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Measurement, NAP-E3-NC13

Tenzing started his trek at 5:30 am.

He arrived at his destination `14 1/2` hours later.

At what time did he arrive at his destination?

`7:30\ text(pm)` `8:00\ text(pm)` `9:30\ text(pm)` `10:00\ text(pm)`
 
 
 
 
Show Answers Only

`text(8:00 pm)`

Show Worked Solution

`text(One strategy:)`

`5:30\ text(am plus)\ 14 1/2\ text(hours)` `=\ text(5:30 pm plus)\ 2 1/2\ text(hours)`
  `=\ text(8:00 pm)`

Geometry, NAP-E3-NC09

Irene placed three identical tiles together at their edges.

She drew around the outside to make this new shape.
 

 
Which of these could have been the shape of her tiles?

`text(triangles)` `text(rectangles)` `text(trapeziums)` `text(rhombuses)`
 
 
 
 
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`text(rhombuses)`

Show Worked Solution

`text(rhombuses)`

Measurement, NAP-F3-CA06

Two sides of a triangle measure 6 cm and 12 cm.

Which one of these statements about the length of the third side is true?

 
 Its length is 6 cm.
 
 Its length is less than 6 cm.
 
 Its length is greater than 18 cm.
 
 Its length is greater than 6 cm but less than 18 cm.
Show Answers Only

`text(Its length is greater than 6 cm but less than 18 cm.)`

Show Worked Solution

`=>\ text(One side of a triangle cannot be longer than)`

`text(the sum of the 2 other sides.)`

`=>\ text(One side of a triangle cannot be shorter than)`

`text(the difference between the other 2 sides.)`

`:.\ text(Its length is greater than 6 cm but less)`

`text(than 18 cm)` 

Geometry, NAP-F3-NC12

Kimoko cut a regular pentagon into several identical pieces with no paper left over.
 

 
Which of these could be the shape of the pieces?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(A pentagon can be made up of 5 isosceles)`

`text(triangles as shown below.)`

`:.\ text(The shape of the pieces could only be:)`

Number, NAP-F3-NC08

Manou placed an apple pie into his oven.

The 1st measurement of the apple pie's temperature was  − 4°C.

Twenty minutes later, a second temperature reading was taken, which measured 21°C.

What was the change in temperature between the two measurements?

decrease of  25°C decrease of 17°C increase of 25°C increase of  17°C
 
 
 
 
Show Answers Only

`text(increase of)\  25^@text(C)`

Show Worked Solution
`text(Change in temperature)` `=21-(-4)`
  `=25^@ text(C)`

 

`:.\ text(An increase of  25°C.)`

Number, NAP-F3-NC05

A circle is divided into 5 equal areas and labelled, as shown in the diagram below.
 

 
What percentage of the circle's area has been labelled with an odd number?

`text(3%)` `text(15%)` `text(30%)` `text(40%)` `text(60%)`
 
 
 
 
 
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`text(60%)`

Show Worked Solution

`text(S)text(ince all areas are equal,)`

`text(Percentage labelled with an odd number)`

`=text(odd sections)/text(total sections)`

`=3/5`

`=60text(%)`

Measurement, NAP-G3-NC14

The flask pictured below can hold up to 100 mL of water.
 

 
How much water is in the flask?

`60\ text(mL)` `70\ text(mL)` `80\ text(mL)`  `90\ text(mL)`
 
 
 
 
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`text(80 mL)`

Show Worked Solution

`text(Flask is filled until the 60 mL mark.)`

`text(Flask is half filled between 60-100 mL marks.)`

`:.\ text(Volume of water in the flask)`

`=60 + (1/2 xx 40)`

`=80\ text(mL)`

Number, NAP-G3-NC11

The Park Run is a 5 kilometre fun run.

Paul completes the Park Run in 40 minutes.

Iris runs at the same speed as Paul.

How long will it take her to run 3 kilometres?

`text(24 minutes)` `text(28 minutes)` `text(32 minutes)` `text(38 minutes)`
 
 
 
 
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`text(24 minutes)`

Show Worked Solution

`text(Time taken for Iris to run 3 kilometres)`

`=3/5 xx 40`

`= 24\ text(minutes)`

Algebra, NAP-G3-NC08

Rob uses sticks to make a pattern.

He starts with 3 sticks for Design 1.
 

 
How many sticks does Rob need for Design 5?

`39` `42` `45` `48`
 
 
 
 
Show Answers Only

`45`

Show Worked Solution

`text(One possible strategy:)`

`text(3 sticks are added to each “point” on the base)`

`text(of the triangle to form the next design.)`

`=>\ text(Design 4 has 5 points on the base.)`

`:.\ text(Total sticks)` `= 30 + (5 xx 3)`
  `= 30 + 15`
  `= 45`

Geometry, NAP-G3-CA10


 

Daniel is at the Racoon Ridge Inn.

Which of these directions should Daniel follow to get to Darlington?

 
 Go north-east to York, then turn left.
 
 Go north-west to York, then turn left.
 
 Go north-east to York, then turn right.
 
 Go north-west to York, then turn right.
Show Answers Only

`text(Go north-east to York, then turn right.)`

Show Worked Solution

`text(Go north-east to York, then turn right.)`

Number, NAP-G3-CA09

Penny has $5.

Chocolate bars cost $1.80.

How many chocolate bars can Penny buy?

`2`    `3`   `5`   `9`
 
 
 
 
Show Answers Only

`text(2 chocolate bars)`

Show Worked Solution

`text(Strategy 1)`

`2 xx $1.80` `= $3.60`
`3 xx $1.80` `= $5.40`

 

`text(Strategy 2)`

`5/1.80 = 2.77…\ \ text{(round down)}`

 

`:.\ text(Penny can only buy 2.)`

Number, NAP-G3-CA07

Jeet bought 4 pineapples and 3 mangos.

He used this calculation to work out the total cost

3 × 3.99 + 4 × 2.70

How much did one pineapple cost?

`$2.70` `$3` `$3.99` `$4`
 
 
 
 
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`$2.70`

Show Worked Solution

`text(S)text(ince 4 pineapples were bought,)`

`text(the cost of one is $2.70.)`

Probability, NAP-G3-CA05

Shane rolls a standard 6-sided dice once.

Which of the following is Shane most likely to roll?

 
 a number less than 3
 
 a number greater than 2
 
 an even number
 
 the number 3 or 4
Show Answers Only

`text(a number greater than 2)`

Show Worked Solution

`text(Consider the probability of each option:)`

`P\ text{(a number less than 3)} = 2/6`

`P\ text{(a number greater than 2)} = 4/6`

`P\ text{(an even number)} = 1/2`

`P\ text{(3 or 4)} = 2/6`
 

`:.\ text(A number greater than 2 is most likely.)`

Probability, NAP-H3-NC09

Two standard dice are rolled at the same time and the two numbers are added up.
 

nap-159-nc03 

 
Which total is most likely?

`2` `3` `4` `7`
 
 
 
 
Show Answers Only

`7`

Show Worked Solution

`text(A total of 7 is most likely.)`

`text{Note that a 7 can occur in the following ways:}`

`(6,1), (1,6), (5,2), (2,5), (4,3) or (3,4)`

`text(No other option given has as many)`

`text(combinations.)`

Number, NAP-H3-NC05

Nick had a $10 note only.

At the service station, he bought 5 iceblocks that cost $1.20 each.

How much change should he get?

`$4.00` `$4.50` `$6.00` `$8.80`
 
 
 
 
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`$4.00`

Show Worked Solution
`text(Change)` `= 10 – (5 xx 1.20)`
  `= 10 – 6`
  `= $4.00`

Algebra, NAP-H3-CA20

An unknown number is added to 6.

The result is multiplied by 3 to give an answer of 12.

Which of these is the unknown number?

`− 3` `− 2` `2` `30`
 
 
 
 
Show Answers Only

`−2`

Show Worked Solution

`text(Working backwards:)`

`text(S)text(ince 4 is multiplied by 3 to make 12,)`

`=>\ text(unknown + 6 = 4)`
 

`:.\ text(Unknown number = − 2)`

Number, NAP-I3-CA10

Nigella had 1 kilogram of chocolate.

She used  `3/4`  kilogram in a cake recipe.

How much chocolate did Nigella have left?

`0.75\ text(kg)` `0.70\ text(kg)`  `0.33\ text(kg)`  `0.25\ text(kg)`
 
 
 
 
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`0.25\ text(kg)`

Show Worked Solution
`text(Chocolate left)` `=1 – 3/4`
  `= 1/4`
  `= 0.25\ text(kg)`

Number, NAP-I3-CA08

Peter had 5 cups of flour to use for baking 2 loaves of bread.

He used `1 1/8` cups for the first loaf, and  `2 1/8` cups for the second loaf.

How many cups of flour did Peter have left?

`1 3/4` `1 1/2`  `2 1/2`  `8 1/4`
 
 
 
 
Show Answers Only

`1 3/4`

Show Worked Solution

`text(Cups of flour left)`

`=5 – (1 1/8 + 2 1/8)`

`= 5- 3 1/4`

`=1 3/4`

Measurement, NAP-I3-CA06

A conservationist is studying gorillas in Uganda.

Which unit would be the most appropriate to record the mass of a gorilla?

`text(gram)` `text(kilogram)` `text(litre)` `text(millimetre)`
 
 
 
 
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`text(kilogram)`

Show Worked Solution

`text(A gorilla will weigh hundreds of kilograms.)`

`:.\ text(The best unit is kilogram.)`

Algebra, NAP-I3-CA03

Penelope is making a pattern with black and white tiles, as shown below.
 

 
If the pattern continues, how many black tiles will there be in Design 8?

`4`   `16` `32` `44`
 
 
 
 
Show Answers Only

`32`

Show Worked Solution

`text(Each design adds 4 black tiles.)`

`:.\ text(Black tiles in design 8)` `=8 xx 4`
  `=32`

Number, NAP-I3-CA01

Kate just turned 11 years old.

Patrick is 3 years older than twice Kate's age.

How old is Patrick?

`28` `56` `31` `25`
 
 
 
 
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`25`

Show Worked Solution
`text(Patrick’s age)` `= (11 xx 2) + 3`
  `= 25`

Geometry, NAP-H3-CA04

A regular hexagon is folded in half along the dotted line.
 

 

 
The folded shape can also be called a

`text(pentagon)` `text(hexagon)` `text(quadrilateral)` `text(triangle)`
 
 
 
 
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`text(quadrilateral)`

Show Worked Solution

`text{The folded shape has four sides.}`

`text(quadrilateral)`

Number, NAP-H3-CA03

Tim is selling milkshakes at a school fete.

He makes $48 from selling 8 milkshakes.

All milkshakes cost the same.

How much will Tim make if he sells 11 milkshakes.

`$43` `$63` `$66` `$88`
 
 
 
 
Show Answers Only

`$66`

Show Worked Solution
`text(Price of 1 milkshake)` `=($48)/8=$6`

 

`:.\ text(Price of 11 milkshakes)` `=11 xx $6`
  `=$66`

Measurement, NAP-I3-NC12

Oliver's karate grading started at 9:15 am and went for  `3 1/4`  hours.

He then went straight home, which took him  `3/4`  hours.

What time did Oliver get home?

`text(12:30 pm)` `text(1:00 am)` `text(1:00 pm)` `text(1:15 am)` `text(1:15 pm)`
 
 
 
 
 
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`text(1:15 pm)`

Show Worked Solution

`text(Karate finishes at 9:15 plus 3 hours and 15)`

`text(minutes, which is 12:30 pm.)`

`text(12:30 plus 45 minutes means Oliver arrives)`

`text(home at 1:15 pm.)`

Statistics, NAP-I3-NC09

The number of students that could solve a Rubik's cube in less than 2 minutes were counted at 7 different primary schools.

The results were recorded in the graph below.
 

 
How many students, in total, could solve the cube in less than 2 minutes?

`3` `14` `15` `18`
 
 
 
 
Show Answers Only

`15`

Show Worked Solution

`text(Total students who can solve in less than 2 mins)`

`= 2+2+3+0+3+2+3`

`=15`

Algebra, NAP-I3-NC07

Point `Q` is translated down 3 units.

 
What are the new coordinates of  `Q`?

`(4,5)` `(1,2)` `(7,2)` `(4,−1)`
 
 
 
 
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`(4,−1)`

Show Worked Solution

`Q\ text(has coordinates)\ (4,2)`

`text(When translated 3 down, the)`

`ytext(-value decreases by 3.)`

`:.\ text{New coordinates are  (4, −1)}.`

Probability, NAP-I3-NC06 SA

Peter has a marble bag that contains 20 marbles that are either red or green in colour.

The probability of randomly picking a green marble is 70%.

What is the probability of randomly picking a red marble?

  %
Show Answers Only

`text(30%)`

Show Worked Solution
`P(text(green)) + P(text(red))` `= 100text(%)`
`text(70%)\ + P(text(red))` `= 100text(%)`
`:. P(text(red))` `= 30text(%)`

Geometry, NAP-C3-NC06

An orientation course is set up with 4 drinking stations.

Runners start and then progress through the course in the order of the drinking stations labelled 1-4 in the diagram below.
 

 
At which drinks station do the runners make the greatest change of direction?

Station 1 Station 2 Station 3 Station 4
 
 
 
 
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`text(Station 2)`

Show Worked Solution

`text(Station 2)`

Geometry, NAP-C3-NC04

Rahul draws a net, which is pictured below.
 

 
What 3D object will it make?

 
 Pentagonal prism
 
 Pentagonal pyramid
 
 Hexagonal pyramid
 
 Hexagonal prism
Show Answers Only

`text(Pentagonal pyramid)`

Show Worked Solution

`text(The net will have a pentagon shaped base, and)`

`text(converge to a point.)`

`:.\ text(Net will make a pentagonal pyramid.)`