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Number and Algebra, NAP-G2-35 SA

Archer has blocks with two square faces.

He builds the model below.
 

 
What is the height of the model in centimetres?

  centimetres
Show Answers Only

`12\ text(cm)`

Show Worked Solution

`text(2 × length of block = 18 cm)`

`=>\ text(Length of 1 block = 9 cm)`

`=>\ text(Side length of the square face)`

`= 9 ÷ 3`

`= 3\ text(cm)`
 

`:.\ text(Height)` `= 3 xx 4`
  `= 12\ text(cm)`

Number and Algebra, NAP-G2-34 SA

In a card game, Shane gets 4 cards and earn points.
 

 
Each black triangle is worth double the points of each white triangle.

How many points is a white triangle worth?
Show Answers Only

`5\ text(points)`

Show Worked Solution

`text(Shane’s hand is worth the same as having)`

`text(6 white triangles.)`

`6 xx`   `= 30`
`:.`     `= 30 ÷ 6`
     `= 5\ text(points)`

Geometry, NAP-G2-33

 
Prudence walked south along Bond Street and then turned left on to Bridge Street.

What was the first street she passed on her left?

Ivy Lane Kemp Street King Street Crown Street
 
 
 
 
Show Answers Only

`text(Kemp Street)`

Show Worked Solution

`text(Kemp Street)`

Measurement, NAP-H2-33 SA

Shelly and Rhonda are the first two runners in a cross country relay team.

Shelly runs 1 lap of the course and passes a baton to Rhonda for the second lap.

Their results are in the table below.

How long after Shelly started, in seconds, did Rhonda finish her lap?

`text(seconds)`
Show Answers Only

`text(470 seconds)`

Show Worked Solution
`text(Total time)` `= 4:28 + 3:22`
  `= 7\ text(minutes and)\ \ 50\ text(seconds)`
  `=(7xx60) +50`
  `=420 + 50`
  `=470\ text(seconds)`

Number and Algebra, NAP-H2-39 SA

Soda cans are sold in three different ways at the supermarket.
 

 
What is the cheapest price that someone can buy 13 cans for?
Show Answers Only

`$17.5`

Show Worked Solution

`text(Two six packs and a single can:)`

`text(C)text(ost)` `=(2 xx 8) + 1.50`
  `=$17.50`

 

`text(One ten pack and 3 single cans:)`

`text(C)text(ost)` `=(1 xx 14) + (3 xx 1.50)`
  `=14 + 4.50`
  `=$18.50`

Number and Algebra, NAP-H2-34 SA

Bonnie and Clyde ate 43 cherries between them.

Bonnie ate 9 less cherries than Clyde.

How many cherries did Bonnie eat?
Show Answers Only

`17\ text(cherries)`

Show Worked Solution

`text(Strategy 1:)`

`text(Consider the possible splits,)`

`22 – 21:\ text(Bonnie eats 1 less)`

`23 – 20:\ text(Bonnie eats 3 less`

`vdots`

`26 – 17:\ text(Bonnie eats 9 less)`

`:.\ text(Bonnie eats 17.)`

 

`text(Strategy 2:)`

`text(Let)\ \ c = text(number of cherries Bonnie eats)`

`=> c + 6 =\ text(number of cherries Clyde eats)`

`c + c + 9` `= 43`
`2c` `= 34`
`:. c` `= 17`

Measurement, NAP-G2-28

What is the temperature reading in this thermometer?
 


 

 
 `8^@text(C)`
 
 `14^@text(C)`
 
 `16^@text(C)`
 
 `18^@text(C)`
Show Answers Only

`18^@text(C)`

Show Worked Solution

`text(Each section measures 10°C and each smaller mark is)`

`text(worth an extra 2°C.)`
 

`:.\ text(Temperature reading)`

`=9 xx 2°`

`=18°\ text(C)`

Number and Algebra, NAP-D2-32

 
Which number is the arrow pointing to on this number line?

`22.15` `22.50` `22.05` `22.25`
 
 
 
 
Show Answers Only

`22.25`

Show Worked Solution

`text(Strategy one:)`

`text(The arrow points to the midpoint between 0)`

`text(and 0.50 of the number 22,)`

`=>\ text(22.25 is the midpoint).`

 

`text(Strategy two:)`

`text(Halfway between 22.0 and 22.5)`

`=(22.0 + 22.5)/2`

`=44.5 /2`

`= 22.25`

Number and Algebra, NAP-D2-31 SA

A ticket to Sea World for two adults costs $36 in total.

A ticket to Sea World for one child is two thirds the cost of an adult ticket.

What is the cost of a ticket for one child?

$  
Show Answers Only

`$12`

Show Worked Solution

`text(C)text(ost of 1 adult ticket)`

`= 36 -: 2`

`= $18`
 

`:.\ text(C)text(ost of 1 child ticket)`

`= 2/3 xx 18`

`= $12`

Number and Algebra, NAP-D2-30 SA

The prices at an ice cream shop can be seen below.

Each extra scoop of ice cream costs the same amount of money.

How much will an ice cream with 5 scoops cost?

$  
Show Answers Only

`$8.80`

Show Worked Solution

`text(C)text(ost of 1 extra scoop)`

`= 6.25-5.40`

`= 0.85`
 

`:.\ text(C)text(ost of an icecream with 5 scoops)`

`= $5.40 + 4\ text(extra scoops)`

`= 5.40 + (4 xx 0.85)`

`= 5.40 + 3.40`

`= $8.80`

Measurement, NAP-I2-38

The table shows the dimensions of four different rectangles in centimetres.
 

 
Which rectangle has a perimeter of 28 centimetres?

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

`text(Rectangle 1)`

Show Worked Solution

`text(Consider rectangle 1,)`

`text(Perimeter)` `= 2 xx text(length) + 2 xx text(width)`
  `= (2 xx 9) + (2 xx 5)`
  `=28\ text(cm)`

 

`:.\ text(Rectangle 1 has a perimeter of 28 cm.)`

Number and Algebra, NAP-I2-35 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-C4-CA15

Jack was given a question without a calculator.
 

`22 - 16 xx sqrt (8.5 + 7.5^­) =`
 

Which operation should Jack perform first?

`22 - 16` `16 xx sqrt (8.5^­)` `sqrt (8.5^­)` `8.5 + 7.5`
 
 
 
 
Show Answers Only

`8.5 + 7.5`

Show Worked Solution

`text(The sum of the numbers under the square root)`

`text(symbol need to be calculated first.)`

`:.\ text(The first operation is  8.5 + 7.5.)`

Geometry, NAP-C4-CA14

Jill has a jewellery box in the shape of a hexagonal prism.

Jill takes off the lid and rotates it.
 

 
What is the minimum number of degrees of rotation that are needed for it to fit again?

`30^@` `33^@` `60^@` `120^@`
 
 
 
 
Show Answers Only

`60^@`

Show Worked Solution

`text(The lid needs a rotation of)\ 1/6\ text(of a full circle)`

`text(to fit again.)`

`:.\ text(Minimum degrees)` `=360/6`
  `=60°`

Algebra, NAP-D4-CA22

Renee went bike riding on a holiday.

The hiring charges are  listed in the table below:
 

 

 
Which rule shows the relationship between `C` and `h`?

`C = 12 + 6h` `C = 6 + 12h` `C = 18 + 12h` `C = 12 + 18h`
 
 
 
 
Show Answers Only

`C = 12 + 6h`

Show Worked Solution

`text(Consider Option 1:)`

`12 + (6 xx 1) = 12+6=18`

`12 + (6 xx 2) = 12+12=24`

`12 + (6 xx 3) = 12+18=30`

`text(etc …)`

`:.\ text(The rule is:)\ \ C = 12 + 6h`

Probability, NAP-D4-CA20

Sharney has a bag of 50 coloured marbles.

This table shows how many marbles of each colour are in the bag.
 

   
 
One marble is picked at random from the bag.

What is the probability of the marble being yellow or red?

`0.15` `0.20` `0.25` `0.30`
 
 
 
 
Show Answers Only

`0.30`

Show Worked Solution

`text(Total of yellow and red marbles)`

`5 + 10 = 15`

`:.\ Ptext{(yellow or red)}` `=15/50`
  `=0.30`

Number, NAP-D4-CA18 SA

A coffee jar weighs 2400 grams when it is purchased.
 

 
When exactly half of the coffee has been used, the half full jar has a mass of 1750 grams.

What is the mass of the coffee jar when all the coffee has been used?

   grams
Show Answers Only

`1100\ text(grams)`

Show Worked Solution

`text(Mass of half the coffee)`

`= 2400 – 1750`

`= 650\ text(grams)`
 

`=>\ text(Mass of coffee) = 650 xx 2 = 1300\ text(grams)`
 

`:.\ text(Mass of jar)` `= 2400 – 1300`
  `= 1100\ text(grams)`

Number, NAP-D4-CA17

A health food packet had the following information on its label.
 

 
What was the mass of the health food packet to the nearest gram?

`1328\ text(grams)` `990\ text(grams)` `698\ text(grams)` `578\ text(grams)`
 
 
 
 
Show Answers Only

`578\ text(grams)`

Show Worked Solution

`text(Multiple of 100 grams in one packet:)`

`844 ÷ 146 = 5.78…`

`5.78 xx 100 = 578.08…`

`:.\ text(The mass of the packet is about 578 grams.)`

Statistics, NAP-D4-CA16

Lea collects comic books.

She sells some of them.

The selling prices are listed below.

  `$5, \ $7, \ $7, \ $7, \ $9, \ $12, \ $12, \ $14, \ $35`

What is their mean (average) price?

`$9` `$10` `$11` `$12`
 
 
 
 
Show Answers Only

`$12`

Show Worked Solution

`5 + 7 + 7 + 7 + 9 + 12 + 12 + 14 + 35 = 108`

`:.\ text(Average selling price)` `=108/9`
  `=$12`

Geometry, NAP-D4-CA13

Libby plays on a hockey field that is 120 metres long.

She makes a scale diagram of the field using a ratio of  1 : 400.
 

How long should Libby make the scale diagram of the field?

`text(3 cm)` `text(30 cm)` `text(90 cm)` `text(300 cm)`
 
 
 
 
Show Answers Only

`text(30 cm)`

Show Worked Solution

`text(Ratio is)\ \ 1:400`

`text(S)text(ince 120 m = 12 000 cm,)`

`text(Length of the scale diagram)`

`=12\ 000 ÷ 400`

`= 30\ text(cm)`

Number, NAP-B3-CA22 SA

This calculation gives the average speed (kilometres per hour) of a satellite over a small time interval.

`(86.365 - 5.125)/0.06`

What is the average speed of the satellite?

  kilometres per hour
Show Answers Only

`1354\ text(kph)`

Show Worked Solution
`(86.365 – 5.125)/0.06` `= 81.24/0.06`
  `= 1354\ text(kph)`

Measurement, NAP-B3-CA21 SA

Aslan's computer shows the time of day as 02:33.

A program takes 45 minutes to run.

What time will Aslan's computer show at the end of the program?
Show Answers Only

`3:18`

Show Worked Solution

`33 + 45 = 78\ text(minutes)`

`78\ text(minutes) = 1\ text(hour and 18 minutes)`

`:.\ text(At the end, Aslan’s computer will show 03:18.)`

Number, NAP-B3-CA15

Michelle is tiling a walkway that is 5.6 metres long.

She is using cement tiles that are 0.08 metres wide.

There are no gaps between the tiles.
 

 
How should Michelle calculate how many cement tiles she will need?

 
 `5.6 ÷ 0.08`
 
 `0.08 ÷ 5.6`
 
 `5.6 xx 0.08`
 
 `5.6 - 0.08`
Show Answers Only

`5.6 ÷ 0.08`

Show Worked Solution

`5.6 ÷ 0.08`

Statistics, NAP-D3-CA24 SA

The school canteen collected data on the number of lunches that students ordered from the canteen in one given week.
 

 

 
What was the total number of lunches ordered for the week?
Show Answers Only

`189`

Show Worked Solution

`text(Total number of lunches ordered)`

`= (1 xx 8) + (2 xx 6) + (3 xx 26) + (4 xx 4) + (5 xx 15)`

`= 8 + 12 + 78 + 16 + 75`

`= 189`

Measurement, NAP-D3-CA21

Brendan had to swim 400 metres in less than 8 minutes to earn his Bronze Medallion.

When he finished, he had 130 seconds to spare.

How long did Brendan take to swim the 400 metres?

 
 5 minutes 10 seconds
 
 5 minutes 30 seconds
 
 5 minutes 50 seconds
 
 6 minutes 50 seconds
Show Answers Only

`text(5 minutes 50 seconds)`

Show Worked Solution

`text(S)text(econds in 8 minutes)`

`= 8 xx 60`

`= 480`
 

`:.\ text(Swim time)` `= 480 – 130`
  `= 350`
  `= 5\ text(minutes 50 seconds)`

Geometry, NAP-D4-NC22

Which one of the following triangles is impossible to draw?

 
 a right angled triangle with two acute angles
 
 an isosceles triangle with one right angle
 
 a scalene triangle with three acute angles
 
 a right angled triangle with one obtuse angle
Show Answers Only

`text(a right angled triangle with one obtuse angle.)`

Show Worked Solution

`text(A right angle = 90°.)`

`text(S)text(ince an obtuse angle is greater than 90°, it)`

`text(is impossible for a triangle, with an angle sum)`

`text(less than 180°, to have both.)`

Measurement, NAP-D4-NC20

Digby played cricket on a Saturday.

His game began at 8:15 am and finished at 1:05 pm.

How long did the cricket game go for?

 
 4 hours 50 minutes
 
 5 hours 10 minutes
 
 5 hours 50 minutes
 
 6 hours 50 minutes
Show Answers Only

`text(4 hours 50 minutes)`

Show Worked Solution

`text(One strategy:)`

`text(8:15 am to midday) =>\ text(3 hours and 45 minutes)`

`text(Midday to 1:05 pm)\ =>\ text(1 hour and 5 minutes)`

 

`:.\ text(Time that the game lasted)` `= 3:45 + 1:05`
  `= 4:50`

Number, NAP-D4-NC18

Jamie buys a 200 gram bag of pumpkin seeds at the market for making muesli.

Each pumpkin seed has a mass of 0.19 grams.

Which of these is the best estimate for the number of seeds in the 200 gram bag?

`100` `500` `1000` `5000`
 
 
 
 
Show Answers Only

`1000`

Show Worked Solution

`text(Mass of 10 seeds = 1.90 g)`

`text(Mass of 100 seeds = 19 g)`

`text(Mass of 1000 seeds = 190 g)`

`:. 1000\ text(is the best estimate.)`

Statistics, NAP-D4-NC17

In 4 games of netball, Finn scores 7, 14, 11 and 11 goals.

In the fifth game, she scores a season high 23 goals.

Which of these will not change after Finn's fifth game.

 
 the median of her goal scores
 
 the mean of her goal scores
 
 the range of her goal scores
 
 the total number of her goal scores
Show Answers Only

`text(the median of her goal scores)`

Show Worked Solution

`text(After 4 games,)`

`text(Median)` `= (11 + 11)/2 = 11`

 

`text(After 5 games,)`

`text(Median)` `=\ text(3rd highest score)`
  `=\ 11`

 

`:.\ text(The median will not change.)`

Number, NAP-D4-NC16

A glass of water containing 255 mL of water is poured into a jug that already contains 1.65 L of water in it.

How much water is now in the jug?

`text(256.65 mL)` `text(420 mL)` `text(1.805 L)` `text(1.905 L)`
 
 
 
 
Show Answers Only

`text(1.905 L)`

Show Worked Solution
`1.65\ text(L) + 255\ text(mL)` `=1.65\ text(L) + 0.255\ text(L)`
  `=1.905\ text(L)`

Algebra, NAP-D3-CA20

Matt is 12 years younger than Mark.

Which statement is correct?

 
 `text(Mark's age)\ +\ text(Matt's age) = 12`
 
 `text(Mark's age) = text(Matt's age) + 12`
 
 `text(Matt's age)\ -\ text(Mark's age) = 12`
 
 `text(Matt's age) = text(Mark's age) + 12`
Show Answers Only

`text(Mark’s age) = text(Matt’s age) + 12`

Show Worked Solution

`text(Mark’s age) = text(Matt’s age) + 12`

Statistics, NAP-D3-CA19

Lea collects comic books.

She sells some of them.

The selling prices are listed below.

   `$5, \ $7, \ $7, \ $7, \ $9, \ $12, \ $12, \ $14, \ $35`

What is their mean (average) price?

`$9` `$10` `$11` `$12`
 
 
 
 
Show Answers Only

`$12`

Show Worked Solution

`5 + 7 + 7 + 7 + 9 + 12 + 12 + 14 + 35 = 108`

`:.\ text(Average selling price)` `=108/9`
  `=$12`

Measurement, NAP-C4-NC22

A square field has an area of 8000 m².

The length of one side is between

 
 `40 - 44\ text(m)`
 
 `80 - 84\ text(m)`
 
 `85 - 90\ text(m)`
 
 `400 - 404\ text(m)`
Show Answers Only

`text(85 – 90 m)`

Show Worked Solution

`text(Let)\ \ x =\ text(length of one side)`

`x^2` `=8000`

`text(Strategy for approximation:)`

` 90 xx 90 = 8100`

`:.\ text(85 – 90 m is the best estimate.)`

Algebra, NAP-C4-NC21

In these expressions  `m`  and  `n`  are positive whole numbers and  `l`  is a negative whole number.

Which expression gives the largest positive value?

 
 `(m + n) xx l`
 
 `(m - n) ÷ l`
 
 `(m - n) ÷ −l`
 
 `(m + n) xx −l`
Show Answers Only

`(m + n) xx −l`

Show Worked Solution

`text(Consider each option:)`

`(m + n) xx l\ \ to\ \ text(negative)`

`(m – n) ÷ l\ \ to\ \ text(negative)`

`(m – n) ÷ −l\ \ to\ \ text(postive)`

`(m + n) xx −l\ \ to\ \ text(postive)`

 

`text(S)text(ince)\ \ (m + n) > (m – n), text(and)\ – l\ \ text(is)`

`text(is a positive whole number,)`

`=>\ (m + n) xx −l\ \ \ text(gives the largest positive value.)`

Measurement, NAP-B3-NC22

This table shows the time difference between London, Tokyo and Brisbane on a given day.
 

 
When it is 7:15 am on Wednesday in Brisbane, what time is it in London?

 
 9:15 pm on Wednesday
 
 9:15 pm on Tuesday
 
 5:15 pm on Tuesday
 
 5:15 pm on Wednesday
Show Answers Only

`text(9:15 pm on Tuesday)`

Show Worked Solution

`text(4:30 pm in Brisbane is 6:30 am in London,)`

`=>\ text(Brisbane is 10 hours ahead of London.)`

`:.\ text(7:15 am Wednesday less 10 hours is  9:15 pm)`

`text(on Tuesday.)`

Statistics, NAP-C4-NC20

A vet measured the height of 21 dogs that came through his clinic.

The vet recorded the length of each dog.
  

 
What is the median length?

`52\ text(cm)` `53\ text(cm)` `56\ text(cm)` `57\ text(cm)`
 
 
 
 
Show Answers Only

`text(52 cm)`

Show Worked Solution

`text(The median of 21 data points is the 11th)`

`text(data point.)`

`:.\ text(The median is 52.)`

Algebra, NAP-C4-NC17

Peter thinks of a number, `n`.

He triples the number.

He then halves that answer and subtracts 25.

Which expression shows what Peter did?

`(3n - 25)/2` `(n^3)/2 - 25` `(3n)/2 - 25` `(n^3 - 25)/2`
 
 
 
 
Show Answers Only

`(3n)/2 – 25`

Show Worked Solution

`text(Triples the number:)\ \ n to 3n`

`text(Halves the answer:)\ \ 3n to (3n)/2`

`text(Deducts 25:)\ \ (3n)/2 to (3n)/2 – 25`

Number, NAP-D3-NC22

Jamie buys a 200 gram bag of pumpkin seeds at the market for making muesli.

Each pumpkin seed has a mass of 0.19 grams.

Which of these is the best estimate for the number of seeds in the 200 gram bag?

`100` `500` `1000` `5000`
 
 
 
 
Show Answers Only

`1000`

Show Worked Solution

`text(Mass of 10 seeds = 1.90 g)`

`text(Mass of 100 seeds = 19 g)`

`text(Mass of 1000 seeds = 190 g)`

`:. 1000\ text(is the best estimate.)`

Algebra, NAP-D3-NC20 SA

The prices at an ice cream shop can be seen below.
 

 
Each extra scoop of ice cream costs the same amount of money.

How much will an ice cream with 5 scoops cost?

$  
Show Answers Only

`$8.80`

Show Worked Solution

`text(C)text(ost of 1 extra scoop)`

`= 6.25 – 5.40`

`= 0.85`
 

`:.\ text(C)text(ost of an icecream with 5 scoops)`

`= $5.40 + 4\ text(extra scoops)`

`= 5.40 + (4 xx 0.85)`

`= 5.40 + 3.40`

`= $8.80`

Number, NAP-E3-CA20

The number 27 982 can be rounded in different ways.

Which two ways of rounding give the same answer?

 
 rounding to the nearest ten and nearest hundred
 
 rounding to the nearest ten and nearest thousand
 
 rounding to the nearest hundred and nearest thousand
 
 rounding to the nearest thousand and nearest ten thousand
Show Answers Only

`text(rounding to the nearest hundred and nearest thousand)`

Show Worked Solution

`27\ 982 = 28\ 000\ \ text{(rounding to nearest 100)}`

`27\ 982 = 28\ 000\ \ text{(rounding to nearest 1000)}`

`:.\ text(Rounding to the nearest hundred and nearest)`

`text(thousand give the same answer.)`

Algebra, NAP-F3-CA23

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\ text(tonnes)` `58\ text(tonnes)` `126\ text(tonnes)` `136\ text(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)`