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Measurement, NAPX-p116893v02

Jane painted some hexagons in the four figures pictured below.

All hexagons are the same size.

Which of these figures has the largest area that is painted green.

 
 
 
 
Show Answers Only

Show Worked Solution

`text{Largest area painted = figure with the most hexagons painted green.}`

`text{Check each option:}`

`text{1st Figure – 11 hexagons}`

`text{2nd Figure – 9 hexagons}`

`text{3rd Figure – 13 hexagons}`

`text{4th Figure – 9 hexagons}`

`therefore \ text{3rd Figure has the largest area painted green.}`

Filed Under: Perimeter, Area and Volume, TESTLET B Tagged With: Band 5, NAPX-MultipleChoice

Number, NAPX-p116838v04

In a bakery Michelle bought one slice of cake, one donut and a croissant.
 


 

She gave the cashier $10.00.

How much change should Michelle receive?

$5.10 $5.60 $5.80 $6.00
 
 
 
 
Show Answers Only

`$6.00`

Show Worked Solution
`text{Total cost}` `= 1.35 + 1.20 + 1.45 `
  `= $4.00`

 

`text{Change}` `= 10 – 4`
  `= $6.00`

Filed Under: Fractions and Decimals Tagged With: Band 5, NAPX-MultipleChoice

Number, NAPX-p116838v03

Alexander went shopping and bought the following items.
 


 

He gave the cashier $50.

How much change should Alexander receive?

$17.00 $18.20 $31.80 $33.00
 
 
 
 
Show Answers Only

`$17.00`

Show Worked Solution
`text{Total cost}` `= 9.50 + 12.10 + 11.40 `
  `= $33.00`

 

`text{Change}` `= 50 – 33.00 `
  `= $17.00`

Filed Under: Fractions and Decimals Tagged With: Band 5, NAPX-MultipleChoice

Measurement, NAPX p124557v03

Timothy started with 53 millilitres of oil in a beaker.

He saw that there was some unused oil in a test tube and returned it to the beaker.


 

How much of the chemical solution was poured int0 the test tube?

 
 13 millilitres
 
 23 millilitres
 
 27 millilitres
 
 37 millilitres
Show Answers Only

`27 \ text{millilitres}`

Show Worked Solution
`text{Oil in the test tube }` `= text{New volume} – text{Original volume}`
  `= 80 – 53`
  `= 27 \ text{millilitres}`

Filed Under: Units of Measurement Tagged With: Band 5, NAPX-MultipleChoice

Measurement, NAPX p124557v02

A chemist started with 685 millilitres of a solution.

He then poured some of the solution into a test tube.
 


 

How much of the chemical solution was poured into the test tube?

 
 90 millilitres
 
 135 millilitres
 
 145 millilitres
 
 185 millilitres
Show Answers Only

`185 \ text{millilitres}`

Show Worked Solution
`text{Solution in test tube }` `= text{New volume} – text{Original volume}`
  `= 685 – 500`
  `= 185 \ text{millilitres}`

Filed Under: Units of Measurement Tagged With: Band 5, NAPX-MultipleChoice

Statistics, NAPX-p116802v04

In a neighborhood 10 villagers were asked if how many pets they own.

The results were: 3, 2, 1, 1, 1, 4, 2, 4, 5, 2

Select the dot plot that displays the data recorded

 
 
 
 
Show Answers Only

Show Worked Solution

`text{A dot represents the number of persons that owns N pets}`

`text{From the data above:}`

`text{Owns one pet = 3}`

`text{Owns two pets = 3}`

`text{Owns three pets = 1}`

`text{Owns four pets = 2}`

`text{Owns five pets = 1}`

`therefore \ text{the correct dot plot is:}`
 

Filed Under: Data and Interpretation Tagged With: Band 5, NAPX-MultipleChoice

Statistics, NAPX-p116802v03

10 people were asked how often they went to the doctor in the last 12 months.

Their responses were: 2, 3, 3, 4, 1, 2, 5, 1, 1, 2

Choose the dot plot which correctly displays the data.

 
   
 
   
       
 
   
 
   
Show Answers Only

Show Worked Solution

`text{From the data above:}`

`text{1 visit =  3 people}`

`text{2 visits =  3 people}`

`text{3 visits =  2 people}`

`text{4 visits =  1 person}`

`text{5 visits =  1 person}`
 

   

Filed Under: Data and Interpretation, TESTLET E Tagged With: Band 5, NAPX-MultipleChoice

Geometry, NAPX-p116732v03

A bridge is drawn below.
 

   
 

The angle `y°` is marked from the foot of the bridge to the diagonal support.

The value of angle `y°`  is

 
 Less than 90°
 
 More than 180°
 
 Equal to 90°
 
 More than 90° but less than 180°
Show Answers Only

`text{Less than} \ 90^@`

Show Worked Solution

`text{The angle from the foot to the diagonal support is less than} \ 90^@`

Filed Under: Location, Directions and Angles Tagged With: Band 5, NAPX-MultipleChoice

Geometry, NAPX-p116732v02

A door was opened and not closed.
 


 

The angle `x°`, measured from the opening to the door is

 
  Exactly 90°
 
  More than 90°
 
  Less than 90°
 
  More than 180°
Show Answers Only

`text{More than} \ 90^@`

Show Worked Solution

`text{The door is opened more than} \ 90^@`

Filed Under: Location, Directions and Angles, TESTLET E Tagged With: Band 5, NAPX-MultipleChoice

Statistics, NAPX-p110558v02

A charity event was held for three weeks. On the first week $5000 was raised, on the second week $3500 was raised and on the last week $2000 was raised.

In the tables below, O = $500

Which table correctly shows the amount of donations raised in the 3 weeks?

 
 
 
 
 
 
 
   
Show Answers Only

Show Worked Solution

`text{O represents $500 in donations.}`

`text{1st week:} \ 5000 \div 500 = 10`

`therefore \ text{Ten O symbols needed.}`
 

`text{2nd week:} \ 3500 \div 500 = 7`

`therefore \ text{Seven O symbols needed.}`
 

`text{3rd week:} \ 2000 \div 500 = 4`

`therefore \ text{Four O symbols needed.}`

Filed Under: Data and Interpretation Tagged With: Band 5, NAPX-MultipleChoice

Statistics, NAPX-p110558v01

In a certain school, the number of Year 7 students is 120, Year 8 students is 80, and Year 9 students is 100.

In the tables below, V = 20 students

Which table correctly shows the number of students per year level?

 
   
 
   
 
   
 
   
Show Answers Only

Show Worked Solution

`text{V represents 20 students.}`

`text{Year 7 students:} \ 120 \div 20 = 6`

`therefore \ text{Six V symbols needed}`
 

`text{Year 8 students:} \ 80 \div 20 = 4`

`therefore \ text{Four V symbols needed}`
 

`text{Year 9 students:} \ 100 \div 20 = 5`

`therefore \ text{Five V symbols needed}`

Filed Under: Data and Interpretation, TESTLET E Tagged With: Band 5, NAPX-MultipleChoice

Number, NAPX-p110532v02

Ana recycles 3 kilograms of plastic bottles in her first week of recycling.

She then recycles twice as much as she recycled the previous week for the next 5 weeks.

The total weight, in kilograms, of the plastic bottles she recycles in any given week will be

 
 always even
 
 always odd
 
 sometimes even or sometimes odd
 
 none of the above
Show Answers Only

`text{Always odd}`

Show Worked Solution

`text{1st week: 3 kg (odd)}`

`text{2nd week: 3 + 6 = 9 kg (odd)}`

`text{3rd week: 9 + 18 = 27 kg (odd)}`

   `vdots`

`text{Any week: odd + even = odd}`

Filed Under: Patterns Tagged With: Band 4, NAPX-MultipleChoice

Number, NAPX-p110532v01

Leo puts $15 into his piggy bank to start saving money.

He then puts the same amount into the piggy bank at the end of each month.

The total amount of money in his piggy bank will be which of the following:

 
 Always an even number
 
 Always an odd number
 
 Sometimes odd sometimes even
 
 None of the above
Show Answers Only

`text{Sometimes odd sometimes even}`

Show Worked Solution

`text{Starting amount = $15 (odd)}`

`text{End of 1st month = 15 + 15 = $30 (even)}`

`text{End of 2nd month = 30 + 15 = $45 (odd)}`

`:.\ text{Total amount will be either an odd or even number.}`

Filed Under: Patterns Tagged With: Band 4, NAPX-MultipleChoice

Geometry, NAPX-p110494v02

Michael’s company is shown in the map.
 

   
 

Michael rides home 5 kilometres west, walks 3 kilometres south and walks another 1 kilometre west.

In which cell on the map is Michael’s home?

D1 E2 C1 D2
 
 
 
 
Show Answers Only

`text{D1}`

Show Worked Solution

`text{Each grid width (or height) on the map represents 1 kilometre.}`

`therefore \ text{Michaels’s house lies at D1 on the map.}`

Filed Under: Location, Directions and Angles Tagged With: Band 4, NAPX-MultipleChoice

Geometry, NAPX-p110494v01

Phil’s home is shown in the map below.

Everyday he drives 3 kilometres east and 2 kilometres south from home to work

In which cell on the map is Phil’s office?

A5 B5 E5 D5
 
 
 
 
Show Answers Only

`text{E5}`

Show Worked Solution

`text{Each box  in the map represents 1 kilometre.}`

`therefore \ text{Phil’s office lies on E5 on the map.}`

Filed Under: Location, Directions and Angles, TESTLET C Tagged With: Band 4, NAPX-MultipleChoice

Algebra, NAPX-p116707v03

Louise donated money to two charities

She donated $125 to the first charity and donated $45 to the second charity.

Which number sentence could be used to find total amount of money Louise donated?

 
 120 + 40 = 160
 
 130 + 50 = 180
 
 120 + 40 + 5 = 165
 
 130 + 50 – 10 = 170

Show Answers Only

`130 + 50 – 10 = 170`

Show Worked Solution

`text(Total amount donated to charity)`

`= 125 + 45`

`= 130 – 5 + 50 – 5`

`= 130 + 50 – 10`

`= 170`

Filed Under: Solving Problems - Add/Subtract Tagged With: Band 4, NAPX-MultipleChoice

Algebra, NAPX-p116707v02

Shane played two basketball games.

She scored 35 points in the first game.

In the second game she scored 25 points.

Which number sentence could be used to find the total number of points Shane scored in the first two games?

30 + 20 + 5 = 55 40 + 30 = 70 30 + 20 + 10 = 60 30 + 20 = 50
 
 
 
 
Show Answers Only

`30 + 20 + 10 = 60`

Show Worked Solution

`text(Total points in first 2 games)`

`= 35 + 25`

`= 30 + 5 + 20 + 5`

`= 30 + 20 + 10`

`= 60`

Filed Under: Solving Problems - Add/Subtract Tagged With: Band 4, NAPX-MultipleChoice

Geometry, NAPX-p116721v03

Sarah drew a straight line on a shape.

The line divided the shape into two rectangles.

Which of these could have been Sarah’s shape?

 
 
 
 
Show Answers Only

Show Worked Solution

`text{Drawing any horizontal straight line on this shape divides it}`

`text{into two rectangles.}`

Filed Under: Transformations and Symmetry Tagged With: Band 5, NAPX-MultipleChoice

Geometry, NAPX-p116721v02

Troy drew a straight line through a shape.

The line divided the shape into two equal triangles.

Which of these could not have been Troy’s shape?

 
 
 
 
Show Answers Only

Show Worked Solution

`text{Drawing a diagonal line will produce two quadrilaterals.}`

Filed Under: Transformations and Symmetry Tagged With: Band 5, NAPX-MultipleChoice

Algebra, NAPX-p116672v03

Rudy uses the number sentence  24 – 6 = 18

Which of the following problems can he solve with this number sentence?

 
  Rudy shared 24 slices of cake equally between 6 of his friends.
  How many slices does each of his friends get?
 
  Rudy has 24 slices of cake and gave 6 slices to his friends.
  How many slices does Rudy have left?
 
  Rudy took 6 slices of cake and shared them between 24 of his friends.
  How many slices does each friend receive?
 
  Rudy has 24 slices of cake and gave 18 of them to his friends.
  How many slices does Rudy have left?
Show Answers Only

`text{Rudy has 24 slices of cake and gave 6 slices to his friends.}`

`text{How many slices does Rudy have left?}`

Show Worked Solution

`text{Rudy has 24 slices of cake and gave 6 slices to his friends.}`

`text(Expressing this as an equation:)`

`text(Slices Rudy has left)` `=24 -6`  
`18` `=20 – 6`  

Filed Under: Solving Problems - Multiply/Divide Tagged With: Band 5, NAPX-MultipleChoice

Algebra, NAPX-p116672v02

Shawn uses the number sentence  20 × 6 = 120

Which of the following problems can he solve with this number sentence?

 
  Shawn buys 20 toys and gave 6 of them to his nephew.
  How many toys does Shaun's nephew have now?
 
  Shawn buys 20 toys and received another 6 toys from friends.
  How many toys does Shaun have now?
 
  Shawn buys 20 toys and divides them up between his 6 nephews.
  How many toys does each nephew get?
 
  Shawn has 20 nephews and gives 6 toys to each one.
  Altogether, how many toys does Shaun give to his nephews?
Show Answers Only

`text{Shawn has 20 nephews and gives 6 toys to each one.}`

Show Worked Solution

`text{Shawn has 20 nephews and gives 6 toys to each one.}`

`text(Expressing this as an equation:)`

`text(Total toys to nephews)` `=20 xx 6`  
`120` `=20 xx 6`  

Filed Under: Solving Problems - Multiply/Divide Tagged With: Band 5, NAPX-MultipleChoice

Number, NAPX-p116663v04

Danica decided to travel a total of two thousand, nine hundred and nine kilometres from Brisbane to Adelaide.
 


 

The distance travelled can be written as:

2090 km 2099 km 2909 km 2990 km
 
 
 
 
Show Answers Only

`2909 \ text{km}`

Show Worked Solution

`text{Two thousand, nine hundred and nine = 2909.}`

Filed Under: Number and Place Value Tagged With: Band 4, NAPX-MultipleChoice

Number, NAPX-p116663v03

A man travelled a total of three thousand four hundred and six kilometres from Perth to Melbourne.

The distance travelled can be written as:

3046 km 3460 km 3406 km 4306 km
 
 
 
 
Show Answers Only

`3406 \ text{km}`

Show Worked Solution

`text{Three thousand four hundred and six = 3406}`

Filed Under: Number and Place Value, TESTLET B Tagged With: Band 4, NAPX-MultipleChoice

Geometry, NAPX-p116636v03

Gary folded this piece of paper along the dashed lines to make a solid figure.
 

 
 

Which of these models did Gary make?

 
 
 
 
Show Answers Only

Show Worked Solution

`text{By folding the paper along the dashed lines we could obtain a figure of:}`

Filed Under: 2D-3D Shapes Tagged With: Band 4, NAPX-MultipleChoice

Geometry, NAPX-p116636v02

Lance folded this piece of card board along the dotted line to make a solid figure.
 


 

Which of these models did Lance made?

 
 
 
 
Show Answers Only

Show Worked Solution

`text{By folding the cardboard along the dotted lines we could obtain a figure of:}`

Filed Under: 2D-3D Shapes Tagged With: Band 4, NAPX-MultipleChoice

Number, NAPX-p116616v04

Justin owns a collection of action figures which is more than 674 action figures and less than 764.

Which of these numbers could represent the number of action figures that Justin owns?

 792  724  648  772
 
 
 
 
Show Answers Only

`724`

Show Worked Solution

`text{The number of action figures must be between 674 and 764 action figures}`

`text{Check each option:}`

`text{792 is more than 764 ⇒ incorrect}`

`text{724 is more than 674 and less than 764 ⇒ correct}`

`text{648 is less than 674 ⇒ incorrect}`

`text{772 is more than 764 ⇒ incorrect}`

Filed Under: Number and Place Value, TESTLET C Tagged With: Band 3, NAPX-MultipleChoice

Number, NAPX-p116616v03

Eric owns a book which has more than 258 pages but less than 285 pages

Which of these could represent the number of pages in Eric’s book?

 287  294  249  262
 
 
 
 

Show Answers Only

`262`

Show Worked Solution

`text{Check each option:}`

`text{287 is more than 285 ⇒ incorrect}`

`text{294 is more than 285 ⇒ incorrect}`

`text{249 is less than 258 ⇒ incorrect}`

`text{262 is more than 258 and less than 285 ⇒ correct}`

Filed Under: Number and Place Value Tagged With: Band 3, NAPX-MultipleChoice

Number, NAPX-p116602v04

Kiara receives 5 cents for every used soft drink she recycles.

If she recycled 12 of these cans, how much did she earn?

  $0.12  $0.40   $0.60   $1.20
 
 
 
 

Show Answers Only

`$0.60`

Show Worked Solution
`text{Total money earned }` `= 12 \ text{cans} xx 5 \ text{cents}`
  `= 60\ text(cents)`
  `= $0.60`

Filed Under: Financial Maths, TESTLET C Tagged With: Band 3, NAPX-MultipleChoice

Number, NAPX-p116602v03

George wants to make doughnuts that cost him 10 cents to make each.

If he makes 28 of these donuts, how much will it cost him?

  $1.60  $2.80   $3.20  $4.80
 
 
 
 

Show Answers Only

`$2.80`

Show Worked Solution
`text{Total money earned }` `= 28 xx 10\ text(cents)`
  `= $2.80`

Filed Under: Solving Problems - Multiply/Divide Tagged With: Band 3, NAPX-MultipleChoice

Number, NAPX-p167229v02

A circle is divided into 8 equal parts, as shown in the image below.
 


 

What percentage of the circle’s area has been labelled with letters?

 
30%
 
37.5%
 
42.5%
 
45%
 
47.5%

Show Answers Only

`text(37.5%)`

Show Worked Solution

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

`text(Percentage)` `= text(Number of letters)/text(Total number of sections) xx 100`
  `= 3/8 xx 100`
  `= 37.5text(%)`

Filed Under: Percentages, TESTLET B Tagged With: Band 6, NAPX-MultipleChoice

Geometry, NAPX-p167209v02

Yohan was driving from the hospital to his house.
 


 

What directions best describe Yohan’s travel from the hospital to his house?

 
East, north-east, north
 
West, north-west, north
 
East, north-east, south
 
West, north-west, south

Show Answers Only

`text(East, north-east, north)`

Show Worked Solution

`text(The directions travelled by Yohan:)`
 

 
 

`text(The direction was East, North-East, and North)`

Filed Under: Maps and Bearings, TESTLET D Tagged With: Band 6, NAPX-MultipleChoice

Geometry, NAPX-p167209v01

A man drives from his house to his office.
 


 

What directions best describe his way to the office?

 
North, north-west, west, south-west
 
North, north-east, east, south-east
 
North, north-east, east, south
 
North, north-west, east, south-east

Show Answers Only

`text(North, north-east, east, south-east)`

Show Worked Solution

`text(The directions travelled by the man:)`
 


 

`:.\ text(The direction was north, north-east, east, south-east.)`

Filed Under: Maps and Bearings, TESTLET D Tagged With: Band 6, NAPX-MultipleChoice

Measurement, NAPX-p167202v02

Four triangular shaped playgrounds are shown below.

Which of these play grounds has the least surface area?

 
 
 
 

Show Answers Only

Show Worked Solution

`text(Check each option:)`

`text(Option 1 -)\ \ 1/2 xx 34 xx 15 = 255\ text(m)^2`

`text(Option 2 -)\ \ 1/2 xx 20 xx 26 = 260\ text(m)^2`

`text(Option 3 -)\ \ 1/2 xx40 xx 18 = 360\ text(m)^2`

`text(Option 4 -)\ \ 1/2 xx28 xx 25 = 350\ text(m)^2`
 

`:.\ text(The backyard with the least area is:`

Filed Under: Perimeter, Area and Volume Tagged With: Band 6, NAPX-MultipleChoice

Measurement, NAPX-p167202v01

In a suburb, four families measured the dimensions of their rectangular backyards.

Which backyard has the largest area?

 
 
 
 

Show Answers Only

   

Show Worked Solution

`text(Checking each option:)`

`text(Option 1:)\ 11 xx 18 = 198 text(m)^2`

`text(Option 2:)\ 16 xx 6 = 96 text(m)^2`

`text(Option 3:)\ 15 xx 10 = 150 text(m)^2`

`text(Option 4:)\ 14 xx 12 = 168 text(m)^2`
 

`:. text(The backyard with the largest area is the)\ 11\ text(m) xx 18\ text(m)`

`text(with a total area of 198 square metres.)`

   

Filed Under: Perimeter, Area and Volume, TESTLET D Tagged With: Band 6, NAPX-MultipleChoice

Probability, NAPX-p167310v04

A man spins a wheel with 5 different coloured sections and records which colour it lands on each time.

He repeats the process multiple times.

The table below shows the results.
 

     
 

Using the table, what is the probability that the next spin will be yellow?

 
`6/31`
 
`16/84`
 
`1/7`
 
`2/5`

Show Answers Only

`1/7`

Show Worked Solution
`P(text(Yellow))` `= text(Number of yellow)/text(Total number of throws)`
  `= 24/(42 + 24 + 38 + 27 + 37)`
  `= 24/168`
  `=1/7`

Filed Under: Probability Tagged With: Band 8, NAPX-MultipleChoice

Measurement, NAPX-p167325v01

Sam painted grids in the larger square areas pictured below.

All of the grids are the same size.

Which of the following squares has the largest area painted?

 
 
 
 

Show Answers Only

Show Worked Solution

`text(The largest area painted is the figure with the most squares painted grey.)`

`text(Checking each option:)`

`text(Option 1 – 9 square grids painted)`

`text(Option 2 – 13 square grids painted)`

`text{Option 3 – 16 square grids painted (Correct)}`

`text(Option 4 – 14 square grids painted)`

Filed Under: Perimeter, Area and Volume Tagged With: Band 5, NAPX-MultipleChoice

Probability, NAPX-p167310v03

Andrei has a stack of cards that contains only Aces, Kings, Queens, Jacks and Jokers.

He picks one card without looking, records the card and puts it back again with the others.

He repeated this process 62 times.

   

Using the table, what are the chances of Andrei randomly selecting the Joker in his next pick?

 
`8/33`
 
`6/31`
 
`11/62`
 
`6/25`

Show Answers Only

`6/31`

Show Worked Solution
`P(text(Joker))` `= text(Number of Jokers)/text(Total number of draws)`
  `= 12/62`
  `= 6/31`

Filed Under: Probability, TESTLET D Tagged With: Band 8, NAPX-MultipleChoice

Probability, NAPX-p167310v02

Marie grabs a coloured ball from a bag and records the colour. She then puts the ball back to the bag and repeats this process 96 times.

The results are shown in the table below.
 

     
 

Using the table, what is the probability that the next ball picked up by Marie will be yellow?

 
`5/48`
 
`6/25`
 
`5/43`
 
`7/36`

Show Answers Only

`5/48`

Show Worked Solution
`P(5)` `= text(Number of yellow)/text(Total number)`
  `= 10/96`
  `= 5/48`

Filed Under: Probability Tagged With: Band 8, NAPX-MultipleChoice

Probability, NAPX-p167310v01

A biased die has 6 faces numbered from 1 to 6.

Raven throws the die 50 times and recorded the results in the table below.
 

   
 

Using the table, what is the probability that Raven will be throwing a 5 on her next throw?

 
`6/44`
 
`2/17`
 
`11/25`
 
`3/25`

Show Answers Only

`3/25`

Show Worked Solution
`P(5)` `= text(Number of 5’s)/text(Total number of throws)`
  `= 6/50`
  `= 3/25`

Filed Under: Probability Tagged With: Band 8, NAPX-MultipleChoice

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)`  

Filed Under: Perimeter, Area and Volume Tagged With: Band 7, NAPX-MultipleChoice

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)`  

Filed Under: Perimeter, Area and Volume Tagged With: Band 7, NAPX-MultipleChoice

Algebra, NAPX-p115542v02

Shane is drawing a repeated pattern in the grid.

Which of these points will be part of Shane’s pattern?

 
(8, 3)
 
(2, 7)
 
(7, 3)
 
(2, 6)

Show Answers Only

`(8, 3)`

Show Worked Solution

`text(If the pattern continues:)`

`text{The point (8, 3) will be part of the pattern.}`

Filed Under: Patterns and The Number Plane Tagged With: Band 8, NAPX-MultipleChoice

Algebra, NAPX-p115542v01

Patricia is drawing a repeating pattern on the grid pictured below.

Which of these points will be part of Patricia’s pattern?

 
(16, 6)
 
(14, 8)
 
(14, 7)
 
(16, 8)

Show Answers Only

`(16, 8)`

Show Worked Solution

`text(If the pattern continues:)`

 
`:.\ text{The point (16, 8) will be part of the pattern.}`

Filed Under: Patterns and Coordinate Geometry, TESTLET D Tagged With: Band 8, NAPX-MultipleChoice

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`

Filed Under: Probability, TESTLET D Tagged With: Band 7, NAPX-MultipleChoice

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`

Filed Under: Probability Tagged With: Band 7, NAPX-MultipleChoice

Geometry, NAPX-p167266v02

Which dotted line is a line of symmetry?

 
 
   
 
 

Show Answers Only

Show Worked Solution

`text(Option 3: the left side is the mirror reflection of the right side.)`

Filed Under: 2D-3D Shapes and Location, TESTLET D Tagged With: Band 7, NAPX-MultipleChoice

Geometry, NAPX-p167266v01

Which dotted line is a line of symmetry?

 
   
 
 
 

Show Answers Only

Show Worked Solution

`text(Option 1: the top side is the mirror reflection of the bottom side.)`

Filed Under: 2D-3D Shapes and Location Tagged With: Band 7, NAPX-MultipleChoice

Geometry, NAPX-p167252v02

A certain plane rises 2 metres for every 12 metres of its base length.

If it rises by 1.6 metres, what will be its base length?

 
12.4 m
 
10.8 m
 
  9.6 m
 
  8.4 m

Show Answers Only

`text(9.6 m)`

Show Worked Solution

`text(Every 2 metres of height → 12 metres of base)`

`text(Every 1 metre of height → 6 metres of base)`

`:.\ text(Base length)` `= 1.6 xx 6`  
  `=9.6\ text(m)`  

Filed Under: Ratio and Scale in Geometry, TESTLET D Tagged With: Band 7, NAPX-MultipleChoice

Geometry, NAPX-p167252v01

A one-metre tall person casts a 4-metres shadow on level ground.

If a 1.8 metre tall person stands at the same position, how long will the shadow be?

 
6.8 m
 
7.2 m
 
8.0 m
 
8.6 m

Show Answers Only

`text(7.2 m)`

Show Worked Solution

`text(1 metre height → 4 metre shadow)`

`:.\ text(1.8 m height shadow)` `= 1.8 xx 4`  
  `=7.2/ text(m)`  

Filed Under: Triangles and Other Geometrical Properties Tagged With: Band 7, NAPX-MultipleChoice

Number, NAPX-p109105v02

William has a St Bernard puppy that weighs 25 kilograms.

After another 8 months, the St Bernard weighs 12% more.

How much does the dog weigh now?

 
28 kg
 
30 kg
 
32 kg
 
37 kg

Show Answers Only

`text(28 kg)`

Show Worked Solution
`text(Weight)` `= 25 + (25 xx 12text(%))`
  `= 25 + 3`
  `= 28\ text(kg)`

 
`:.\ text(The weight of the St Bernard after 8 months is 28 kilograms.)`

Filed Under: Percentages, TESTLET D Tagged With: Band 7, NAPX-MultipleChoice

Number, NAPX-p109105v01

Paul’s height is 146 centimetres when he was 15 years old.

On his 18th birthday he was 10% taller than when he was at 15 years old.

How tall was Paul when he was 18?

 
160.6 cm
 
150.8 cm
 
168.2 cm
 
180.3 cm

Show Answers Only

`text(160.6 cm)`

Show Worked Solution
`text(Pauls new height)` `= 146 + (146 xx 10text(%))`
  `= 146 + 14.6`
  `= 160.6\ text(cm)`

 
`:.\ text(Paul’s height on his 18th birthday is 160.6 centimetres.)`

Filed Under: Percentages, TESTLET D Tagged With: Band 7, NAPX-MultipleChoice

Statistics, NAPX-p167236v02

A store sells second hand mobile phones.

The graph below shows the price of 2 similar second-hand phones.
 


 

Which of the following is true based on the graph shown?

 
Phone A is older and less expensive than Phone B
 
Phone B is older and more expensive than phone A
 
Phone A is newer and more expensive than Phone B
 
Phone A is older and more expensive than Phone B

Show Answers Only

`text(Phone A is newer and more expensive than Phone B)`

Show Worked Solution

`text(Phone A is left of Phone B → it is newer.)`

`text(Phone A is higher than Phone B → it is more expensive.)`

`:.\ text(Phone A is newer and more expensive than Phone B.)`

Filed Under: Data and Statistics Tagged With: Band 6, NAPX-MultipleChoice

Statistics, NAPX-p167236v01

A man bought a plot of land in the past and now he is selling it.

The graph marks the price of the land when the man bought it and the price of the land now.
 


 

Which of the following is true based on the graph shown?

 
The land is less expensive now than when it was purchased.
 
The land is more expensive years ago than now.
 
The land is more expensive now than years ago.
 
The price of the land does not change with time.

Show Answers Only

`text(The land is more expensive now than years ago.)`

Show Worked Solution

`text(Z is further right on the x-axis → most recent price.)`

`text(Z is higher on the y-axis → more expensive.)`

`:.\ text(The land is more expensive now than years ago.)`

Filed Under: Data and Statistics, TESTLET D Tagged With: Band 6, NAPX-MultipleChoice

Number, NAPX-p167229v01

A circle is divided into 8 equal parts, as shown in the diagram below.
 


 

What percentage of the circle’s area has been labelled with even numbers?

 
37.5%
 
50%
 
57.5%
 
62.5%
 
70%

Show Answers Only

`text(62.5%)`

Show Worked Solution

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

`text(Percentage)` `= text(Number of even numbers)/text(Total number of sections) xx 100`
  `= 5/8 xx 100`
  `= 62.5text(%)`

Filed Under: Percentages, TESTLET B, TESTLET D Tagged With: Band 6, NAPX-MultipleChoice

Number, NAPX-p73124v02

Julian was driving into town and hit a kangaroo `3/4` of a kilometre into his trip.

Which of these represent where Julian hit the kangaroo?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Each spacing is worth)\ 1/4\ text(km.)`
 

Filed Under: Fractions and Decimals Tagged With: Band 6, NAPX-MultipleChoice

Number, NAPX-p73124v01

Axe went jogging and stopped after  `2/6`  of a kilometre to take a rest. 

Which of these represents where Axe stopped jogging?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Each spacing is worth)\ 1/6\ text(km.)`

Filed Under: Fractions and Decimals Tagged With: Band 6, NAPX-MultipleChoice

Algebra, NAPX-p73022v02

Aaron wants to find the missing number that will make this number sentence correct.
 

 
  `+ 12 = 106`

 
Which of these could Aaron use to find the missing number?

`106 -: 12` `106 xx 12` `106-12` `12+106`
 
 
 
 
Show Answers Only

`106-12`

Show Worked Solution
 
  `+12= 106`

 

`text(Subtract 12 from both sides:)`

 
  `= 106 – 12`

Filed Under: Basic Algebra, Solving Problems - Add/Subtract Tagged With: NAPX-MultipleChoice

Algebra, NAPX-p73022v01

Carryn wants to find the number that will make this number sentence correct.

 
  `xx 9 = 72`

Which of these could Carryn use to find the missing number?

`72 -: 9` `9 xx 72` `72-9` `9+72`
 
 
 
 
Show Answers Only

`72-:9`

Show Worked Solution
 
  `xx 9 = 72`

 

`text(Divide both sides by 9:)`

 
  `= 72 -: 9`

Filed Under: Solving Problems - Multiply/Divide, TESTLET D Tagged With: NAPX-MultipleChoice

Geometry, NAPX-p72864v02

Nathan places a notepad along a line of symmetry of a star shape.
 

 
How many points does the star have?

`6` `8` `9` `10` `12`
 
 
 
 
 
Show Answers Only

`10`

Show Worked Solution

`text(Number of points = 10)`

Filed Under: TESTLET E, Transformations and Symmetry Tagged With: NAPX-MultipleChoice

Measurement, NAPX-p73132v01

Each square in the figure has a side length of 2 metres.
 


 

What is the perimeter of the figure?

18 m 24 m 32 m 36 m
 
 
 
 
Show Answers Only

`text(36 m)`

Show Worked Solution

`text(Starting at the bottom right corner and)`

`text(moving clockwise:)`

   

`text(Perimeter)` `=10+6+2+2+2+2+4+2+2+4`
  `=36\ text(m)`

Filed Under: Perimeter, Area and Volume, TESTLET E Tagged With: NAPX-MultipleChoice

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