When 1 mm of rain falls on 1 m² of a pool, 1 litre of water is collected.
A pool of what surface area is needed to collect 6000 litres from a rainfall of 15 mm?
| m² |
Geometry, NAP-D4-NC29 SA
A star is drawn on the inside of a regular pentagon, as shown below.
What is the size of the angle marked
| degrees |
Show Worked Solution
STRATEGY: The internal angle sum is 3 × 180 = 540 (since 3 triangles can be drawn internally from one point).
Measurement, NAP-C4-NC32 SA
The total surface area of a cube is 150 cm².
How long is an edge of the cube?
| cm |
Probability, NAP-C4-NC31 SA
Sharif has a lock on his bike.
To open his lock he moves the 4-digit dial to show 1221.
If each dial can be any number 0-9, how many different 4-digit codes, including Sharif's, are possible?
Number, NAP-C4-NC30 SA
Terry picked some pears from his orchard.
Exactly 45% of the pears picked were not good to eat.
What is the smallest total number of pears that he could have collected?
| pears |
Algebra, NAP-C4-NC28 SA
Freya buys 2 of the same chocolate bars from the shop.
She breaks the first chocolate bar into 3 identical pieces.
She then breaks the second chocolate bar into 6 identical pieces.
One of the larger pieces of chocolate weighs 12 grams more than one of the smaller pieces.
What is the mass of one whole chocolate bar?
| grams |
Geometry, NAP-C4-NC27
Eloise is taking a ride on a ferris wheel.
It takes her 5 minutes to complete a full lap.
What angle does the Ferris wheel turn through in 75 seconds?
| ° |
Measurement, NAP-D3-NC32 SA
Anthony creates a tile pattern using tiles in the shape of regular hexagons.
The perimeter of each tile is 24 cm.
He arranges them in the following way.
He keeps adding tiles in the same way until he has a row with a perimeter of 120 cm.
How many tiles are in Anthony's row?
Number, NAP-D3-NC31 SA
Probability, NAP-D3-NC30 SA
In any standard six-sided dice, the sum of the opposite faces is 7.
Milo rolls 3 dice and the total of the top faces is 5.
What is the sum of the three opposite faces?
Algebra, NAP-E3-CA29 SA
Bill creates a pattern of branches and nodes on a computer.
Bill continued the pattern until the shape had 3279 branches.
How many nodes did the shape have?
Measurement, NAP-E3-CA28 SA
Guy builds a brick structure that is pictured below.
The structure is 7 bricks high, 7 bricks wide and 6 bricks deep.
The structure is solid brick but has a hole that goes from one side to the other which is 3 bricks high and two bricks wide, as shown in the diagram.
How many bricks are in the stack?
Number, NAP-E3-CA32
Cassie has a money box with only 50 cent and 20 cent coins in it.
The total mass of the coins in her money box is 91.8 grams.
Cassie knows that:
- the mass of a 50 cent coin is 10.7 grams.
- the mass of a 20 cent coin is 7 grams
What is the smallest mass of exactly $1.20.
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What is the total value of the coins in Cassie's money box?
| $ |
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Measurement, NAP-E3-NC31 SA
This triangle was made by cutting a square in half.
The perimeter of the triangle is 51.21 cm.
What is the area of the triangle?
| square centimetres |
Geometry, NAP-E3-NC30 SA
The design below is created using squares and equilateral triangles only.
What is the length of the design?
| cm |
Algebra, NAP-E3-NC28 SA
Damon bought 2 identical bags of salt for his swimming pool.
After he used
How many kilograms of salt were in one full bag?
| kilograms |
Measurement, NAP-F3-CA32 SA
A square has an area of 169 square centimetres.
What is the perimeter?
| centimetres |
Number, NAP-F3-CA31 SA
Gary used 4 litres of paint to paint a wall.
The wall was a rectangle 2 metres high and 3 metres wide.
How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 5 metres wide?
| litres |
Number, NAP-F3-CA30 SA
A pet store sells its high growth dog food in four different sizes.
What is the lowest price a customer can pay for 10 kg of high growth dog food?
| $ |
Geometry, NAP-F3-CA29 SA
Towns
The distance from Town
What is the distance from Town
| kilometres |
Number, NAP-F3-CA28 SA
Richard bought a second hand snowboard at a cost of $390.
Richard had to spend 65% of his savings to buy the snowboard.
How much did Richard have in his savings after buying the snowboard?
| $ |
Number, NAP-E3-NC27 SA
Nona makes maple syrup on her farm.
The mass of 400 millilitres of her maple syrup is 600 grams.
How many litres is 2.4 kilogram of Nona's maple syrup?
| litres |
Number, NAP-C3-CA32 SA
John's old tractor used 8.3 litres of fuel per 100km.
His new tractor uses 5.9 litres of fuel per 100 km.
John pays $1.35 per litre and drives 20,000 km each year.
How much money will John save on fuel each year with his new tractor?
| $ |
Algebra, NAP-C3-CA31 SA
A construction company uses the following rule to calculate the cost of concrete.
cost in dollars = ($59.50 × volume in cubic metres) + ($8.90 × delivery distance in km)
Jim paid the company $713 for 6 cubic metres of concrete.
What delivery distance was Jim charged for?
| km |
Number, NAP-C3-CA29 SA
Natalie is building a brick wall 9 metres high.
The height of a column of 15 bricks is 1.8 metres as shown.
How many bricks will Natalie need for a wall 9 metres high?
Measurement, NAP-F3-NC32 SA
A farmer uses an existing stone wall and fencing to create a large grazing paddock for his sheep, as shown in the diagram below.
The fencing has 3-strand wiring which is also shown below.
How many kilometres of fencing will be required?
| kilometres |
Number, NAP-F3-NC31 SA
Adam is laying tiles in the pattern shown below.
He uses three white tiles for every four gray tiles as shown.
He uses a total of 133 tiles.
How many gray tiles does he use?
Number, NAP-F3-NC29
The graph below can be used to calculate the width of any photograph from its height.
Using the graph, a photo with a height of 5 centimetres should be approximately what width?
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Statistics, NAP-F3-NC28 SA
Tom collected data on the number of big game animals in an African wildlife park.
This graph shows how many big game animals lived in the park.
There were 16 more elephants than rhinos in the wildlife park.
How many big game animals were in the park in total?
Number, NAP-G3-NC32 SA
The fraction
What does
Number, NAP-G3-NC27
Which fraction is halfway between
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Number, NAP-G3-CA32
Ali had a bag of different coloured marbles.
Her bag contained 4 more yelllow marbles than blue.
How many marbles were in Ali's bag?
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Number, NAP-G3-CA31 SA
One litre of softdrink contains 90 grams of sugar.
How many millilitres of softdrink contain 4.5 grams of sugar?
| millilitres |
Measurement, NAP-G3-CA30 SA
Sam moves into a new rectangular office that measures 4.5 m × 3 m.
He decides to cover the floor with square carpet tiles.
How many boxes of carpet tiles does Sam need to order?
Number, NAP-H3-NC32 SA
Charlie is buying sweets for a party.
He buys twice as many candy canes as chocolate bars, and six times as many candy canes as sherbert sticks.
He has 24 more chocolate bars than sherbert sticks.
How many sherbert sticks does Charlie have?
Number, NAP-H3-NC30
Which of these is not equal to
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Number, NAP-H3-NC28
Which two odd numbers, greater than 1, have a product of 91?
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Measurement, NAP-I3-CA32 SA
Ky designs an outdoor table that is in the shape of a trapezium.
The dimensions of the table top are shown in the picture below.
What is the area of Ky's table top?
| cm² |
Number, NAP-I3-CA30 SA
Kurt is travelling from Newcastle to Sydney. The journey is 165 kilometres.
His car uses 8.35 litres of fuel per 100 kilometres.
How much fuel will Kurt need to make the journey?
Round your answer to the nearest litre.
| litres |
Algebra, NAP-I3-CA27 SA
Tim is going on a golfing trip.
He wants to purchase balls before the trip, which are sold in boxes of a dozen.
The more boxes of balls that Tim buys, the less it costs per box, as shown in the table below.
If this price pattern continues, how much will it cost for 7 boxes of balls?
| $ |
Geometry, NAP-H3-CA32 SA
In the diagram
What is the size of the angle marked
| degrees |
Show Worked Solution
Number, NAP-H3-CA31
Maria has a square photo with an area of 16 cm².
She enlarges the photo to have an area of 64 cm².
The enlargement multiplied the side lengths of the original photo by a factor of
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Number, NAP-H3-CA29 SA
Charlie is five years younger than Murray.
Murray is four years younger than half of Barry's age.
The sum of all three ages is 59.
How old is Barry?
Number, NAP-H3-CA28 SA
Harrison was saving his money to buy a cricket bat.
After 1 month, he had saved 45% of the bat's cost.
After 2 months, he had saved another $90 and now had 75% of the bat's cost.
How much does the bat cost?
| $ |
Geometry, NAP-I3-NC32 SA
The objects below can be used as dice in a board game.
How many edges does one of these objects have?
Number, NAP-I3-NC31 SA
Jack is at school and his age this year is a prime number and a factor of 65.
In two years' time, Jack's age will again be a prime number.
What is Jack's age this year?
Number, NAP-I3-NC27 SA
A box of golf balls normally cost $19.50.
During a sale, the golf shop took 10% off the regular price of the balls.
What is the new sale price of the golf balls?
| $ |
Measurement, NAP-E4-CA32 SA
Two views of a trapezoidal prism are shown below.
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Each square on this grid has an area of one square centimetre.
The vertical edges of the prism are 4 centimetres.
What is the volume of the prism in cubic centimetres?
| cubic centimetres |
Show Worked Solution
Measurement, NAP-E4-CA31 SA
A net of a cube is pictured below.
The cube has a volume of 512 cubic centimetres.
What is the height of the net in centimetres?
| centimetres |
Algebra, NAP-E4-CA30 SA
In a ping pong competition with 4 players, each person plays all other players once.
In a competition with 4 players, there are 6 games.
The formula below gives the total number of games
What is the value of
Geometry, NAP-E4-CA29
A company logo is 14 cm by 9 cm.
Pablo wants to project it onto a screen that is 4.2 m by 3 m.
Pablo enlarges the logo as big as possible without distorting its proportions.
What are the dimensions of the enlarged logo, once projected, in cm?
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cm by |
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Geometry, NAP-E4-CA28 SA
Gabby put 5 points on a grid and labelled them
Point
Gabby adds a sixth point,
How far is point
| millimetres |
Show Worked Solution
Number, NAP-E4-CA27 SA
A marine conservationist records the number of eggs laid by 3 turtles and the number of those eggs that hatched.
Her results are recorded in the table below:
What percentage of the eggs from all 3 turtles hatched?
| % |
Measurement, NAP-E4-CA26
A tiler is tiling a wall that is 90 cm wide and 160 cm high.
He uses triangular tiles that are drawn below.
The tiler uses all of his tiles and has no gaps between them.
How many tiles does he need?
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Geometry, NAP-C3-NC32 SA
Two squares are drawn on the sides of an equilateral triangle as shown.
A straight line was drawn through the point where the 3 shapes touch.
What is the size of the shaded angle?
| ° |
Show Worked Solution
Number, NAP-C3-NC31 SA
Billy has some bananas to give to his friends.
If he gives each friend 3 bananas. he will have 5 left over.
He cannot give each friend 4 bananas because he would need 7 more bananas.
How many bananas does Billy have?
Number, NAP-C3-NC29 SA
Freya buys 2 of the same chocolate bars from the shop.
She breaks the first chocolate bar into 3 identical pieces.
She then breaks the second chocolate bar into 6 identical pieces.
One of the larger pieces of chocolate weighs 12 grams more than one of the smaller pieces.
What is the mass of one whole chocolate bar?
| grams |
Statistics, NAP-C3-NC28
Each bar on this graph shows the population of a country and the population of its capital city.
The white section is the population that lives in the capital city.
The black section is the population that lives outside the capital city.
Which of the following countries has the highest percentage of its population living in its capital city?
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Number, NAP-E4-CA24 SA
John and Fiona each bought a quantity of the same prawns from the fish markets.
John bought a quarter of the quantity that Fiona bought.
The total cost of John and Fiona's prawns was $30.60.
What was the cost of Fiona's prawns?
| $ |
Geometry, NAP-E4-NC32 SA
Two circles have the same centre,
The radius of the small circle is
Arc
What is the length of the arc
| cm |