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Measurement, NAP-F3-NC13v1

Sam went to sleep at 9:45 pm.

She woke up at 6:20 am.

How long did Sam sleep for?

 
 3 hours 25 minutes
 
 6 hours 35 minutes
 
 7 hours 25 minutes
 
 8 hours 35 minutes
Show Answers Only

`text(8 hours 35 minutes)`

Show Worked Solution

`text(One possible strategy:)`

`text(9:45 pm plus 2:15 gets to 12:00 midnight.)`

`text(12:00 midnight plus 6:20 gets to 6:20 am.)`
 

`:.\ text(2 hours 15 minutes plus 6 hours 20 minutes)`

`=\ text(8 hours 35 minutes)`

Measurement, NAP-E3-CA15v1

Spiro's kebab shop is open 10 am to 10 pm from Monday to Friday and 10 am to midnight on Saturday.

Spiro is closed on Sunday.

What is the total number of hours Spiro's shop is open in 1 week?

`48` `50` `62` `74`
 
 
 
 
Show Answers Only

`68\ text(hours)`

Show Worked Solution
`text(Total hours)` `=\ text(weekday hours + weekend hours)`
  `= (5 xx 12) + 14`
  `= 68\ text(hours)`

Measurement, NAP-H3-CA18v1

A rectangle has a length of 16 cm and a width of 7 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?

`5.75` `9` `11.5` `46`
 
 
 
 
Show Answers Only

`11.5`

Show Worked Solution
`text(Perimeter of rectangle)` `= (2 xx 16) + (2 xx 7)`
  `=46\ text(cm)`

 

`:.\ text(Side length of square)` `=46/4`
  `=11.5\ text(cm)`

Measurement, NAP-D3-CA11v1

Strop drew a triangle.

The perimeter of Strop's triangle was 20 cm.

Which of these could be the side lengths of his triangle?

 
 `text(3 cm, 3 cm, 14 cm)`
 
 `text(4 cm, 5 cm, 11 cm)`
 
 `text(5 cm, 6 cm, 9 cm)`
 
 `text(5 cm, 5 cm, 10 cm)`
Show Answers Only

`text(5 cm, 6 cm, 11 cm)`

Show Worked Solution

`text(The sum of any two sides of a triangle must be)`

`text(longer than the third side.)`

`:.\ text(Only possible side lengths are: 5 cm, 6 cm, 9 cm)`

Number, NAP-C3-NC11v1

Archie is 3.5 years old.

His sister Ruby is exactly 15 months old.

How many months older than Ruby is Archie?

`20` `25` `27` `31`
 
 
 
 
Show Answers Only

`27`

Show Worked Solution
`text(Archie’s age)` `=3.5 xx 12`
  `=42\ text(months)`

 
`:.\ text(Months that Archie is older than Ruby)`

`=42-15`

`=27\ text(months)`

Number, NAP-J3-CA18v1

One year, a horse breeder has chestnut, black and grey foals.

There are:

    • 5 more grey foals than black foals
    • 3 fewer black foals than chestnut foals
    • 12 chestnut foals

How many foals, in total, did the breeder have?

`20` `24` `27` `30` `35`
 
 
 
 
 
Show Answers Only

`35`

Show Worked Solution

`text{12 chestnut foals (given)}`

`=> 12 – 3 = 9\ text(black foals)`

`=> 9 + 5 = 14\ text(grey foals)`

`:.\ text(Total foals)` `= 12 + 9 + 14`
  `= 35`

Number, NAP-I3-CA17v1

A brewery can make 1250 cans of ale and 900 cans of lager per hour.

The brewery runs non-stop and each can weighs 350 grams.

How many kilograms of ale and lager, altogether, does the brewery make in 1 full day?

 
 `226\ text(kilograms)`
 
 `753\ text(kilograms)`
 
 `18\060\ text(kilograms)`
 
 `21\ 240\ text(kilograms)`
Show Answers Only

`18\060\ text(kilograms per day)`

Show Worked Solution

`text(Total cans made per hour)`

`=1250 + 900`

`= 2150`
 

`text(Kilograms made in 1 hour)` 

`=2150 xx 350`

`= 752\ 500\ text(grams)`

`= 752.5\ text(kilograms)`

`:.\ text(Kilograms made in 1 day)` `=752.5 xx 24`
  `=18\ 060`

Algebra, NAP-G3-CA15v1

Dickson takes part in a bike ride to raise money for charity.

His aunty sponsors him $40 in total.

His brother sponsors him $1.25 for each kilometre he rides.

In order to raise $100, how many kilometres does Dickson need to ride?

`8`  `32` `50` `48` `60`
 
 
 
 
 
Show Answers Only

`48\ text(kilometres)`

Show Worked Solution

`text(Let)\ \ x = text(number of kilometres)`

`100` `= 1.25x + 40`
`1.25x` `= 60`
`:. x` `= 60/1.25`
  `= 48\ text(kilometres)`

Number, NAP-G4-CA06v1

Which number shows 7 thousands, 4 hundreds and 3 tenths?

`7402.03` `7649.3` `7420.3` `7431.2`
 
 
 
 
Show Answers Only

`7420.3`

Show Worked Solution

`text(Order: thousands, hundreds, tens, ones, tenths.)`

`5090.3`

Number, NAP-H4-NC14v1

Dilbert and Smacka were playing a game where they both started with zero points.

Dilbert's final score was 165 points and Smacka's final score was  − 90.

How many more points did Dilbert have than Smacka?

`−255` `−75` `75` `255`
 
 
 
 
Show Answers Only

`255`

Show Worked Solution
`text(Difference)` `= 165 – (−90)`
  `= 255`

Measurement, NAP-B1-33v1

Wim held his breath for 135 seconds.

The time he held his breath can also be written as

`1 1/2\ text(minutes)` `2 1/4\ text(minutes)` `2 1/2\ text(minutes)` `2 3/4\ text(minutes)`
 
 
 
 
Show Answers Only

`2 1/4\ text(minutes)`

Show Worked Solution

`text(There are 60 seconds in 1 minute.)`

`=> 135\ text(seconds = 2 mins 15 seconds)`

`=>\ text(Wim held his breath for)\ 2 1/4\ text(minutes.)`

Measurement, NAP-C2-26v1

Archie is 5 years old.

His sister Ruby is exactly 18 months old.

How many months older than Ruby is Archie?

`32` `36` `42` `56`
 
 
 
 
Show Answers Only

`42\ text(months)`

Show Worked Solution

`text(Age of Archie in months)`

`= 5 xx 12`

`= 60\ text(months)`
 

`:. 60 – 18 = 42\ text(months)`

Number, NAPX-p169640v02

Ana wants to make some dumplings.

A batch of dumplings requires 4 eggs and 200 grams of flour.

If Ana uses 64 eggs to make a larger batch of dumplings, how much flour will she need?

 
   3.2 kg
 
   4.0 kg
 
   6.2 kg
 
   8.0 kg
Show Answers Only

`3.2 \ text{kg}`

Show Worked Solution

`text(Flour : Eggs)\ = 200:4 = 50:1`

`text{Let} \ \ x =\ text{amount of flour needed}`

`frac{x}{64}` `= frac{50}{1}`
`x` `= 50 xx 64`
  `=3200\ text(g)`
  `=3.2\ text(kg)`

Number, NAPX-p169640v01

A chemist makes 70 millilitres of a compound by mixing 20 millilitres of Chemical A and 50 millilitres of Chemical B.

If 250 millilitres of Chemical B is used to make a larger batch of the compound, how much Chemical A is needed?

 
   200 mL
 
   180 mL
 
   120 mL
 
   100 mL
Show Answers Only

`100 \ text{mL}`

Show Worked Solution

`text(Chemical A : Chemical B)\ = 20:50 = 2:5`

`text{Let} \ \ x =\ text{amount of Chemical A needed}`

`frac{x}{250}` `= frac{2}{5}`
`x` `= frac{2 xx 250}{5}`
  `=100\ text(mL)`

Algebra, NAPX-p169742v01

Three corners of a rectangle are shown below.
 


 

Which point represents the fourth corner of the rectangle?

 
 (3, –1)
 
 (3, –2)
 
 (–2, 3)
 
 (-1, 3)

Show Answers Only

`(3, -2)`

Show Worked Solution

`text(Consider the top left point on the graph (-1, 1),)`

`text(The point below is 3 grid lines down.)`

`text{Consider the top right point on the graph (3, 1),}`

`text{The point (3, -2) is 3 grid lines down.}`

Number, NAPX-p169733v02

Hilary wants to buy second hand furniture for her new flat.

She went to a charity store that sold furniture with the pricing listed in the table below.
 

   

She decided to buy one of each furniture item listed.

Which of these gives the correct range of the total cost of the furniture that she bought?

 
 $475 – $500
 
 $500 – $525
 
 $525 – $550
 
 $550 – $575

Show Answers Only

`$550 – $575`

Show Worked Solution

`text(Estimate the price of each furniture:)`

`$69.20 ≈ $70`

`$298.75 ≈ $300`

`$79.50 ≈ $80`

`$112.30 ≈ $110`
 

`text(Total cost of furniture)` `= 70 + 300 + 80 + 110`
  `= $560`

 
`:.\ text(The range of the total cost is around $550 – $575.)`

Number, NAPX-p169733v01

Nicolas wants to build his own desktop gaming setup.

The shop’s prices for different gaming components are as follows:
 

   

Nicolas bought all 4 components from the shop.

Which of these gives the correct range of the total cost of his purchase?

 
 $450 – $475
 
 $475 – $500
 
 $500 – $525
 
 $525 – $550

Show Answers Only

`$475 – $500`

Show Worked Solution

`text(Estimate the prices of the components)`

`$54.30 ≈ $ 55`

`$23.50 ≈ $25`

`$248.60 ≈ $250`

`$158.25 ≈ $160`
 

`text(Total estimated price)` `= 55 + 25 + 250 + 160`
  `= $490`

 
`:.\ text(The range of the total cost is around $475 – $500)`

Number, NAPX-p169590v02

Some beverages are for sale in a convenience store.

The table below shows the different prices of beverages being sold.
 


 

Which of the following beverages is the most expensive per litre?

 
 Water
 
 Soft drinks
 
 Milkshake
 
 Tea

Show Answers Only

`text(Milkshake)`

Show Worked Solution

`text(Conversion: 1000 millilitres = 1 litre)`

`text(Check each option:)`

`text(Water: $1 per 1 litre)`

`text(Soft drinks: $0.65 per 500 millilitres = 2 x 0.65 = $1.30 per litre)`

`text(Milkshake: $0.45 per 250 millilitres = 4 x 0.45 = $1.80 per litre)`

`text(Tea: $0.30 per 200 millilitres = 5 x 0.30 = $1.50 per litre)`

`:.\ text(Milkshake is the most expensive per litre.)`

Measurement, NAPX-p169727v02

Brock decided to cut out a small rectangle from a piece of rectangular paper.
 


 

The rectangle cut out has a length of 60 mm and a height of 40 mm.

Which of the following expressions gives the area of Brock’s paper that was left after cutting out the smaller rectangle?

 
 `(120 xx 200) - (60 xx 160)`
 
 `60 xx 160`
 
 `(120 xx 200) + (40 xx 60)`
 
 `(120 xx 200) - (60 xx 40)`

Show Answers Only

`(120 xx 200) – (60 xx 40)`

Show Worked Solution
`text(Area)` `= text(Area of large rectangle) – text(Area of small rectangle)`
  `= (120 xx 200) – (60 xx 40)`

Measurement, NAPX-p169727v01

Trisha cuts out a triangular shape from a rectangular piece of cardboard.
 


 

The triangle has a height of 2 cm and base of 8 cm.

Which of the following expression gives the area of Trisha’s cardboard after cutting out the triangle?

 
 `(32 xx 60) - (8 xx 2)`
 
 `(52 xx 30)`
 
 `(32 xx 60) - (1/2 xx 8 xx 2)`
 
 `(60 xx 32) - (1/2 + 8 + 2)`

Show Answers Only

`(32 xx 60) – (1/2 xx 8 xx 2)`

Show Worked Solution
`text(Area)` `= text(Area of rectangle) – text(Area of triangle)`
  `= (32 xx 60) – (1/2 xx 8 xx 2)`

Number, NAPX-p169590v01

The table below shows the prices of different kinds of fruit sold at a supermarket.

   

Which type of fruit is the most expensive per kilogram?

 
 Banana
 
 Apple
 
 Orange
 
 Melon

Show Answers Only

`text(Orange)`

Show Worked Solution

`text(Conversion: 1000 grams = 1 kilogram)`

`text(Check each option:)`

`text(Banana: $2.50 for 500 g = 2 x 2.50 = $5 per kilogram)`

`text(Apple: $1.3 for 250 g = 4 x 1.30 = $5.20 per kilogram)`

`text(Orange: $1.15 for 200 g = 5 x 1.15 = $5.75 per kilogram)`

`text(Melon: $5.25 for 1 kilogram = $5.25 per kilogram)`

`:\.text(Oranges are the most expensive per kilogram.)`

Measurement, NAPX-p169635v01

Two circles have radii of different lengths.
 

   
 

The larger circle’s radius is 3.5 times the radius of the smaller circle.

Which of the following is the circumference of the larger circle?

 
   `56pi\ text(cm)`
 
   `42pi\ text(cm)`
 
   `40pi\ text(cm)`
 
   `36pi\ text(cm)`
Show Answers Only

`42 pi \ text{cm}`

Show Worked Solution
`text{Large radius}` `= 6 xx 3.5`
  `= 21 \ text{cm}`

 

`text{C}_text(large)` `= 2 xx R xx pi`
  `= 2 xx 21 xx pi`
  `= 42 pi \ text{cm}`

Measurement, NAPX-p169631v01

Derrick has a backyard in the shape of a rectangle.
 

   
 

The longer side is  `1 1/3`  times longer than the shorter side.

What is the perimeter of Derick’s backyard?

 
    82 m
 
    98 m
 
   115.5 m
 
   133.5 m
Show Answers Only

`98 \ text{m}`

Show Worked Solution
`text{Longer side}` `= 21 xx 1 1/3`
  `= 28 \ text{m}`

 

`:.\ text{Perimeter}` `= (2 xx 21) + (2 xx 28)`
  `= 42 + 56`
  `= 98 \ text{m}`

Number, NAPX-p169627v02

A box of fruit contains 12 apples, 16 oranges, and 13 pears.

About what percentage of the fruit in the box are apples?

 
   29%
 
   32%
 
   37%
 
   41%
Show Answers Only

`29text(%)`

Show Worked Solution
`text(Percentage of apples)` `= text(number of apples)/text(total pieces of fruit)`  
  `=12/(12+16+13)`  
  `=0.292`  
  `=29text(%)`  

Number, NAPX-p169627v01

In a classroom there are 24 boys and 36 girls.

About what percentage of the students in the classroom are girls?

 
   48%
 
   57%
 
   60%
 
   64%
Show Answers Only

`60text(%)`

Show Worked Solution
`text(Percentage of girls)` `= text(number of girls)/text(total students)`  
  `=36/(24+36)`  
  `=0.6`  
  `=60text(%)`  

Measurement, NAPX-p169480v02

A father and his son attended a video game convention, arriving at 9:15 am.

They left the convention at 2:05 pm.

How long did they spend at the convention?

 
 2 hours and 50 minutes
 
 3 hours and 10 minutes
 
 4 hour and 10 minutes
 
 4 hours and 50 minutes

Show Answers Only

`text(4 hours and 50 minutes)`

Show Worked Solution

`text(9:15 am to 10:00 am → 45 minutes)`

`text(10:00 am to 2:00 pm → 4 hours)`

`text(2:00 pm to 2:05 pm → 5 minutes)`

`:.\ text(Time at convention = 4 hours and 50 minutes.)`

Measurement, NAPX-p169480v01

Ashley attended a seminar about marketing which started at 8:30 am.

The seminar ended at 12:10 pm.

How long was the seminar held?

 
 2 hours and 10 minutes
 
 3 hours and 10 minutes
 
 3 hours and 40 minutes
 
 4 hours and 40 minutes

Show Answers Only

`text(3 hours and 40 minutes)`

Show Worked Solution

`text(8:30 am to 9:00 am → 30 minutes)`

`text(9:00 am to 12:00 am → 3 hours)`

`text(12:00 pm to 12:10 pm → 10 minutes)`

`:.\ text(Duration of seminar = 3 hours and 40 minutes.)`

Statistics, NAPX-p169099v01

Charlie wants to determine the number of students enrolled in both Mathematics and Physics.

Which shaded region of the following Venn diagrams shows the information that is needed by Charlie?

 
  
 
  
 
  
 
  
Show Answers Only

Show Worked Solution

`text{This diagram shows the intersection of students enrolled in both Math and Physics.}`

Probability, NAPX-p168831v02

In a deck of 52 playing cards, Ian draws one without looking.

Which card is most likely to be drawn?

 
   A king
 
   A number four or five
 
   A black suit
 
   A diamond suit
Show Answers Only

`text{A black suit card}`

Show Worked Solution

`text{Check each option:}`

`Ptext{(King)} = frac{4}{52} = 1/13`

`Ptext{(Number 4 or 5)} = frac{8}{52} = 2/13`

`Ptext{(Black suit)} = frac{26}{52} = 1/2`

`Ptext{(Diamond)} = frac{13}{52} = 1/4`
 

`:. therefore \ text{A black suit card is most likely.}`

Probability, NAPX-p168831v01

Two fair dice were rolled and the numbers on each die were added up.
 


 

Which resulting sum is most likely to occur?

 
     2
 
     9
 
   11
 
   12
Show Answers Only

`9`

Show Worked Solution

`text{Check each option:}`

`text{Sum of 2 – (1, 1)}`

`text{Sum of 9 – (3, 6), (6, 3), (4, 5), (5, 4)}`

`text{Sum of 11 – (5, 6), (6, 5)}`

`text{Sum of 12 – (6, 6)}`

`:. \ text{Sum of 9 is most likely.}`

Algebra, NAPX-p109338v02

The table shown below represents a rule of changing each into a .
 


 

Which rule is used?

 
   `=`        `xx 4 - 1`
 
   `=`        `xx 2 -2`
 
   `=`        `xx 3 -2`
 
   `=`        `xx 5 - 6`
Show Answers Only
` = \ \ ` ` xx 4 – 1 `
Show Worked Solution

`text{Consider option 1:}`

`5 xx 4 – 1 = 19\ text{(Correct)}`

`7 xx 4 – 1 = 27\ text{(Correct)}`

`9 xx 4 – 1 = 3 \ text{(Correct)}`

` = \ \ ` ` xx 4 – 1 `

Algebra, NAPX-p109338v01

The table below shows the results of a rule that changes each     into a  .

 


 

Which rule is used?

 
   `=`        `xx 4 - 4`
 
   `=`        `xx 2 -2`
 
   `=`        `xx 3 - 2`
 
   `=`        `xx 5 - 6`
Show Answers Only
` = \ \ ` ` xx 3 – 2 `
Show Worked Solution

`text{Check each option:}`

`2 xx 4 – 4 = 4 \ text{(Correct)}`

`4 xx 4 – 4 = 12 \ text{(Incorrect)}`
  

`2 xx 2 + 2 = 6 \ text{(Incorrect)}`
  

`2 xx 3 – 2 = 4\ text{(Correct)}`

`4 xx 3 – 2 = 10\ text{(Correct)}`

`6 xx 3 – 2 = 16 \ text{(Correct)}`
 

`2 xx 5 – 6 =  4\ text{(Correct)}`

`4 xx 10 – 6 = 34 \ text{(Incorrect)}`

 

` = \ \ ` ` xx 3 – 2 `

Geometry, NAPX-p168507v02

Anthony is driving south-east along Sterling road and turns left 90° turn into Faraday road.
 


 

In which direction is Anthony driving along Faraday road?

 
  North-east
 
  South-east
 
  South-west
 
  North-west
Show Answers Only

`text{North-east}`

Show Worked Solution

`therefore \ text{Anthony was heading in the North-east direction}`

Geometry, NAPX-p168507v01

Cesar was driving north-east along Leo street.

In which direction is Cesar travelling if he turns right 90° into Grove street?

 
   North-west
 
   South-east
 
   South-west
 
   North-east
Show Answers Only

`text{South-east}`

Show Worked Solution

`therefore \ text{Cesar was heading in the South-East direction.}`

Algebra, NAPX-p168506v01

The regular hexagon below has a side length of `a`.
 


 

Which expression cannot be used to calculate the perimeter?

 
   `6 xx a`
 
   `3 xx (a+ a)`
 
   `2 xx (a + 4a)`
 
   `(a + a + a) xx 2`
Show Answers Only

`2 xx (a + 3a)`

Show Worked Solution

`text{Perimeter of the regular hexagon} = 6a`

`text{Check each option:}`

`6 xx a = 6a \ \ text{(Correct)}`

`3 xx (a + a) = 3 xx 2a = 6a \ \ text{(Correct)}`

`2 xx (a + 4a) = 2 xx 5a = 10a \ \ text{(Incorrect)}`

`(a + a + a) xx 2 = 3a xx 2 = 6a \ \ text{(Correct)}`

Probability, NAPX-p167455v02

A partial deck of cards consists of 8 diamonds, 9 clubs, 4 spades and 3 hearts.

Patrick draws a card from the deck without looking.

What is the probability that he draws a spade?

 
 `1/4`
 
 `4/21`
 
 `1/3`
 
 `1/6`

Show Answers Only

`1/6`

Show Worked Solution
`P(text(Spade))` `= text(Total Number of spades)/text(Total cards)`
  `= 4/(8 + 9 + 4 + 3)`
  `= 4/24`
  `= 1/6`

Probability, NAPX-p167455v01

A bag of coloured balls contains 12 blue balls, 10 white balls, 6 black balls, 2 red balls, and 8 orange balls.

Kimberly grabs a ball from the bag without looking what is inside.

What is the probability that she grabs an orange ball?

 
 `3/5`
 
 `5/17`
 
 `8/21`
 
 `4/19`

Show Answers Only

`4/19`

Show Worked Solution
`P(text(Orange ball))` `= text(Total orange balls)/text(Total balls)`
  `= 8/(12 + 10 + 6 + 2 + 8)`
  `= 8/38`
  `= 4/19`

Algebra, NPAX-p167453v02

Andrew produced a pattern of small stars and diamonds.
 

If this pattern continues how many diamonds will the 9th figure contain?

 
 21
 
 19
 
 17
 
 15

Show Answers Only

`17`

Show Worked Solution

`text(Each succeeding figure adds 2 diamonds)`

`text(Number of diamonds)`

`text(Figure 4 = 7 diamonds)`

`text(Figure 5 = 9 diamonds)`

`vdots`

`text(Figure 8 = 15 diamonds)`

`:.\ text(Figure 9 contains 17 diamonds.)`

Algebra, NAPX-p167453v01

Rica produced a pattern of small circles and trapeziums.

If this pattern continues how many small circles will be in the 10th figure?

 
 10
 
 11
 
 19
 
 21

Show Answers Only

`19`

Show Worked Solution

`text{Each succeeding figure adds 2 circles}.`

`text{Number of small circles}`

`text{Figure 4: 7 circles}.`

`text{Figure 5: 9 circles}.`

`vdots`

`:.\ text(Figure 10 contains 19 circles.)`

Measurement, NAPX-p167451v01

Dexter owns a backyard in the shape of a trapezoid.

What is the perimeter of the backyard owned by Dexter?

 

 
 537 metres
 
 613 metres
 
 469 metres
 
 488 metres

Show Answers Only

`537\ text(metres)`

Show Worked Solution
`text(Perimeter)` `= (2 xx 68) + 212 + 189`
  `= 136 + 212 + 189`
  `= 537\ text(metres)`

Algebra, NAPX-p167449v02

Jason creates the following figures using toothpicks.
 


 

How many toothpicks will figure 9 have?

 
 36
 
 38
 
 41
 
 46

Show Answers Only

`46`

Show Worked Solution

`text(Each succeeding figure adds 5 extra toothpicks.)`

`text(Figure 4: 21 toothpicks)`

`text(Figure 5: 26 toothpicks)`

`text(Figure 6: 31 toothpicks)`

`text(Figure 7: 36 toothpicks)`

`text(Figure 8: 41 toothpicks)`

`:.\ text(Figure 9 will have 46 toothpicks)`

Algebra NC13v1, NAP-Z3-13

Marley creates the following figures using sticks.

How many sticks will Figure 7 has?

 
    20
 
    15
 
    12
 
    18

Show Answers Only

`15`

Show Worked Solution

`text(Each succeeding figure adds 2 extra sticks.)`

`text(Figure 4: 9 sticks)`

`text(Figure 5: 11 sticks)`

`text(Figure 6: 13 sticks)`

`:.\ text(Figure 7 will have 15 sticks)`

Measurement, NAPX-p167302v02

The image below is a plan of a commercial garden.
 


 

The total planted area is 48 square metres.

What is the total unplanted area?

 
 60 m²
 
 64 m²
 
 78 m²
 
 81 m²

Show Answers Only

`text(64 m)^2`

Show Worked Solution

`text(6 planted areas = 48 m)^2`

`text(1 hexagon grid) = 48 ÷ 6 = 8\ text(m)^2`

`text(Number of unplanted areas: 8)`

`:.\ text(Total unplanted area)` `=8 xx 8`  
  `=64\ text(m²)`  

Measurement, NAPX-p167302v01

The image below shows a layout of a village.
 

The total area of the occupied lots is 60 m².

What is the total area of the unoccupied lots in the village?

 
 36 m²
 
 42 m²
 
 50 m²
 
 54 m²

Show Answers Only

`50\ text(m)^2`

Show Worked Solution

`text(12 occupied lots = 60 m)^2`

`text(1 lot = 60 ÷ 12 = 5 m)^2`

`text(Number of unoccupied lots = 10)`

`:.\ text(Area of unoccupied lots)` `=10 xx 5`  
  `=50\ text(m²)`  

Probability, NAPX-p167455v04

A bookmaker's bag is filled with different types of notes.

The bag contains 16 ten-dollar notes, 11 twenty-dollar notes, 8 fifty-dollar notes and 3 hundred-dollar notes.

The bookmaker reaches in to the bag and randomly selects one note.

What is the chance that a fifty-dollar note is selected?

 
 `4/19`
 
 `8/29`
 
 `6/17`
 
 `4/17`

Show Answers Only

`4/19`

Show Worked Solution
`P(text($50 bill))` `= text(Number of $50 bills)/text(Total number of bills)`
  `= 8/(16 + 11 + 8 + 3)`
  `= 8/38`
  `= 4/19`

Probability, NAPX-p167455v03

A bag contains different coloured balls.

It contains 4 red balls, 8 green balls, 3 pink balls, 6 grey balls and 11 yellow balls.

Nathalie picks a ball from the bag without looking.

What is the chance that she draws a grey ball?

 
 `1/5`
 
 `3/16`
 
 `6/31`
 
 `4/13`

Show Answers Only

`3/16`

Show Worked Solution
`P(text(Grey ball))` `= text(Number of grey balls)/text(Total number of balls)`
  `= 6/(4 + 8 + 3 + 6 + 11)`
  `= 6/32`
  `=3/16`