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Number, NAP-E3-NC23 SA

Nel grows 2 types of lettuces, iceberg and butter lettuce.

One week she took 900 lettuces to market.

Two thirds were iceberg and the rest were butter lettuces.

One quarter of the iceberg lettuces didn't sell.

How many iceberg lettuces didn't sell?
Show Answers Only

`150`

Show Worked Solution

`text(Number of iceberg)`

`= 2/3 xx 900`

`= 600`
 

`:.\ text(Number of unsold iceberg)`

`= 1/4 xx 600`

`= 150`

Number, NAP-E3-NC22 SA

Kurt, Shane and Harry collect guitars and own 70 guitars between them.

Kurt owns half as many as Shane.

Harry owns four times as many as Kurt.

How many guitars does Kurt own?
Show Answers Only

`10`

Show Worked Solution

`text(Strategy 1)`

`text(Try some values for Kurt:)`

`text(If Kurt has 5, Harry has 20, Shane has 10.)`

`=>\ text(i.e. a total of 35 guitars)`

`:.\ text(When Kurt has 10 guitars, there are 70 in total.)`
 

`text{Strategy 2 (using algebra)}`

`text(Expressing the information as equations:)`

`K + S + H = 70\ …\ (1)`

`K` `= 1/2 S`
`=> S` `= 2K\ …\ (2)`
`H` `= 4K\ …\ (3)`

 
`text{Substitute (2) and (3) into (1)}`

`K + 2K + 4K` `= 70`
`7K` `= 70`
`K` `= 10`

 
`:.\ text(Kurt owns 10 guitars.)`

Measurement, NAP-E3-NC20

Renee lives in Sydney. Mandeep lives in New Delhi.

When it is 8:05 am in Sydney, it is 2:35 am in New Delhi.

Renee makes a phone call to Mandeep when it is 7:00 am in New Delhi.

What time is it in Sydney?

`text(12:00 pm)` `text(12:30 pm)` `text(1:00 pm)` `text(1:30 pm)`
 
 
 
 
Show Answers Only

`text(12:30 pm)`

Show Worked Solution

`text(8:05 am less 2:35 am is)\ \ 5 1/2\ \ text(hours.)`

`=> text(Sydney is)\ \ 5 1/2\ \ text(hours ahead.)`
  

`:.\ text(When it is 7:00 am in New Delhi,)`

`text(it is 12:30 pm in Sydney.)`

Probability, NAP-E3-NC16

Shane rolls a standard six-sided die.

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(rolling a number) >= 6) = 1/6,`

`text(which is less than 0.5.)`

Number, NAP-C3-CA22

Which of these numbers is a multiple of both 4 and 11?

`411` `444` `4114` `4444`
 
 
 
 
Show Answers Only

`4444` 

Show Worked Solution

`text(Test if each option is divisible by both 4 and 11.)`

`4444/4 = 1111`

`4444/11 = 404`
 

`:. 4444\ text(is divisible by 4 and 11.)`

Geometry, NAP-F3-CA21

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(If Brian enters the park travelling in a north-east)`

`text(direction, he enters through Entry 2 or Entry 3.`

`text(Once he turns in a south-east direction, point B or C)`

`text(are possible although point D is too short a distance.)`

 `:. text(Brian ends up at Point B)`

Algebra, NAP-F3-CA20

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-F3-CA18

Leonardo used this rule to make a number pattern.

Start with 2.

To get the next number add 5 and then double.

The first four numbers in his pattern were  2, 14, 38, 86.

What was the sixth number in his pattern?

`182` `192` `292` `374`
 
 
 
 
Show Answers Only

`374`

Show Worked Solution
`text(5th number)` `= (86 + 5) xx 2`
  `= 182`
`text(6th number)` `= (182 + 5) xx 2`
  `= 374`

Algebra, NAP-F3-CA17

There are 74 year 7 students enrolled at a school.

There are 12 more girls enrolled than boys.

How many boys are enrolled in year 7?

`30` `31` `43` `62`
 
 
 
 
Show Answers Only

`31\ text(boys)`

Show Worked Solution

`text(Let)\ \ n = text(number of boys enrolled)`

`=> n + 12 = text(number of girls enrolled)`

`n + n + 12` `= 74`
`2n` `= 62`
`n` `= 31`

 

`:.\ text(There are 31 boys enrolled.)`

Number, NAP-F3-NC22

A television broadcasting tower is 800 metres high.

A model of the tower is built with a scale of  1 : 4000.

What is the height of the model?

`5\ text(cm)` `20\ text(cm)` `200\ text(cm)` `320\ text(cm)`
 
 
 
 
Show Answers Only

`20\ text(cm)`

Show Worked Solution
`text(Model height)` `= 800/4000`
  `= 0.2\ text(m)`
  `= 20\ text(cm)`

Number, NAP-F3-NC16

A mixture requires an amount of salt to be added.

No more than 0.75 grams of salt is allowed in the mixture.

Which amount below is the heaviest mass of salt that can be added?

`text(0.55 grams)` `text(0.6 grams)` `text(0.8 grams)` `text(1.5 grams)` `text(6 grams)`
 
 
 
 
 
Show Answers Only

`0.6\ text(grams)`

Show Worked Solution

`text(0.8 grams, 1.5 grams and 6 grams are all > 0.75 grams.)`

`text(0.6 grams > 0.55 grams and less than 0.75 grams.)`

`:.\ text(0.6 grams is the heaviest mass.)`

Algebra, NAP-G3-NC26 SA

Gina and Bob are dog breeders.

The total number of dogs they currently own is 21.

Gina owns 5 more dogs than Bob.

How many dogs does Gina own?
Show Answers Only

`13`

Show Worked Solution
`text(Let)\ \ n` `=\ text(number of dogs Bob owns)`
`=> n + 5` `=\ text(number of dogs Gina owns)`

 

`n + n + 5` `= 21`
`2n` `= 16`
`n` `= 8`

 
`:.\ text(Gina owns 13 dogs.)`

Measurement, NAP-G3-CA22

Paul is driving from Wollongong to Taree via Hexham.

His estimated travel times are in the table below.
 

Paul plans to leave Wollongong at 8:30 am and take a 15 minute rest stop in Hexham

Using these driving times and rest time, when should Paul arrive in Taree?

about 12:00 pm about 12:30 pm about 1:00 pm about 1:30 pm
 
 
 
 
Show Answers Only

`text(about 1:30 pm)`

Show Worked Solution

`text(8:30 am plus 3 hours 20 minutes ⇒ 11:50 am)`

`text(11:50 am plus 15 minutes rest ⇒ 12:05 pm)`

`text(12:05 pm plus 1 hour 20 m minutes ⇒ 1:25 pm)` 

`:.\ text(Paul arrives about 1:30 pm)`

Algebra, NAP-G3-CA21

Pasta is sold in bags of 3 sizes: small, medium, and large.

A medium bag of pasta costs $3.25 more than a small bag.

A large bag of pasta costs $4.75 more than a small bag.

Which equation correctly states the cost of a medium bag of pasta?

 
 cost of a medium pasta = cost of a large pasta – $1.50
 
 cost of a medium pasta = cost of a large pasta – $3.25
 
 cost of a medium pasta = cost of a large pasta – $4.75
 
 cost of a medium pasta = cost of a large pasta – $8
Show Answers Only

`text(cost of a medium pasta = cost of a large pasta – $1.50)`

Show Worked Solution

`text(The extra cost of a large pasta over a medium pasta)`

`=$4.75 – $3.25`

`=$1.50`
 

`:.\ text(C)text(ost of a medium pasta = cost of a large pasta – $1.50)`

Number, NAP-H3-NC22

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(Using slightly higher round numbers to get an)`

`text(estimate of the cost:)`

`text(40 minutes × 20 cents = $8)`

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

Algebra, NAP-H3-NC21

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\ text(m)`

Show Worked Solution

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

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

Measurement, NAP-H3-CA30

Squares with sides 3 cm are cut out from the corners of a rectangular piece of cardboard.

The sides are then folded to make a rectangular box with no lid.
 

 
What is the volume of the box?

`text(24 cm³)` `text(48 cm³)` `text(56 cm³)` `text(72 cm³)` `text(240 cm³)`
 
 
 
 
 
Show Answers Only

`72\ text(cm³)`

Show Worked Solution
`text(Volume)` `=\ text(base area × height)`
  `= (4 xx 6) xx 3`
  `= 72\ text(cm³)`

Statistics, NAP-H3-CA25

Spiro records the number of students who can play different instruments in his class.

He records the results in the table below.
 

 
Some students play more than one instrument.

What is the least number of girls that could be in Spiro's class?

`20` `13` `9` `1`
 
 
 
 
Show Answers Only

`9`

Show Worked Solution

`text(S)text(ince students can play more than 1 instrument,)`

`text(Spiro’s class could have only 9 girls since this is)`

`text(the largest number of girls that play any single)`

`text(instrument.)`

Measurement, NAP-H3-CA23

 
Which of these could be used to calculate the area of the shape in square centimetres?

`(10 xx 4) + (6 xx 2)` `(10 xx 6) - (8 xx 4)`
 
 
`(10 xx 8) + (2 xx 4)` `(10 xx 6) - (8 xx 2)`
 
 
Show Answers Only

`(10 xx 6) – (8 xx 2)`

Show Worked Solution
`text(Area)` `=\ text(Area of large rectangle – Area of cut-out rectangle)`
  `=(10 xx 6) – (8 xx 2)`

Geometry, NAP-I3-CA24

The trapezium `ABCD` is moved to the new position shown by trapezium `RSPQ.`
 

 
Which of these transformations resulted in the new position?

 
 Rotate `ABCD\ 180°` clockwise about the origin.
 
 Rotate `ABCD\ 270°` clockwise about the origin.
 
 Reflect `ABCD` across the `x`-axis, then translate `8` units right.
 
 Reflect `ABCD` across the `y`-axis, then translate `6` units down.
Show Answers Only

`text(Rotate)\ ABCD\ 180°\ text(clockwise about the origin.)`

Show Worked Solution

`text(Rotate)\ ABCD\ 180°\ text(clockwise about the origin.)`

Number, NAP-I3-CA23

The table below lists the original price and the amount of discount of a pair of jeans at four different shops.
 

 

 
Which shop has the lowest sale price for the jeans?

`text(A)` `text(B)` `text(C)` `text(D)`
 
 
 
 
Show Answers Only

`text(Shop B)`

Show Worked Solution

`text(Consider the sale price at each shop:)`

`text(A)` `= 20 – (25text{%} xx 20) = $15`
`text(B)` `= 21 – (1/3 xx 21) = $14`
`text(C)` `= 18 – (20 text{%} xx 18) = $14.40`
`text(D)` `= 17 – 2 = $15`

 

`:.\ text(Shop B has the lowest sale price.)`

Measurement, NAP-I3-CA22 SA

A class is making ice-cubes for a science experiment.

One ice-cube container requires 0.35 litres of water to fill it.

How many millilitres of water would a student need to fill up one container?

   millilitres
Show Answers Only

`350`

Show Worked Solution

`text(S)text(ince there are 1000 mL in 1 litre,)`

`text(Volume)` `= 0.35 xx 1000`
  `= 350\ text(millilitres)`

Number, NAP-I3-CA21

A christmas pudding recipe uses 3 cups of sugar for every 4 cups of sultanas.

Select the correct combination of sugar and sultanas for this recipe.

 
 `1/3` cup of sugar, `1/4` cup of sultanas
 
 `1` cup of sugar, `1.5` cups of sultanas
 
 `1.5` cups of sugar, `2` cups of sultanas
 
 `4` cups of sugar, `5` cups of sultanas
Show Answers Only

`text(1.5 cups of sugar, 2 cups of sultanas.)`

Show Worked Solution
`text(Ratio)` `= 3:4`
  `=1.5:2` 

 

`:.\ text(1.5 cups of sugar, 2 cups of sultanas is)`

`text(in the correct ratio.)`

Probability, NAP-I3-CA18

Archer did a survey of his class, asking everyone what their favourite ice cream flavour is.

This table below shows the results.
 

   

 
What is the probability that a randomly selected classmate's favourite flavour is chocolate?

Round your answer to the nearest hundredth.

`0.15` `0.39` `0.48` `0.61`
 
 
 
 
Show Answers Only

`0.39`

Show Worked Solution

`Ptext{(Classmate selected likes chocolate)}`

  `= text(number who chose chocolate) / text(total number of classmates)`
  `=15/(15+16+7)`
  `=15/38`
  `=0.39\ \ text{(nearest hundredth)}`

Probability, NAP-H3-CA17

Claire baked 18 cookies.

She baked equal numbers of chocolate chip, macadamia nut and plain cookies.

Claire randomly picked one of the cookies.

What are the chances it was chocolate chip or plain?

`2/18` `1/18` `10/18` `2/3` `1/3`
 
 
 
 
 
Show Answers Only

`2/3`

Show Worked Solution

`P(text(choosing chocolate chip or plain))`

`= text(number of chocolate chip and plain)/text(total number of cookies)`

`= 12/18`

`= 2/3`

Probability, NAP-I3-NC24 SA

Ricky rolled a standard dice 80 times.

He recorded if an odd or even number was rolled, each time, and wrote the results in the table below.
 

   

What is the difference between the expected number of odd rolls and the actual number recorded?
Show Answers Only

`3`

Show Worked Solution

`text(50% = the probability of an odd roll.)`

`text(Expected odd rolls)`

`= 50text(%) xx 80`

`= 40`
 

`:.\ text(Difference)` `= 40 – 37`
  `= 3`

Geometry, NAP-I3-NC22

Which statement about the triangle pictured above is correct?

 
 it is a right-angled triangle.
 
 it is a scalene triangle.
 
 it s an equilateral triangle.
 
 it is an obtuse triangle.
Show Answers Only

`text(it is an equilateral triangle.)`

Show Worked Solution

`text(The third angle of the triangle)\ = 180-(60+60) = 60°`

`:.\ text(It is an equilateral triangle.)`

Measurement, NAP-C3-NC26 SA

Abdul's wages are paid on the first Wednesday of each month.

His wages were paid on 5 July.

What is the date that he can expect his wages to be paid in August?

  August
Show Answers Only

`text(2 August)`

Show Worked Solution

`text(S)text(ince 5 July was a Wednesday, so is 12, 19, and 26.)`

`text(July has 31 days, therefore 31 July is a Monday.)`

`=>\ text(2 August is a Wednesday.)`

Number, NAP-C3-NC24

Gary is a painter and buys 25 tins of paint.

Each tin costs $36.

The total cost of the paint is  $36 × 25.

Which calculation is another way of working out the total cost?

`9 xx 100` `26 xx 250` `(72 ÷ 2) xx 50` `6 + (30 xx 25)`
 
 
 
 
Show Answers Only

`9 xx 100`

Show Worked Solution
`36 xx 25` `=9 xx 4 xx 25`
  `=9 xx 100`

Geometry, NAP-E4-CA21

A triangle has two acute angles.

What type of angle couldn't the third angle be?

 
 an acute angle
 
 an obtuse angle
 
 a right-angle
 
 a reflex angle
Show Answers Only

`text(reflex angle)`

Show Worked Solution

`text(A triangle’s angles add up to 180°, and a)`

`text(reflex angle is greater than 180°.)`

`:.\ text(The third angle cannot be reflex.)`

Algebra, NAP-E4-CA19

Choon designs a line of tiles that repeats 5 different tiles in the same order, as shown below.

Each tile costs $11.50 and Choon uses $322 worth of tiles.

Which of these is the last tile in his line of tiles?

 
 
 
 
 
Show Answers Only

Show Worked Solution

`text(Total number of tiles used)`

`=322/11.50`

`=28`

 

`:.\ text(5 rows of 5 are used and the last tile is the 3rd)`

`text(in the pattern.)`