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Algebra, NAPX-H3-CA20

An unknown number is added to − 3.

The result is multiplied by 2 to give an answer of 6.

Which of these is the unknown number?

`− 3` `− 1` `6` `15`
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text(Working backwards:)`

`3 xx 2 = 6`

`=>\ text{unknown} + (− 3) = 3`

`:.\ text(Unknown number = 6)`

Measurement, NAPX-H3-CA18

A rectangle has a length of 12 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?

`4.75` `9.5` `10.25` `21`
 
 
 
 
Show Answers Only

`9.5`

Show Worked Solution
`text(Perimeter)` `= (2 xx 12) + (2 xx 17)`
  `= 38\ text(cm)`

 

`:.\ text(Square side)` `= 38 ÷ 4`
  `= 9.5\ text(cm)`

Statistics and Probability, NAPX-H3-CA17

Chester baked 21 muffins.

He baked equal numbers of chocolate chip, blueberry and banana.

Chester randomly picked one of the muffins.

What are the chances it was banana or chocolate chip?

`2/21` `1/3` `2/7` `2/3` `4/7`
 
 
 
 
 
Show Answers Only

`2/3`

Show Worked Solution

`text{P(banana or choc chip)}`

`= text(Number of possibilities)/text(Total possibilities)`

`= (7 + 7)/21`

`= 2/3`

Number, NAPX-H3-CA15

Carmen has three blocks of chocolate that are identical.

She also has a 4th smaller block of chocolate that weighs 175 grams.

Carmen has 1480 grams of chocolate in total.

Which expression can be used to calculate the mass of one of the large blocks of chocolate?

`(1480 + 175) ÷ 3` `3 xx (1480 + 175)` `(1480 - 175) ÷ 3` `3 xx (1480 + 175)`
 
 
 
 
Show Answers Only

`(1480 – 175) ÷ 3`

Show Worked Solution

`text(Mass of the 3 larger blocks)`

`= 1480 – 175`
 

`:.\ text(Mass of 1 larger blocks)`

`= (1480 – 175) ÷ 3`

Measurement, NAPX-H3-CA14

A tennis match starts at 10:21 am and goes for 135 minutes.

What time does the match finish?

`text(11:56 am)` `text(11:56 pm)` `text(12:36 am)` `text(12:36 pm)`
 
 
 
 
Show Answers Only

`text(12:36 pm)`

Show Worked Solution

`text(135 minutes = 2 hours and 15 minutes)`
 

`:.\ text(Finishing time of the tennis match)`

`text(= 10:21 am plus 2 hours and 15 minutes,)`

`text(= 12:36 pm.)`

Number, NAPX-H3-CA13

Which of the following lists the numbers in increasing order?

 
 `7/8, 0.7, 0.78, text(85%)`
 
 `text(85%), 7/8, 0.7, 0.78`
 
 `0.7, 0.78, 7/8, text(85%)`
 
 `0.7, 0.78, text(85%), 7/8`
Show Answers Only

`0.7, 0.78, text(85%), 7/8`

Show Worked Solution

`text(Converting all to decimals:)`

`85text(%) = 0.85`

`7/8 = 0.875`

 
`:.\ text(Increasing order is)`

`0.7, 0.78, text(85%), 7/8`

Algebra, NAPX-H3-CA12

 

What is the rule connecting dress sizes in Country A and Country B?

 
 `text{Country B = ( 3 × Country A) + 11}`
 
 `text{Country B = (2 × Country A) + 18}`
 
 `text{Country B = Country A − 25}`
 
 `text{Country B = Country A + 25}`
Show Answers Only

`text{Country B = Country A + 25}`

Show Worked Solution

`text{Country B = Country A + 25}`

Number, NAPX-H3-CA10

A box of chocolates contains 7 wrapped chocolates and 16 unwrapped chocolates.

About what percentage of the chocolates in the box are wrapped chocolates?

`7text(%)` `23text(%)` `30text(%)` `44text(%)`
 
 
 
 
Show Answers Only

`30text(%)`

Show Worked Solution

`text(Percentage of wrapped chocolates)`

`= text(number wrapped)/text(total chocolates) xx 100`

`= 7/((7 + 16)) xx 100`

`= 30.4 text(%)`

Statistics and Probability, NAPX-H3-CA05

Steph randomly picks one disk from a group of white and grey disks, pictured below.
 

 

 
What is the probability Steph chooses a grey disk?

`1/3` `8/13` `8/21` `13/21`
 
 
 
 
Show Answers Only

`8/21`

Show Worked Solution
`text{P(Black disc)}` `= text(Number of black disks) / text(Total disks)`
  `= 8/21`

Geometry, NAPX-H3-CA04

A regular octagon is folded in half along the dotted line.

 

The folded shape can also be called a

`text(quadrilateral)` `text(pentagon)` `text(hexagon)` `text(triangle)`
 
 
 
 
Show Answers Only

`text(pentagon)`

Show Worked Solution

`text(The resulting shape has 5 sides.)`

`:.\ text(Pentagon.)`

Number, NAPX-H3-CA03

Mick is selling egg and bacon rolls at a school fete.

He makes $54 from selling 9 egg and bacon rolls.

All egg and bacon rolls cost the same.

How much will Mick make if he sells 11 egg and bacon rolls.

`$63` `$66` `$77` `$99`
 
 
 
 
Show Answers Only

`$66`

Show Worked Solution
`text(Price of 1 roll)` `= ($54)/9 = $6`

 

`:.\ text(Price of 11 rolls)` `= 11 xx $6`
  `= $66`

Geometry, NAPX-H3-CA01

This is a street map.
 

 

 
About how far is it from Ali's house to Zilda's house?

`60\ text(metres)` `150\ text(metres)` `210\ text(metres)` `270\ text(metres)`
 
 
 
 
Show Answers Only

`text(210 metres)`

Show Worked Solution

`text(The distance is approximately 3.5 times the)`

`text(width of the scale interval.)`

`:.\ text(Distance)\ ~~ 3.5 xx 60 ~~ 210\ text(metres)`

Measurement, NAPX-I3-NC30

Ralph has a rectangular puppy playground in his backyard with an area of 10 m².

He decides to make it bigger and increases each side to 3 times its current length.

What is the new area of the puppy playground?

`text(90 m²)` `text(60 m²)` `text(40 m²)` `text(30 m²)`
 
 
 
 
Show Answers Only

`text(90 m²)`

Show Worked Solution

`text(Area of original playground)`

`= l xx w`

`= 10\ text(m²)`
 

`:.\ text(Area of new playground)`

`= 3l xx 3w`

`= 9 xx l xx w`

`= 9 xx 10`

`= 90\ text(m²)`

Measurement, NAPX-I3-NC26, NAPX-I2-38

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

Which rectangle has a perimeter of 32 centimetres?

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

`text(Rectangle 2)`

Show Worked Solution
`text(Perimeter)` `= 2 xx text(length) + 2 xx text(width)`
  `= (2 xx 12) + (2 xx 4)`
  `= 32\ text(cm)`

 

`:.\ text(Rectangle 2 has a perimeter of 32 cm.)`

Number, NAPX-I3-NC19

Monty wants to buy some cricket equipment.

The sports shop's prices of the equipment he wants is listed in the table below.

Monty buys all 4 items.

Which of these gives the correct range for the total cost of this equipment?

`$175 - $200` `$200 - $225` `$225 - $250` `$250 - $275`
 
 
 
 
Show Answers Only

`$250 – $275`

Show Worked Solution

`text(One strategy for estimating:)`

`$32.60 + $51.95 ~~ $33 + 52 ~~ $85`

`$38.60 + $129.50 ~~ $40 + 130 ~~ $170`

`text(Estimate)` `~~ 85 + 170`
  `~~ $255`

 
`:.\ text(Range is:)\ \ $250 – $275`

Geometry, NAPX-I3-NC18

Hunter drew a shape that is pictured below.
 

 
He reflected the shape across the dotted line.

He rotated it 90 degrees anticlockwise.

Which shape below shows what it looks like after this?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(After reflection:)`

`text{After rotation:}`

Statistics and Probability, NAPX-I3-NC16, NAPX-I2-31

An ice hockey competition has six teams playing on the same day.

The table below shows the game order.
 

  
If no match ends in a draw, which of the following is possible?

 
 Rangers and Oilers are the only teams that lose.
 
 Oilers, Flames, Canucks and Rangers all win.
 
 Penguins and Canucks both lose.
 
 Kings win and Oilers win.
Show Answers Only

`text(Penguins and Canucks both lose.)`

Show Worked Solution

`text{Penguins and Canucks both lose (this is possible because}`

`text{they are playing different teams).}`

Number, NAPX-I3-NC14, NAPX-I2-30

Mia does odd jobs around the house to earn pocket money.

She gets $4 per job.

The table below shows all the jobs she did in one week.
 

 
If Mia does the same jobs for two weeks, how much money will she earn altogether?

`$13` `$26` `$52` `$104`
 
 
 
 
Show Answers Only

 `$104`

Show Worked Solution

`text(Total jobs in 1 week)`

`= 6 + 4 + 3`

`= 13`
 

`:.\ text(Money earned in 2 weeks)`

`= 2 xx 13 xx 4`

`= $104`

Measurement, NAPX-I3-NC12, NAPX-I2-25

An end of term school assembly started at 10:30 am and went for `2 3/4` hours.

School then finished `1/4` hour after the assembly ended.

What time did school finish?

`text(12:15 pm)` `text(1:15 am)` `text(1:15 pm)` `text(1:30 am)` `text(1:30 pm)`
 
 
 
 
 
Show Answers Only

`text(1:15 pm)`

Show Worked Solution

`text(Finish time of assembly)`

`text(= 10:30 am plus 2 hr 45 mins)`

`text(= 1:15 pm)`

 
`:.\ text(School finishes at 1:30 pm.)`

Algebra, NAPX-I3-NC11, NAPX-I2-24

The first number in a pattern is 4.25.

Each number in the pattern is formed by subtracting 0.55 from the previous number.

What is the third number in this pattern?

`4.8` `3.7` `3.15` `2.6`
 
 
 
 
Show Answers Only

`3.15`

Show Worked Solution

`text(2nd number:)\ \ 4.25 – 0.55 = 3.7`

`text(3rd number:)\ \ 3.7 – 0.55 = 3.15`

Statistics and Probability, NAPX-I3-NC09, NAPX-I2-22

The number of students that could kick a soccer ball more than 50 metres were counted at 7 different primary schools.

The results were recorded in the graph below.

How many students, in total, could kick the soccer ball more than 50 metres?

`1` `16` `17` `18`
 
 
 
 
Show Answers Only

`18`

Show Worked Solution

`text(Number of students)`

`= 4 + 2 + 3 + 1 + 3 + 2 + 3`

`= 18`

Statistics, NAPX-I3-NC04, NAPX-I2-12

Tim was recording the colour of cars that drove past his school in 1 hour.

In the hour, Tim saw 14 blue, 8 silver and 6 white cars.

In the tables below, `text(X)` = 2 cars.

Which table correctly shows the number of cars that Tim saw?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(S)text(ince)\ X = 2\ text(cars,)`

`text(14 Blue cars)` `= 7 xx text(X)`
`text(8 Silver cars)` `= 4 xx text(X)`
`text(6 White cars)` `= 3 xx text(X)`

Algebra, NAPX-I3-NC02, NAPX-I2-11

Ronald has no money in his bank account.

He deposits $9 in his account in week 1.

He then deposits twice the amount into his account each week than he did the previous week.

The total amount in his account is?

 
 always odd.
 
 always even.
 
 sometimes odd and sometimes even.
Show Answers Only

`text(always odd.)`

Show Worked Solution

`text(Initial deposit is an odd number.)`

`text(Each week an even number amount is added.)`

`text(Week 2 ⇒ odd + even = odd)`

`text(Week 3 ⇒ odd + even = odd)`
 

`:.\ text(The total amount is always odd.)`

Measurement, NAPX-I3-CA25

The rectangular prism, pictured below, has a volume of 19 000 cm³ and a height of 25 cm.
 

 
What could be the length and width of the prism?

`40\ text(cm) xx 19\ text(cm)` `30\ text(cm) xx 25\ text(cm)` `20\ text(cm) xx 29\ text(cm)` `40\ text(cm) xx 12\ text(cm)`
 
 
 
 
Show Answers Only

`40\ text(cm) xx 19\ text(cm)`

Show Worked Solution
`V` `= l xx w xx h`
`19\ 000` `= l xx w xx 25`
`760` `= l xx w`
  `= 40 xx 19`

 

`:. 40\ text(cm) xx 19\ text(cm)`

Geometry, NAPX-I3-CA24

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

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 left.
 
 Reflect `ABCD` across the `y`-axis, then translate `7` units down.
Show Answers Only

`text(Reflect)\ ABCD\ text(across the)\ xtext(-axis, then translate 8 units left.)`

Show Worked Solution

`text(Reflection in the)\ xtext(-axis:)`

`ABCD -> A′B′C′D′`

`text(Translate 8 units left:)`

`A′B′C′D′ -> SRQP`

Number, NAPX-I3-CA19

Santiago needs to buy some olive oil.

The farmers' market sells Santiago's favourite olive oil in a number of different sizes.

Which size costs him the least per mL?

 
 `text(150 mL bottle for $3.00)`
 
 `text(200 mL bottle for $3.20)`
 
 `text(350 mL bottle for $5.95)`
 
 `text(500 mL bottle for $8.75)`
Show Answers Only

`text(200 mL bottle for $3.20)`

Show Worked Solution

`text(Calculate the cost per mL for each option:)`

`text(150 mL for $3.00 = 300/150 = 2 cents/mL)`

`text(200 mL for $3.20 = 1.6 cents/mL)`

`text(350 mL for $5.95 = 1.7 cents/mL)`

`text(500 mL for $8.75 = 1.75 cents/mL)`

 

`:. 200\ text(mL bottle costs the least per mL.)`

Statistics and Probability, NAPX-I3-CA18

Petal did a survey of her class, asking everyone what their favourite season is.

This table below shows the results.
 

 
What is the probability that a randomly selected classmate's favourite season is Spring?

Round your answer to the nearest hundredth.

`0.10` `0.27` `0.40` `0.43`
 
 
 
 
Show Answers Only

`0.27`

Show Worked Solution

`text{P(Classmate chose Spring)}`

  `= text(number who chose Spring) / text(total classmates)`
  `= 10/(17 + 8 + 2 + 10)`
  `= 10/37`
  `= 0.270…`

Number, NAPX-I3-CA17

A soft drink factory can make 750 cans of lemonade and 1100 cans of ginger ale per hour.

Each can weighs 300 grams.

How many kilograms of soft drink does the factory produce in 1 hour?

 
 `4.65\ text(kilograms)`
 
 `55\ text(kilograms)`
 
 `465\ text(kilograms)`
 
 `555\ text(kilograms)`
Show Answers Only

`555\ text(kilograms per day)`

Show Worked Solution

`text(Total cans made per hour)`

`= 750 + 1100`

`= 1850`
  

`:.\ text(Kilograms made per hour)` 

`= 1850 xx 300`

`= 555\ 000\ text(grams)`

`= 555\ text(kilograms)`

Algebra, NAPX-I3-CA13

Ian is enrolled in an intensive summer swimming program.

His swimming program is shown in the table below.

Which statement about Ian's program is true?

Ian's program is to swim:

 
 `text(12 laps more than the previous day.)`
 
 `text(18 laps more than the previous day.)`
 
 `text(1.5 times more laps than the previous day.)`
 
 `text(12 times more laps than the previous day.)`
Show Answers Only

`text(1.5 times more laps than the previous day.)`

Show Worked Solution

`text(Day 2 laps) = 1.5 xx 24 = 36`

`text(Day 3 laps) = 1.5 xx 36 = 54`

`text(etc. …)`

`:.\ text(1.5 times more laps than the previous day.)`

Number, NAPX-I3-CA12

Numbers such as 4, 9, 16, 25, 64, 81 and 100 are called square numbers.

Select the statement that is true about square numbers.

 
 The difference between two consecutive square numbers is always a prime number.
 
 A square number added to another square number cannot be a square number.
 
 The square of an odd number is always an odd number.
 
 The difference between two square numbers is always a square number.
Show Answers Only

`text(The square of an odd number is always an odd number.)`

Show Worked Solution

`text(Consider option 3:)`

`text(Square of odd number)` `=\ text(odd × odd)`
  `=\ text(odd)`

Measurement, NAPX-I3-CA11

A hexagon with equal sides is drawn below.
 

 
5 identical hexagons are connected as shown in the diagram below.
 

 
What is the perimeter of the larger shape?

`209\ text(mm)` `247\ text(mm)`  `285\ text(mm)`  `342\ text(mm)`
 
 
 
 
Show Answers Only

`209\ text(mm)`

Show Worked Solution
`text(Perimeter)` `= text(Number of sides) xx 9.5`
  `= 22 xx 9.5`
  `= 209\ text(mm)`

Number, NAPX-I3-CA10

Dominique had 1 kilogram of chocolate.

She used  `2/5`  kilogram in a cake recipe.

How much chocolate did Dominique have left?

`0.25\ text(kg)` `0.40\ text(kg)`  `0.60\ text(kg)`  `0.75\ text(kg)`
 
 
 
 
Show Answers Only

`0.60\ text(kg)`

Show Worked Solution
`text(Chocolate left)` `= 1 – 2/5`
  `= 3/5`
  `= 0.60\ text(kg)`

Statistics and Probability, NAPX-I3-CA09

The graph shows the origin and type of all vehicles in a city.
 

 
Which statement is most accurate based on the graph?

 
 There are more trucks and vans than sedans.
 
 Utility vehicles are the most common type of vehicles
 
 Sedans are the most common type of vehicles.
 
 There are more European vehicles than Australian vehicles.
Show Answers Only

`text(Sedans are the most common type of vehicles.)`

Show Worked Solution

`text(By trial and error,)`

`text(Consider the 3rd option:)`

`text(Total sedans)= 6 + 4 + 5 = 15`

`text(Total utility)= 1 + 3 + 8 = 12`

`text(Total trucks)= 5 + 3 + 6 = 14`
 

`:.\ text(Sedans are the most common type of vehicles.)`

Number, NAPX-I3-CA08

Rufus had 5 cups of pumpkin seeds to use for baking 2 loaves of pumpkin bread.

He used `1 3/4` cups for the first loaf, and  `1 1/2` cups for the second loaf.

How many cups of pumpkin seeds did Rufus have left?

`1 3/4` `2 3/4`  `3 1/4`  `7 3/4`
 
 
 
 
Show Answers Only

`1 3/4`

Show Worked Solution

`text(Cups of pumpkin seeds left)`

`=5 – (1 3/4 + 1 1/2)`

`= 5 – 3 1/4`

`= 1 3/4`

Statistics and Probability, NAPX-I3-CA07

Bennett creates a game with the spinner shown below.
 

 
If the spinner lands on a 2, he wins a prize.

What is the probability that Bennett will win a prize on his next spin?

`1/4`  `1/3`  `3/8`  `1/2`
 
 
 
 
Show Answers Only

`3/8`

Show Worked Solution
`text{P(landing a 2)}` `= text(Number of 2’s)/text(Total possibilities)`
  `= 3/8`

Measurement, NAPX-I3-CA06

A jeweller is making diamond rings for her collection.

Which unit would be the most appropriate to record the mass of a diamond?

`text(kilogram)` `text(millilitre)` `text(millimetre)` `text(gram)`
 
 
 
 
Show Answers Only

`text(gram)`

Show Worked Solution

`text(Diamonds are very small and light.)`

`:.\ text(The best unit is “gram”.)`

Measurement, NAPX-I3-CA05

Craig started work at 8:35 in the morning and finished at 6:50 in the evening.

How many hours did Craig spend working?

 
 `text(1 hour 45 minutes)`
 
 `text(2 hours 15 minutes)`
 
 `text(8 hours 35 minutes)`
 
 `text(9 hours 45 minutes)`
 
 `text(10 hours 15 minutes)`
Show Answers Only

`text(10 hours 15 minutes)`

Show Worked Solution

`text(8:35 am to 6:35 pm = 10 hours)`

`text(6:35 pm to 6:50 pm = 15 minutes)`

`:.\ text(10 hours and 15 minutes)`

Number, NAPX-I3-CA02

Simon owns a dairy farm.

He keeps 2 cows on every acre of the property.

How many acres would he need for 12 cows?

`6`   `10` `14` `24`
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text(2 cows per acre)`

`:.\ text(Acres needed for 12 cows)` `= 12/2`
  `= 6\ text(acres)`

Statistics and Probability, NAPX-J4-CA*38, NAPX-J3-CA*37

The Strikers and the Hurricanes are playing cricket in a 20 over competition.

The stem-and-leaf plots show the number of runs each side has scored in their last 15 games.
 

 
Which statement about the data below is true?

 
 The Strikers had the lowest run score.
 
 The Strikers had the highest run score.
 
 The Strikers scored over 132 runs more times than the Hurricanes.
 
 The median score for The Strikers is lower than the median score for The Hurricanes.
 
 The range of scores for The Strikers is greater than the range of scores for The Hurricanes.
Show Answers Only

`text{The median score for The Strikers is lower than}`

`text{the median score for The Hurricanes}`

Show Worked Solution

`text(Consider each statement:)`

`text(Low scores:)\ S = 108, H = 107`  
`text(High scores:)\ S = 146, H = 147`  
`text(Scores > 132:)\ S = 6, H = 7`  
`text(Median:)\ S = 127, H = 129`  
`text(Range:)\ S = 146 – 108 = 38, H = 147 – 107 = 40`  

Number, NAPX-J3-NC07, NAPX-J2-39

Which of these numbers has a 7 in the thousandths place?

57 021.4 5.7108 1.3722 0.1272
 
 
 
 
Show Answers Only

`0.1272`

Show Worked Solution

`text{Digits to the right of the decimal place are (in order):}`

`text(tenths, hundredths, thousandths, …)`

`:.\ text(0.1272 is correct.)`

Number, NAPX-J3-NC03

Brocky got a new car and recorded how many litres of petrol he put into the car over 4 weeks.

Week 1: 38.45 litres

Week 2: 51.70 litres

Week 3: 44.85 litres

Week 4: 87.90 litres

To estimate how many litres of petrol he put into his car over the 4 weeks, Brocky rounded the weekly amounts to the nearest 10 litres and added them.

How much was Brocky's estimate?

`240\ text(litres)` `230\ text(litres)` `220\ text(litres)` `210\ text(litres)`
 
 
 
 
Show Answers Only

`220\ text(litres)`

Show Worked Solution
`text{Estimate (after rounding)}` `= 40 + 50 + 40 + 90`
  `= 220\ text(litres)`

Measurement, NAPX-J3-CA31

Wooden beams for building house frames can be purchased in a number of lengths.

A hardware store can supply lengths of 1.9 metres, 290 millimetres, 185 centimetres, 0.295 metres and 300 centimetres.

Which wooden beam is the longest?

 
 1.9 metres
 
 290 millimetres
 
 185 centimetres
 
 0.295 metres
 
 300 centimetres
Show Answers Only

`text(300 centimetres)`

Show Worked Solution

`text(Convert all measurements to metres:)`

`290\ text(mm) = 290/1000 = 0.290\ text(metres)`

`185\ text(cm) = 185/100 = 1.85\ text(metres)`

`300\ text(cm) = 300/100 = 3.0\ text(metres)`

 

`:.\ text(Longest beam is 300 cm)`

Number, NAPX-J3-CA25

The lowest point in Asia is Ayoling Lake at −154 metres, which is below sea level.

Mount Everest, also in Asia, is 8848 metres above sea level.

What is the difference, in metres, between the highest and lowest points in Asia?

9002 metres 8992 metres 8792 metres 8694 metres
 
 
 
 
Show Answers Only

`9002\ text(metres)`

Show Worked Solution
`text(Difference)` `= 8848 – (- 154)`
  `= 9002\ text(metres)`