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Geometry, NAP-I2-13

The crossbar of some goal posts fell down, as shown in the diagram below.

The angle marked `x`, between the ground and the crossbar is

`text(more than 90 degrees.)` `text(equal to 90 degrees.)` `text(less than 90 degrees.)`
 
 
 
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`text(less than 90 degrees)`

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`text(less than 90 degrees)`

Number and Algebra, NAP-D2-14 SA

Mitchell is buying cricket balls from the sporting goods shop.

It costs $12 to buy 3 balls.

If each ball costs the same, how many balls could he buy for $48?
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`12`

Show Worked Solution
`text(C)text(ost of 1 ball)` `= 12 -: 3`
  `=$4`

 

`:.\ text(Number of balls he can buy)`

`=48-:4`

`=12`

Statistics, NAP-I2-12

Matt was recording the colour of cars that drove past his school in 1 hour.

In the hour, Matt saw 9 blue, 12 silver and 6 white cars.

In the tables below, `text(X)` = 3 cars.

Which table correctly shows the number of cars that Matt saw?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(S)text(ince)\ X = 3\ text(cars,)`

`text(9 Blue cars)` `=\ text(XXX)`
`text(12 Silver cars)` `=\ text(XXXX)`
`text(6 White cars)` `=\ text(XX)`

Geometry, NAP-I2-10

Jen is at the starting line of an orienteering course, as shown on the grid diagram below.
 


 

Jen jogs 200 metres north and 300 metres east from the starting line to reach Checkpoint 1.

In which cell is Checkpoint 1?

`text(G5)` `text(B4)` `text(H4)` `text(A3)`
 
 
 
 
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`text(H4)`

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`text(H4)`

Number and Algebra, NAP-I2-07

Emma uses the number sentence  8 × 4 = 32  to solve a problem.

Which of the problems below would the number sentence solve?

 
 Emma has 8 students and gets 4 more.
How many students does she have now?
 
 Emma has 8 students. She gives each of them 4 pencils.
How many pencils does Emma give to her students?
 
 Emma has 8 pencils. She shares them with 4 students.
How many pencils does each student get?
 
 Emma has 8 pencils and gives 4 away.
How many pencils does she have now?
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`text(Emma has 8 students. She gives each of them 4 pencils.)`

`text(How many pencils does Emma give to her students?)`

Show Worked Solution

`text(If Emma has 8 students, and gives each of them)`

`text(4 pencils,)`

`text(Pencils given away)` `=8 xx 4`
`32` `=8 xx 4`

Number, NAP-D4-CA02

The image below shows a game of noughts and crosses in progress.
 

 
What fraction of the available boxes have been filled in?

`1/2`   `4/7`  `5/7`  `7/9`
 
 
 
 
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`7/9`

Show Worked Solution
`text(Fraction)` `=\ text(spaces filled)/text(total spaces) `
  `= 7/9`

Number, NAP-B3-CA04

Barry travelled 120 kilometres in 2 hours.

What was his average speed in kilometres per hour?

`50` `60` `80` `240`
 
 
 
 
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`60\ text(kph)`

Show Worked Solution
`text(Average speed)` `=120/2`
  `=60\ text(km/h)`

Statistics, NAP-E3-CA07

Chris did a survey of the number of female toilets in four shopping centres.

The results were recorded in the table below but the key has been left off the graph?

The total number of female toilets was 44.

How many toilets does represent in the graph?
`1`   `2`  `4`  `5`
 
 
 
 
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`2`

Show Worked Solution

`text(Total number of female symbols)`

`= 5 + 4.5 + 5.5 + 7`

`= 22`
 

`:.\ text(The number of toilets one symbol represents)`

`=44/22`

`= 2`

Statistics, NAP-E3-CA04

Anne taught a kindergarten class and asked her students what their favorite fruit is.

Their answers were used to draw the pie chart below.
 

 

 
Around a quarter of her students preferred which fruit?

`text(Banana)` `text(Apple)` `text(Mango)` `text(Grapes)`
 
 
 
 
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`text(Apple)`

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`text(A quarter of students will represent a sector that)`

`text(is the size of a quarter of the circle.)`

`:.\ text(Apple)`

Measurement, NAP-E3-CA02

The pictures below show a thermometer at two different times.
 

 
By how much has the temperature risen?

`text(4°C)` `text(10°C)` `text(12°C)` `text(16°C)`
 
 
 
 
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`text(16°C)`

Show Worked Solution

`text(Temperature rise)`

`= 4 – (-12)`

`= 4 + 12`

`= 16 text(°C)`

Number, NAP-E3-CA01

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)`
 
 
 
 
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`$110.25\ text(million)`

Show Worked Solution

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

Number, NAP-D3-NC07

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`
 
 
 
 
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`$9`

Show Worked Solution

`$72 ÷ 8 = $9`

`text($9 is the only amount that can be evenly)`

`text(divided into $72 with no remainder.)`

Probability, NAP-D3-NC05

A spinner is spun once.
 

 

 
Each shape on the wheel has an equal chance.

What is the chance that the spinner lands on the triangle .

 
 `text(5 chances in 6)`
 
 `text(6 chances in 6)`
 
 `text(1 chance in 5)`
 
 `text(1 chance in 6)`
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`text(1 chance in 6)`

Show Worked Solution

`text(S)text(ince all shapes have an equal chance,)`​

`Ptext{(triangle)}` `= 1/6`

Number, NAP-D3-NC04

The results from 400 metres running race final was recorded in the table below.
 

 
The time of the runner who came in 3rd place could be

 
 `text(52.57 seconds.)`
 
 `text(52.71 seconds.)`
 
 `text(53.21 seconds.)`
 
 `text(53.94 seconds.)`
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`text(52.71 seconds)`

Show Worked Solution

`text{52.71 is slower than 2nd place (52.62)}`

`text{but faster than 4th place (53.19).}`

Probability, NAP-E3-NC06

Jack rolls a standard dice three times.

He rolls a six each time.

Jack then has a forth roll.

Which of the following is true?

 
 He is more likely to roll a six than a four.
 
 He is certain to roll a six.
 
 He has an equal chance of rolling a six as a four.
 
 He is more likely to roll a four then a six.
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`text(He has an equal chance of rolling a six as a four.)`

Show Worked Solution

`text(S)text(ince all numbers have an equal chance)`

`text(of being rolled,)`

`=>\ text(He has an equal chance of rolling a six as a four.)`

Algebra, NAP-G3-NC01

Mike and Georgia saved $120 together.

Georgia saved twice as much money as Mike.

How much money did Georgia save?

`$20` `$40` `$80` `$240`
 
 
 
 
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`$80`

Show Worked Solution

`text(Let)\ \ x =\ text(Mike’s savings)`

`2x + x` `=120`
`3x` `=120`
`x` `=40`

 

`:.\ text(Georgia saved $80.)`

Geometry, NAP-G3-CA04

Herb is making an animation of a man running.

The picture shows seven frames of his animation.
 

 
He has accidentally swapped two frames.

Which two frames were swapped?

 
 frame 3 and 4
 
 frame 3 and 5
 
 frame 4 and 6
 
 frame 5 and 6
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`text(frame 4 and 6)`

Show Worked Solution

`text(The correct order is:)`

`:.\ text(Frame 4 and 6 have been swapped.)`

Statistics, NAP-G3-CA02

10 of the tallest mountains in the United States are listed in the table below:
 

 

How much taller than Utah's tallest mountain is Colorado's tallest mountain?

`225\ text(metres)` `227\ text(metres)` `273\ text(metres)` `330\ text(metres)`
 
 
 
 
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`273\ text(metres)`

Show Worked Solution

`text(Mount Massive – Kings Peak)`

`= 4398 – 4125`

`= 273\ text(metres)`

Measurement, NAP-I3-CA05

Roger started work at 7:15 in the morning and finished at 6:35 in the evening.

How many hours did Roger spend working?

 
 `text(40 minutes)`
 
 `text(1 hour 20 minutes)`
 
 `text(10 hours 40 minutes)`
 
 `text(11 hours 20 minutes)`
 
 `text(13 hours 50 minutes)`
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`text(11 hours and 20 minutes)`

Show Worked Solution

`text(7:15 am to 6:15 pm = 11 hours)`

`text(6:15 pm to 6:35 pm = 20 minutes)`

`:.\ text(11 hours and 20 minutes)`

Number, NAP-I3-CA04 SA

Brian has an orchard with 17 different types of fruit trees.

He has a total of 306 fruit trees.

He has the same number of each type of fruit tree.

How many fruit trees of each type does Brian have?

   trees
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`18`

Show Worked Solution

`text(Number of trees of each type)`

`= 306 ÷ 17`

`= 18\ text(trees)` 

Geometry, NAP-H3-CA01

This is a street map.
 

 

 
About how far is it from Matt's house to Ali's house?

`40\ text(metres)` `100\ text(metres)` `160\ text(metres)` `200\ text(metres)`
 
 
 
 
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`text(100 metres)`

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`text(The distance between Matt and Ali’s house is)`

`text(about 2.5 times the width of the scale interval)`

`text(that is equal to 40 metres.)`

`:.\ text(Distance)\ ~~ 2.5 xx 40 ~~ 100\ text(metres)`

Measurement, NAP-I3-NC05

Dom is measuring long jump at a school athletics carnival.

She measures a jump at 3 metres and 17 centimetres.

Which of these shows how Dom would write this measurement in metres?

`3.017\ text(m)` `3.17\ text(m)` `4.17\ text(m)` `4.2\ text(m)`
 
 
 
 
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`3.17\ text(m)`

Show Worked Solution

`text(3 metres and 17 centimetres)`

`= 3.17\ text(m)`

Statistics, NAP-I3-NC04

Matt was recording the colour of cars that drove past his school in 1 hour.

In the hour, Matt saw 9 blue, 12 silver and 6 white cars.

In the tables below, `text(X)` = 3 cars.

Which table correctly shows the number of cars that Matt saw?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(S)text(ince)\ X = 3\ text(cars,)`

`text(9 Blue cars)` `=\ text(XXX)`
`text(12 Silver cars)` `=\ text(XXXX)`
`text(6 White cars)` `=\ text(XX)`