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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`
 
 
 
 
Show Answers Only

`$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`
 
 
 
 
Show Answers Only

`$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)`
 
 
 
 
Show Answers Only

`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)`
 
 
 
 
Show Answers Only

`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`
 
 
 
 
Show Answers Only

`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)`
 
 
 
 
Show Answers Only

`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)`
 
 
 
 
 
Show Answers Only

`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)`
 
 
 
 
Show Answers Only

`(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
 
 
 
 
Show Answers Only

`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.)`

Algebra, NAP-C3-CA03

At an apple orchard, apples are picked and put in a basket.

The table below shows the total number of apples in the basket after each minute.

\begin{array} {|c|c|c|}
\hline \textbf{Minutes} & \textbf{Total number of apples} \\
\hline 1 & 4 \\
\hline 2 & 8 \\
\hline 3 & 12 \\
\hline 4 & 16 \\
\hline \end{array}

How many apples are in the basket after 10 minutes? 

`20` `30` `35` `40`
 
 
 
 
Show Answers Only

 `40\ text(apples)`

Show Worked Solution

`text(4 apples are put into the basket each minute.)`

`:.\ text(Apples in basket after 10 minutes)`

`=4 xx 10`

`= 40\ text(apples)`

Statistics, NAP-C3-CA02

For three days, Terry counted the colour of cars he saw drive past his house.
 

   

 
Which column on the graph below shows the total number of Red cars? 

 
 
 
 
Show Answers Only

 `text(The second bar from the left.)`

Show Worked Solution

`text(Option 2: 4 red cars passed.)`

 `text{(The second bar from the left)}`

Number, NAP-E4-CA05

Zilda has 4 children.

Each child needs 6 pens when they start school for the new year.

Zilda has no pens when she goes to the shop.

The shop sells its pens in packets of 5.

How many packets does Zilda need to buy?

`2`    `4`   `5`  `6`
 
 
 
 
Show Answers Only

`5\ text(packets)`

Show Worked Solution
`text(Pens required)` `= 4 xx 6`
  `= 24`

 

`:.\ text(Packets required)` `= 24/5`
  `= 4.8`
  `= 5`

Statistics, NAP-E4-CA03

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)`
 
 
 
 
Show Answers Only

`text(Apple)`

Show Worked Solution

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

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

`:.\ text(Apple)`

Number, NAP-E4-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)`
 
 
 
 
Show Answers Only

`$110.25\ text(million)`

Show Worked Solution

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

Number, NAP-F4-CA07

David buys a surfboard cover online that costs him $128.

The postage costs involved are listed in the table below.
 

 
The surfboard cover weighs 1.1 kg

What does David have to pay, in total, to purchase the surfboard and have it delivered?

`$140` `$145.50` `$149.75` `$153`
 
 
 
 
Show Answers Only

`$149.75`

Show Worked Solution

`text(Surfboard cover cost)\ +\ text(postage)`

`= $128 + $21.75`

`= $149.75`

Number, NAP-F4-NC04

Nigella placed a leg of lamb into her oven in the morning.

The 1st measurement of the lamb's temperature was  −6°C.

Fifteen minutes later, a second temperature reading was taken, which measured  16°C.

What was the change in temperature between the two measurements?

`text(decrease of)\ 22^@text(C)` `text(decrease of)\ 10^@text(C)` `text(increase of)\ 10^@text(C)` `text(increase of)\ 22^@text(C)`
 
 
 
 
Show Answers Only

`text(increase of)\  22^@text(C)`

Show Worked Solution
`text(Change in temperature)` `=16-(-6)`
  `=22^@ text(C)`

 

`:.\ text(An increase of  22°C.)`

Number, NAP-F4-NC03

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%)`
 
 
 
 
 
Show Answers Only

`text(60%)`

Show Worked Solution

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

`text(Percentage labelled with an odd number)`

`=3/5`

`=60text(%)`

Number, NAP-F4-CA04

The first three days of the Brisbane cricket test had the following attendances:

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex}\text{Day 1}\rule[-1ex]{0pt}{0pt} & 20\ 156\\
\hline
\rule{0pt}{2.5ex}\text{Day 2}\rule[-1ex]{0pt}{0pt} & 18\ 397\\
\hline
\rule{0pt}{2.5ex}\text{Day 3}\rule[-1ex]{0pt}{0pt} & 29\ 981\\
\hline
\end{array}

What was the total crowd over the first 3 days, to the nearest `1000?`

`68\ 000` `69\ 000` `70\ 000` `71\ 000`
 
 
 
 
Show Answers Only

`69\ 000\ text{(nearest 1000)}`

Show Worked Solution

`20\ 156 + 18\ 397 + 29\ 981`

`= 68\ 534`

`= 69\ 000\ text{(nearest 1000)}`

Number, NAP-G4-NC02

Ben spent twice as much money as Mark.

If they spent a total of $90, how much did Ben spend?

`$15` `$30` `$60` `$180`
 
 
 
 
Show Answers Only

`$60` 

Show Worked Solution

`text(Strategy 1)`

`text(Ratio)`

`text{Ben : Mark = 2 : 1  (3 parts)}`

`text(1 part)\ = $90-:3=$30`

`:.\ text(Ben spent  2 × $30 = $60)`

 

`text(Strategy 2)`

`text(Let)\ \ $x = text(Amount Mark spent)`

`2x + x` `= 90`
`x` `= $30`

 

`:.\ text(Ben spent $60.)`

Measurement and Geometry, NAP-G4-CA04

Petunia walks along the path from `A` to `B.`

How far does she walk in kilometres?

`0.14` `1.4` `14` `1400`
 
 
 
 
Show Answers Only

`1.4\ text(km)`

Show Worked Solution
`text(Distance)` `= 14 xx 100\ text(m)`
  `= 1.4\ text (km)`