SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, NAPX-F4-NC21

Pepper uses matchsticks to make a pattern of shapes, as shown in the table below.
 

 
The equation used to show the relationship between  `T`  and  `N`  is

`T = N + 1` `T = 6N` `T = 6N + 2` `T = 6N - 4`
 
 
 
 
Show Answers Only

`T = 6N – 4`

Show Worked Solution

`T\ text(increases by 6 each shape.)`

`text(Consider)\ T = 6N – 4:`

`text(When)\ \ N = 1, quad T = 6 xx 1 − 4 = 2`

`text(When)\ \ N = 2, quad T = 6 xx 2 − 4 = 8`

`text(When)\ \ N = 3, quad T = 6 xx 3 − 4 = 14`

`:. T = 6N − 4\ text(is correct)`

Algebra, NAPX-F4-NC18

What expression is equivalent to  `−(8 - p)`?

`p - 8` `− p - 8` `p + 8` `− p + 8`
 
 
 
 
Show Answers Only

`p – 8`

Show Worked Solution
`-(8 – p)` `= -8 + p`
  `= p – 8`

Statistics and Probability, NAPX-F4-NC17

Lauren's basketball team has 5 players.

The height of each player is listed below (in cm):
 

`185, 192, 165, 192, 171`
  

What is the median height of these players?

`171\ text(cm)` `181\ text(cm)` `185\ text(cm)` `192\ text(cm)`
 
 
 
 
Show Answers Only

`185\ text(cm)`

Show Worked Solution

`text(Heights in order are:)`

`165, 171, 185, 192, 192`

`:.\ text(Median) = 185\ text(cm)`

Algebra, NAPX-F4-NC16

Three corners of a parallelogram are drawn below.
 

 
Which point below is the fourth corner?

`(3, 5)` `(4, 3)` `(4, 4)` `(5, 3)`
 
 
 
 
Show Answers Only

`(5, 3)`

Show Worked Solution

`text{Consider the far left point on the graph at (-2, 3),}`

`=>\ text(The point below is 3 grid lines down and four right.)`

 

`text{Consider the top point on the graph at (1, 6),}`

`=>\ text{The point 3 grid lines down and four right is (5, 3).}`

Number NAPX-F4-NC15, NAPX-F3-NC21

Barry has a money jar that contains 1 dollar, 50 cent, 20 cent, 10 cent and 5 cent coins only.

If he buys a pavlova worth $3.65, what is the minimum amount of coins he can pay with?

`5` `6` `7` `8` `10`
 
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text(Minimum number of coins would be:)`

`3 xx $1`

`1 xx 50\ text(c)`

`1 xx 10\ text(c)`

`1 xx 5\ text(c)`

`:.\ text(A minimum of 6 coins is needed.)`

Measurement, NAPX-F4-NC14

Dawn takes 4 minutes 15 seconds to swim 200 metres in the pool.

Murray swims the same distance in 2 minutes 25 seconds.

If they start at the same time, how long after Murray finishes will Dawn finish?

 
 `text(1 minute 50 seconds)`
 
 `text(2 minutes 10 seconds)`
 
 `text(2 minutes 50 seconds)`
 
 `text(6 minutes 40 seconds)`
Show Answers Only

`text(1 minute 50 seconds)`

Show Worked Solution
`text(Extra time)` `= 4\ text(min 15 sec less 2 min 25 sec)`
  `= 1\ text(min 50 sec)`

Geometry, NAPX-F4-NC13

Which of the following triangle types is impossible to draw?

 
 a right-angled, scalene triangle
 
 a right-angled, equilateral triangle
 
 an obtuse-angled, isosceles triangle
 
 an acute-angled, scalene triangle
Show Answers Only

`text(a right-angled, equilateral triangle)`

Show Worked Solution

`text(An equilateral triangle has all angles = 60°.)`

`:.\ text(A right-angled, equilateral triangle is impossible.)`

Number, NAPX-F4-NC08

2028 is a tri-square number because

`2^2 + 0^2 + 2^2 = 8`

The next tri-square number after 1102 is

`2036` `2103` `2105` `2116`
 
 
 
 
Show Answers Only

`2105`

Show Worked Solution

`text(Consider each option:)`

`2036 => 2^2 + 0^2 + 3^2 = 13 != 6`

`2103 => 2^2 + 1^2 + 0^2 = 5 != 3`

`2105 => 2^2 + 1^2 + 0^2 = 5` ✓

`2116 => 2^2 + 1^2 + 1^2 = 6` ✓

 

`:.\ text(The next tri-square number is 2105.)`

Number, NAPX-F4-NC04, NAPX-F3-NC08

Hester placed a leg of lamb into his oven in the morning.

The 1st measurement of the lamb's temperature was  −7°C.

Fifteen minutes later, a second temperature reading was taken, which measured  18°C.

What was the change in temperature between the two measurements?

`text(decrease of)\ 25^@text(C)` `text(decrease of)\ 11^@text(C)` `text(increase of)\ 25^@text(C)` `text(increase of)\ 11^@text(C)`
 
 
 
 
Show Answers Only

`text(increase of)\  25^@text(C)`

Show Worked Solution
`text(Change in temperature)` `= 18 – (-7)`
  `= 18 + 7`
  `= 25 text{°C   (increase)}`

Number, NAPX-F4-NC03, NAPX-F3-NC05

A circle is divided into 5 equal areas and labelled, as shown in the diagram below.
 

 
What percentage of the circle's area has been labelled with an even number?

`text(2%)` `text(20%)` `text(30%)` `text(40%)` `text(60%)`
 
 
 
 
 
Show Answers Only

`text(40%)`

Show Worked Solution
`text(Percentage)` `= text(number of evens)/ text(possible numbers)`
  `= 2/5`
  `= 40 text(%)`

Statistics and Probability, NAPX-F4-NC02, NAPX-F3-NC03

This graph shows the number of cockatoos in a gum tree at 15 minute intervals over 4 hours.
 

 
At which time were the highest number of cockatoos in the gum tree?

`4:45` `6:00` `6:15` `6:30`
 
 
 
 
Show Answers Only

`text(6:30 pm)`

Show Worked Solution

`text(The highest data point is two intervals past 6:00 pm.)`

`:.\ text(The highest number were in the tree at 6:30 pm.)`

Number, NAPX-F4-NC01

A swim squad normally swim 80 laps per training session.

On a light training day, they only do three quarters of the laps of a normal session.

How many laps do they do in a light session?

`20` `25` `60` `65` `75`
 
 
 
 
 
Show Answers Only

`60`

Show Worked Solution
`text(Laps)` `= 3/4 xx 80`
  `= 60`

Algebra, NAPX-F4-CA28

Moonjava stacks up identical cups.
 

 
A stack of 3 cups is 18 cm high.

A stack of 6 cups is 28.5 cm high.

What height will a stack of 12 identical cups be?

`72\ text(cm)` `57\ text(cm)` `51.5\ text(cm)` `49.5\ text(cm)`
 
 
 
 
Show Answers Only

`49.5\ text(cm)`

Show Worked Solution

`text{Height difference between (3 cups and 6 cups)}`

`= 28.5 – 18`

`= 10.5\ text(cm)`

`=>\ text(Each cup adds 10.5 ÷ 3 = 3.5 cm.)`

 

`text(S)text(ince 6 cups are 28.5 cm high,)`

`:.\ text(Height of 12 cups)`

`= 28.5 + (6 xx 3.5)`

`= 49.5\ text(cm)`

Number, NAPX-F4-CA26

A red blood cell and a white blood cell have a combined total mass of `4.2 xx 10^-11` grams.

If the red blood cell has a mass of `2 xx 10^-12` grams, what is the mass of the white blood cell?

 
 `4 xx 10^-11\ text(grams)`
 
 `4 xx 10^-12\ text(grams)`
 
 `2.2 xx 10^-11\ text(grams)`
 
 `2.2 xx 10^-12\ text(grams)`
Show Answers Only

`4.0 xx 10^-11\ text(grams)`

Show Worked Solution

`4.2 xx 10^-11-2 xx 10^-12`

`= 4.0 xx 10^-11\ text{(by calculator)}`

Statistics and Probability, NAPX-F4-CA23

A baseball pitcher throws 10 pitches. The speed of each pitch is measured in kilometres per hour and recorded below.

`137, 155, 161, 157, 135, 172, 137, 137, 153, 168`

What is the range of speeds?

 
 `31\ text(km/hr)`
 
 `33\ text(km/hr)`
 
 `35\ text(km/hr)`
 
 `37\ text(km/hr)`
Show Answers Only

`37\ text(centimetres)`

Show Worked Solution
`text(Range)` `=  text(high − low)`
  `= 172 – 135`
  `= 37\ text(centimetres)`

Measurement, NAPX-F4-CA21

A cube has a side length of 8 cm.

Two smaller cubes of side length 4 cm are attached to the larger cube as shown in the diagram below.
 

 
Including the base, what is the surface area of the new object?

`480\ text(cm²)` `496\ text(cm²)` `512\ text(cm²)` `576\ text(cm²)`
 
 
 
 
Show Answers Only

`480\ text(cm²)`

Show Worked Solution

`text(One strategy:)`

`text{Calculate the surface area (S.A.) of each object}`

`text(then deduct the faces not showing.)`

 

`text{S.A. (large cube)} = 6 xx 8 xx 8 = 384\ text(cm²)`

`text{S.A. (small cube)} = 6 xx 4 xx 4 = 96\ text(cm²)`

`text{S.A. (sides not showing)} = 6 xx (4 xx 4) = 96\ text(cm²)`

 

`:.\ text(Total S.A.)`

`= 384 + (2 xx 96) – 96`

`= 480\ text(cm²)`

Algebra, NAPX-F4-CA20

Vivian throws a cricket ball from a height of 2 metres above the ground.

The graph below shows the height of the ball above ground level against the time after Vivian releases the ball.
 

 
How long does the cricket ball travel at or above 3 metres?

`text(2.5 sec)` `text(2.6 sec)` `text(2.8 sec)` `text(3.2 sec)`
 
 
 
 
Show Answers Only

`2.6\ text(sec)`

Show Worked Solution

`text(Ball initially hits 3 m at 0.6 seconds.)`

`text(Ball drops to 3 m at 3.2 seconds.)`

`:.\ text(Ball is at or above 3 m for 2.6 seconds.)`

Statistics and Probability, NAPX-F4-CA19

A survey of 300 Year 10 students asked what brand of phone they owned.

The results are shown in the table below.

One of these students is chosen at random.

What is the probability that the student owns a Nokia phone?

`0.1` `0.2` `0.3` `0.6`
 
 
 
 
Show Answers Only

`0.1`

Show Worked Solution

`text{Pr(owning a Nokia phone)}`

`=30/300`

`= 0.1`

Number, NAPX-F4-CA18

Sachin's cricket bat is pictured below.

 

The handle of the bat is 29 cm in length.

Which of the following show the length of the handle as a percentage of the total length of the bat?

`text(29%)` `text(32%)` `text(33%)` `text(67%)`
 
 
 
 
Show Answers Only

`text(33%)`

Show Worked Solution

`text(Length of the handle as a percentage)`

`= 29/89.1 xx 100`

`= 32.54…%`
 

`:.\ text(33% is the closest.)`

Algebra, NAPX-F4-CA17, NAPX-F3-CA23

Brogan drives a barge that transports sand.

The table below shows the mass of sand, measured in cubic tonnes, of different sand volumes, measured in cubic metres.

 

Brogan's barge has 130 tonnes of sand loaded on it.

How many cubic metres of sand are on his barge?

`91\ text(m³)` `95\ text(m³)` `180\ text(m³)` `186\ text(m³)`
 
 
 
 
Show Answers Only

`91\ text(m³)`

Show Worked Solution

`text(Cubic metres in 1 tonne)`

`= 35/50`

`= 0.7\ text(m³)`

 

`:.\ text(Cubic metres in 130 tonnes)`

`= 0.7 xx 130`

`= 91\ text(tonnes)` 

Measurement, NAPX-F4-CA16

A child's bike tyre has a circumference of 64 cm.

Which of these is closest to the radius of the tyre?

`10.2\ text(cm)` `20.4\ text(cm)` `32.0\ text(cm)` `100.5\ text(cm)`
 
 
 
 
Show Answers Only

`14.3\ text(cm)`

Show Worked Solution
`C` `= 2 pi r`
`64` `= 2pir`
`:. r` `= 64/(2 pi)`
  `= 10.18…\ text(cm)`

Geometry, NAPX-F4-CA15, NAPX-F3-CA21

Elvis enters a park at one of the entries shown below.

The map is drawn to scale but no scale is given.
  

 
He walks 80 metres in a south-west direction and then turns and walks 20 metres in a north-west direction.

Which point on the map shows where Elvis ended up?

`A`   `B`  `C`  `D`
 
 
 
 
Show Answers Only

`text(Point)\ A`

Show Worked Solution

`text(By inspection, the ratio of distances:)`

`text(Entry → Turn : Turn → Point)`

`text(needs to be)\ ~~ 4 : 1`

 

`:.\ text(Elvis enters via Entry 6 and ends up at point)\ A.`

Number, NAPX-F4-CA14

Kelly drives her moped to a beach 100 km away at an average speed of 60 km.

How long does the trip take?

`text(36 minutes)` `text(1 hour 20 minutes)` `text(1 hour 24 minutes)` `text(1 hour 40 minutes)`
 
 
 
 
Show Answers Only

`text(1 hour 40 minutes)`

Show Worked Solution
`text(Time)` `= text(Distance)/text(Speed)`
  `= 100/60`
  `= 1 2/3`
  `= 1\ text(hour 40 minutes)`

Algebra, NAPX-F4-CA12

In an Aussie Rules club, there are 87 players.

There are 19 fewer girls than boys.

How many girls are in the club? 

`27` `34` `53` `68`
 
 
 
 
Show Answers Only

`37`

Show Worked Solution

`text(Strategy 1)`

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

`(x + 19) + x` `= 87`
`2x` `= 68`
`:. x` `= 34`

 

`text(Strategy 2)`

`text{Check each option:}`

`27 + (27 + 19) = 73 \ text{(Incorrect)}`

`34 + (34 + 19) = 87 \ text{(Correct)}`

`53 + (53 + 19) = 125 \ text{(Incorrect)}`

`68 + (68 + 19) = 155 \ text{(Incorrect)}`

Geometry, NAPX-F4-CA11

A pentagon is drawn below.
 

 

 
What is the sum of the five interior angles? 

`360^@` `420^@` `540^@` `720^@`
 
 
 
  
Show Answers Only

`720^@`

Show Worked Solution
`angleA` `= 45^@`
`angleB` `= 360 – 90 = 270^@`
`angleC` `= 90 – 45 = 45^@`
`angleD` `= angleE = 90^@`

 

`:.\ text(Sum of interior angles)`

`= 45 + 270 + 45 + 90 + 90`

`= 540^@`

Statistics and Probability, NAPX-F4-CA10

In 2017, an estimated 8.7 million vehicle owners in Australia registered their cars.

The average cost of one registration was estimated at  $473.

What was the total amount paid for registrations in 2017?

`$1\ 839\ 323` `$411\ 510\ 000` `$1\ 839\ 323\ 467` `$4\ 115\ 100\ 000`
 
 
 
 
Show Answers Only

`$4\ 115\ 100\ 000`

Show Worked Solution
`text(Total)` `= 8\ 700\ 000 xx 473`
  `= $4\ 115\ 100\ 000`

Measurement, NAPX-F4-CA08

A trapezium is constructed on a grid of 10 rectangles.

Each rectangle measures  3 cm × 7 cm.
 

 

 
What is the area of the trapezium?

`150\ text(cm²)` `168\ text(cm²)` `189\ text(cm²)` `210\ text(cm²)`
 
 
 
  
Show Answers Only

`168\ text(cm²)`

Show Worked Solution
`text(Area 1 rectangle)` `= 3 xx 7`
  `= 21\ text(cm²)`

 

`:.\ text(Total Area)` `= (6 xx 21) + 2\ text(triangles)`
  `= 6 xx 21 + 2 xx (1/2 xx 3 xx 14)`
  `= 126 + 42`
  `= 168\ text(cm²)`

Number, NAPX-F4-CA07

Darryl buys some jousting sticks online that costs him $213.

The postage costs involved are listed in the table below.

The jousting sticks weigh 1.3 kg.

What does Darryl have to pay, in total, to purchase the jousting sticks and have them delivered?

`$225` `$230.50` `$234.75` `$238`
 
 
 
 
Show Answers Only

`$238`

Show Worked Solution
`text(Total Cost)` `= 213 + text(delivery)`
  `= 213 + 25`
  `= $238`

Number, NAPX-F4-CA06

Lloyd walks to work. The distance is 320 metres.

A road closure means that Lloyd's walk is 5% longer.

What distance does he need to walk now?

`304\ text(metres)` `325\ text(metres)` `336\ text(metres)` `480\ text(metres)`
 
 
 
 
Show Answers Only

`336\ text(metres)`

Show Worked Solution
`text(Distance)` `= 320 + 5text(%) xx 320`
  `= 1.05 xx 320`
  `= 336\ text(m)`

Geometry, NAPX-F4-CA05

Clive makes a shape using 5 cubes.
 

 
He paints all sides of the shape green, including the base, and later separates the cubes.

How many cube faces will be green?

`18` `20` `22` `24` `30`
 
 
 
 
 
Show Answers Only

`22`

Show Worked Solution

`text(Faces on top = 5)`

`text(Faces on bottom = 5)`

`text(Side faces)` `= 3 + 1 + 1 + 2 + 1 + 2 + 1 + 1`
  `= 12`

 

`:.\ text(Total green faces = 22)`

Number, NAPX-F4-CA04

The number of visitors to the MONA Museum in Hobart over the three months of Summer is recorded in a table.

What was the total number of visitors to MONA over the whole Summer, to the nearest 1000?

`180\ 000` `188\ 000` `189\ 000` `190\ 000`
 
 
 
 
Show Answers Only

`189\ 000\ text{(nearest 1000)}`

Show Worked Solution

`48\ 321 + 79\ 859 + 60\ 571`

`= 188\ 751`

`= 189\ 000\ \ text{(to nearest 1000)}`

Geometry, NAPX-F4-CA02

The distance between Sydney and Dubbo on the map below is 7 cm.
 

 
The scale of the map is  1 cm = 50 km.

What is the actual distance between Sydney and Dubbo?

`57\ text(km)` `350\ text(km)` `500\ text(km)` `700\ text(km)`
 
 
 
 
Show Answers Only

`350\ text(km)`

Show Worked Solution
`text(Actual Distance)` `= 7 xx 50`
  `= 350\ text(km)`

Number, NAPX-F4-CA01

The distance around a Formula One racetrack is 4.39 kilometres.

How long is a race of 22 laps?

`5.01\ text(km)` `17.61\ text(km)` `26.39\ text(km)` `56.32\ text(km)` `96.58\ text(km)`
 
 
 
 
 
Show Answers Only

`96.58\ text(km)`

Show Worked Solution
`text(Distance)` `= 22 xx 4.39`
  `= 96.58\ text(km)`

Number, NAPX-G4-NC26

The table below shows all the people at Vamp's birthday party.
 

  
What fraction of the children at the party are female?

`20/30` `20/50` `35/50` `20/100` `35/100`
 
 
 
 
 
Show Answers Only

`20/50`

Show Worked Solution
`text(Fraction)` `= text(female children)/text(total children)`
  `= 20/((30 + 20))`
  `= 20/50`

Algebra, NAPX-G4-NC24

Harley solved the following equation:

`4x + 3 = 12`

Which of the following could be two lines of her solution?

`4x` `= 15` `4x` `= 15` `4x` `= 9` `4x` `= 9`
`x` `= 15/4` `x` `= 4/15` `x` `= 9/4` `x` `= 4/9`
 
 
 
 
Show Answers Only

`x = 9/4`

Show Worked Solution
`4x + 3` `= 12`
`4x` `= 9`
`x` `= 9/4`

Number, NAPX-G4-NC22

Kate has a litter of 10 puppies.

They eat 6 kilograms of puppy food per day, in total.

How many kilograms of puppy food would 1 puppy eat in one week?

`0.6\ text(kilograms)` `4.2\ text(kilograms)` `6\ text(kilograms)` `42\ text(kilograms)`
 
 
 
 
Show Answers Only

`4.2\ text(kilograms)`

Show Worked Solution

`text(Food eaten by 1 puppy in 1 day)`

`=6-:10`

`=0.6\ text(kg)`

 

`:.\ text(Food for 1 puppy in 1 week)`

`=7 xx 0.6`

`=4.2\ text(kg)`

Geometry, NAPX-G4-NC21

Wyatt enters a park and wants to get to the pond.
 

 

 
Which route is the shortest distance Wyatt can take?

Route 1 Route 2 Route 3 Route 4
 
 
 
 
Show Answers Only

`text(Route 2)`

Show Worked Solution

`text(Shortest: Route 2)`

`text(Route 2 has the longest diagonal section which is)`

`text(shorter than the distance around the outside of)`

`text(any rectangle.)`

Geometry, NAPX-G4-NC18

 
Two triangles, `AOB` and `DOC` are drawn in a circle with centre `O`.

The two triangles are best described as:

`text(right-angled)` `text(isosceles)` `text(scalene)` `text(equilateral)`
 
 
 
 
Show Answers Only

`text(isosceles)`

Show Worked Solution

`OD = OC = OB = OA\ (text(radii))`

`:. DeltaAOB\ text(and)\ DeltaDOC\ text(are isosceles.)`

Number, NAPX-G4-NC16

A birthday cake is cut into 12 equal pieces.

Only the shaded pieces below are left.
 

 

 
What percentage represents the amount of cake left?

`text(20%)` `text(25%)` `text(27.5%)` `text(33%)`
 
 
 
 
Show Answers Only

`text(33%)`

Show Worked Solution
`text(Percentage)` `=text(pieces left)/text(total pieces)`
  `= 4/12`
  `= 1/3`
  `= 33.33… text(%)`

Statistics and Probability, NAPX-G4-NC13

Kooger spins the arrow on two identical spinners.

The arrow on each spinner is equally likely to land on 1, 2 or 3.
 

 
If Kooger adds up the two results, which total is he least likely to get?

`6` `5` `4` `3`
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text{6 can only result from (3, 3).}`

`text(All other totals can result from)`

`text(more than 1 combination.)`

Number, NAPX-G4-NC11, NAPX-G3-NC15

4 groups of backpackers picked strawberries over two hours.

The weight of the strawberries collected (in kg) by the groups in each hour is shown in the table below.
 

 
Which group picked the greatest mass over the two hours?

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

`text(Group 1:  20.37 kg)`

Show Worked Solution

`text(Group 1:)`

`9.4 + 10.97 = 20.37\ text(kg)`

Algebra, NAPX-G4-NC14

Peter has 6 more golf balls than Roger.

Using  `p`  for the number of Peter's golf balls and  `r`  for Roger's golf balls, which equation correctly describes this fact?

`r = p + 6` `r = 6 - p` `p = 6 - r` `p = r + 6`
 
 
 
 
Show Answers Only

`p = r + 6`

Show Worked Solution

`p = r + 6`

Measurement, NAPX-G4-NC10, NAPX-G3-NC14

The flask pictured below can hold up to 100 mL of water.
 

 
How much water is in the flask?

`50\ text(mL)` `70\ text(mL)` `75\ text(mL)`  `80\ text(mL)`
 
 
 
 
Show Answers Only

`text(75 mL)`

Show Worked Solution

`text(Flask is fully filled until the 50 mL mark.)`

`text(Flask is half filled between 50 – 100 mL marks.)`

`:.\ text(Volume of water in the flask)`

`= 50 + 1/2 xx 50`

`= 75\ text(mL)`

Number, NAPX-G4-NC08

Chloe has $20 to buy fruit from the local farmer's market.

She buys one avocado and a pineapple.

How much change should Chloe be given?

`$13.30` `$14.30` `$16.70` `$26.70`
 
 
 
 
Show Answers Only

`$13.30`

Show Worked Solution
`text(Change)` `= 20 – (2.90 + 3.80)`
  `= 20 – 6.70`
  `= $13.30`