on)`

STRATEGY: The steep line returning home shows he travelled faster than getting there.

`text(a bench and ran home.)`

Probability, NAP-I4-NC20

A group of 125 people were asked if they wear a watch or not.

This table shows the results.
 

 

A man was selected at random.

What is the probability that he wears a watch?

`0.20` `0.28` `0.32` `0.42`
 
 
 
 
Show Answers Only

`0.42` 

Show Worked Solution

`P(text(man wears watch))`

`= text(number of men wearing watch)/text(total men)`

`= 25/60`

`= 0.42`

Geometry, NAP-I4-NC19

nap-169-nc019

Select the statement that is true about triangle `ABC`.

 
 Triangle `ABC` is a scalene triangle.
 
 Triangle `ABC` has exactly 2 equal sides.
 
 Triangle `ABC` is an equilateral triangle.
 
 Triangle `ABC` is an obtuse triangle.
Show Answers Only

`text(Triangle)\ ABC\ text(is an equilateral.)`

Show Worked Solution

`angleA = 180-(60 + 60) = 60^@`

`:. text(All angles are)\ 60^@.`

`:. text(Triangle)\ ABC\ text(is an equilateral.)`

Number, NAP-H4-CA15 SA

The dog population in five continents can be found in the table below.
 

    naplan-2015-15mc

 
How many more dogs live in Europe than in Africa and South America combined?

 
Show Answers Only

`36, 345, 608`

Show Worked Solution

`text(Number of extra dogs)`

`= 59\ 329\ 647 – (9\ 721\ 457 + 13\ 262\ 582)`

`= 36\ 345\ 608`

Number, NAP-H4-CA14 SA

Sophia and Cailen sold raffle tickets to fund their trip to the National Swimming Titles.

If Cailen had collected $20 more, he would have collected exactly twice as much as Sophia.

Which row of the table shows how much money they could have collected?
 

  Sophia Callen
 
 $20 $40
 
 $25 $40
 
 $30 $40
 
 $40 $70
Show Answers Only

`text(Sophia $30, Callen $40)`

Show Worked Solution

`text(Consider the 3rd option:)`

`text(Cailen)\ + $20` `= 2 xx text(Sophia)`
`$40 + $20` `= 2 xx $30`
`$60` `= $60`

 

`:.\ text(Sophia $30, Callen $40)`

Number, NAP-H4-CA13

Alison's petrol tank was empty.

She then spent $55 filling her tank up to half way at a cost of $1.55 per litre.

Approximately how much petrol can Alison's petrol tank hold when it is full?

`35\ text(litres)` `65\ text(litres)` `71\ text(litres)` `85\ text(litres)`
 
 
 
 
Show Answers Only

`71\ text(litres)`

Show Worked Solution
`text(Volume of half tank)` `= 55/1.55`
  `= 35.48…`

 

`:.\ text(Volume of full tank)`

`= 2 xx 35.48…`

`= 70.96…`

`= 71\ text(litres)`

Geometry, NAP-I4-NC15

Alison draws a scale map of Australia on a coordinate grid.
 

nap-169-nc015 

 
She knows that the actual distance between Karratha and Mackay is 2950 kilometres.

Which scale value should Alison use for her map?

`180\ text(km)` `330\ text(km)` `400\ text(km)` `500\ text(km)`
 
 
 
 
Show Answers Only

`text(400 km)`

Show Worked Solution

`text(Mackay is 7.7 grid intervals away from Karratha.)`

`:.\ text(Scale value)` `= 2950/7.7`
  `~~400`

Algebra, NAP-I4-NC18 SA

Renee and Leisa are saving money so they can visit their grandmother on a holiday.

Renee has $100 and plans to save $30 each week.

Leisa has $200 and plans to save $10 each week.

After how many weeks will Renee and Leisa have saved the same amount?

   weeks
Show Answers Only

`text(5 weeks)`

Show Worked Solution

`text(After)\ w\ text(weeks,)`

`text(Renee has saved:)\ \ 100 + 30w`

`text(Leisa has saved:)\ \ 200 + 10w`

`text(If)quad100 + 30w` `= 200 + 10w`
`20w` `= 100`
`w` `= 5`

 

`:.\ text(Amounts are equal after 5 weeks.)`

Statistics, NAP-I4-NC17

The mean height of students at a Year 9 class is 155 cm.

The median height of the same class is 145 cm.

A new student joins the class who is 165 cm tall.

Which of these is possible?

 
 The mean height stays the same and the median height increases.
 
 The mean height stays the same and the median height decreases.
 
 The mean height decreases and the median height increases.
 
 The mean height increases and the median height stays the same.
Show Answers Only

`text(It is possible for the mean height to increase and)`

`text(the median height to stay the same.)`

Show Worked Solution

`text(It is possible for the mean height to increase and)`

`text(the median height to stay the same.)`