Guy uses a rectangular prism pictured below as a basic building block.
He stacks the blocks and makes a solid cube.
What is the smallest possible number of blocks needed to make a cube?
Show Worked Solution
Geometry, NAP-E4-NC30 SA
Igor was designing a shield using 10 identical isosceles triangles, as shown in the diagram below.
How many degrees in the angle marked
| degrees |
Measurement, NAP-E4-NC29 SA
The octagon below is divided into identical squares and identical triangles.
The area of the octagon is a multiple of the area of one of the squares.
The area of the octagon is 252 cm².
What is the side length of each square?
| cm |
Number, NAP-E4-NC28 SA
Write the answer to this division in the box.
Number, NAP-E4-NC27 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-F4-CA32 SA
In this pattern of squares, each smaller square is half the area of the next biggest square.
What is the area of the grey part of the pattern?
| square centimetres |
Measurement, NAP-F4-CA31 SA
Barry pours two identical cubes of cement as foundation for a large sculpture, as shown in the diagram below.
If 432 cubic metres are required to form the foundation, what is the height of the foundation, as shown on the diagram?
| metres |
Geometry, NAP-F4-CA30 SA
5 towns are drawn in the diagram below and labelled T1 to T5.
The range of travel times between towns is shown on the diagram.
What is the shortest possible travel time from T1 to T5?
| minutes |
Algebra, NAP-F4-CA29 SA
The mass of a macaw is 1.44 kilograms.
Its wingspan is 1.26 metres.
A rule that can be used to approximately predict the wingspan of a macaw from its mass is.
where
What is the difference in centimetres between the macaw's actual wingspan and the wingspan predicted by the rule?
| centimetres |
Geometry, NAP-F4-NC32 SA
Trapeziums
What is the distance from
| metres |
Measurement, NAP-F4-NC31 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 wire will be required?
| kilometres |
Number, NAP-F4-NC30 SA
Marshall keeps a tin of lollipops on his desk at home.
His son Dallas takes 1 lollipop out every 3 days.
Marshall adds a new lollipop to the tin every 4 days.
The lollipops in Marshall's tin are decreasing by 1 lollipop every
What is the value of
Measurement, NAP-F4-NC29
A wheelchair ramp is pictured below.
The ramp is in the shape of a triangular prism?
What is the volume of the ramp?
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Algebra, NAP-F4-CA28
Angela stacks up identical cups.
A stack of 3 cups is 21 cm high.
A stack of 6 cups is 30 cm high.
What height will a stack of 10 similar cups be?
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Number, NAP-F4-CA26
A red blood cell and a white blood cell have a combined total mass of
If the red blood cell has a mass of
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Number, NAP-F4-CA24 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?
| $ |
Algebra, NAP-F4-NC28 SA
The distance between
The distance from
The distance from
What is the distance between
| kilometres |
Algebra, NAP-F4-NC27
The graph below can be used to approximately convert kilograms to pounds.
Using the graph, a mass of 6 kilograms is closest to
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Algebra, NAP-F4-NC25
Anthony is tiling his bathroom.
He follows this pattern to make a line of tiles that is 90 cm long.
How many tiles are in this line?
Measurement, NAP-F4-NC24 SA
What is the area of the shaded part of the figure?
| square centimetres |
Geometry, NAP-F4-NC22 SA
Craig has a drum which has the top and bottom in the shape of regular octagons, as shown below.
The other faces are isosceles triangles.
How many edges does Craig's drum have?
Algebra, NAP-F4-NC19 SA
What is the smallest positive whole number
Number, NAP-G4-NC32 SA
Joe is in a 2-day rally car race.
On day 1, Joe takes 1 hour and 15 minutes to travel 105 km.
On day 2, Joe takes 1 hour and 30 minutes to travel 225 km.
What is Joe's average speed over the 2 days.
| kilometres per hour |
Algebra, NAP-G4-NC31 SA
Ian was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes.
The first temperature taken was
The second temperature was
The third measurement showed that the temperature had increased one and a half times the previous increase.
What was the third temperature?
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Algebra, NAP-G4-NC30 SA
Their total savings together is $63.
How much has Cianna saved?
Number, NAP-G4-NC29 SA
Candy has read
If her new book has 400 pages, how many pages has she read?
Geometry, NAP-G4-NC28 SA
The edges of a 4 × 4 × 4 cube are formed using blocks as shown below:
In total, 32 blocks are used.
How many blocks would be needed to make the edges of an 8 × 8 × 8 cube in the same way?
Measurement, NAP-H4-NC27
A regular hexagon is formed using equilateral triangles.
It has a perimeter of 18 cm, and is cut in half.
What it the perimeter of half of the hexagon?
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Measurement, NAP-G4-CA32
The rectangular prism, shown below, is cut in half to form 2 equal cubes.
What is the ratio of the surface area of the rectangular prism to one of the cubes?
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Measurement, NAP-G4-CA31 SA
An ancient building has the shape of a trapezoidal prism.
The shaded side is a trapezium that has an area of 84 m².
What is the volume of the building in m³ ?
| m³ |
Algebra, NAP-G4-CA30
Mark had a small orchard on his farm.
Mark has
How many trees does Mark have?
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Algebra, NAP-G4-CA29 SA
Find the value of
Geometry, NAP-G4-CA28
What is the size of
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Measurement, NAP-G4-CA27 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-G4-CA26 SA
On a weekend, Abbey works 8 hours at her normal pay rate and 12 hours at time and a half of her normal pay.
Abbey was paid $707.20 in total for this work.
What is her normal pay rate per hour?
| $ |
Algebra, NAP-G4-CA25 SA
The rule for the graph is
The graph shows that if a person's eyes are 4 metres above the ground, they can see 6 km to the horizon.
Use this to calculate the value of
Algebra, NAP-H4-NC32 SA
Ralph is
Peter is
Ralph is
How old is Murray in years?
| years |
Algebra, NAP-H4-NC31 SA
Renee created a shape using equilateral triangles and squares.
She begins by using a triangle with side length 1 cm.
She then adds a square, then another triangle, then a square etc... until she has 5 triangles and 5 squares.
What will the perimeter of the whole shape be?
| cm |
Measurement, NAP-H4-NC30
David's backyard is in shape of a rectangle and has an area of 50 m².
Tim's backyard is also rectangular but with side lengths that are double those of David's backyard.
What is the area of Tim's backyard.
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Measurement, NAP-H4-NC29 SA
A rectangular trough in a paddock provides water for horses.
Its measurements can be seen below:
One cubic metre holds 1000 litres of water.
How many litres of water will fill the trough?
| litres |
Algebra, NAP-H4-NC28
Mal drew the line
He then drew
What are the coordinates of the intersection point of these two lines?
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Show Worked Solution
Algebra, NAP-H4-NC26
What is the value of
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Algebra, NAP-H4-NC24
Sharon made a number pattern using this rule:
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are whole numbers. |
Her number pattern is:
What is the next number in Sharon's pattern?
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Numbers, NAP-H4-NC23 SA
It takes 2 people 10 hours to pick 800 lettuces during harvesting.
At the same rate, how many hours should it take for 5 people to pick 1200 lettuces?
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Number, NAP-H4-NC21
Simplify:
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Measurement, NAP-H4-CA32 SA
Pedro cuts a sector from a circle so that
If the circle's radius is 5 cm, what is the perimeter of the shape, to the nearest centimetre?
| cm |
Number, NAP-H4-CA31 SA
The product of three different positive whole numbers is 40.
What is the largest possible sum of the three numbers?
Geometry, NAP-H4-CA30 SA
In the diagram
What is the size of the angle marked
| degrees |
Show Worked Solution
Algebra, NAP-H4-CA29
Which of these equations represents the line in the graph?
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Measurement, NAP-H4-CA28 SA
A cement slab is laid in Bob's backyard that forms a 9 m × 3 m rectangle.
Bob is going to tile around the edge of his slab using one row of 300 mm × 300 mm tiles.
He will use 50% black tiles costing $8 per tile and 50% white tiles costing $5 per tile.
What is the total cost of the tiles he used?
| $ |
Number, NAP-H4-CA27
A dress was on sale with 25% discount.
As a regular customer, Kate received a further 10% on the already discounted price.
What was the overall percentage discount Kate received?
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Geometry, NAP-H4-CA26
Which statement is always true?
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Scalene triangles have two angles that are equal. |
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All angles in a parallelogram are equal. |
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The opposite sides of a trapezium are equal in length. |
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The diagonals of a rhombus are perpendicular to each other. |
Algebra, NAP-H4-CA24 SA
Mike uses match sticks to make a pattern of houses.
When a shape consists of 7 houses, how many sticks will the shape have?
Measurement, NAP-H4-CA25 SA
A large sculpture is made in the shape of a cube.
The total length of all of its edges is 60 metres.
What is the volume of the cube?
| m³ |
Number, NAP-H4-CA22
It takes 15 minutes for all of the sand to flow through a sand timer.
The sand timer contains 475 grams of sand.
Each millilitre of sand weighs 1.5 grams.
How many millilitres of sand flow through the timer per minute?
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Number, NAP-I4-NC32
Mark and Jim have property sizes as shown in the table below:
What is the ratio of the land area of Mark's property to Jim's property.
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Geometry, NAP-I4-NC31 SA
Lee travels from
How many metres less would Lee travel if he travelled directly from
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Number, NAP-I4-NC30 SA
Suzie rents a caravan from a hire company.
The cost to rent the caravan is directly proportional to the number of kilometers driven.
The rental cost to drive 200 km is $112.50.
What is the rental cost to drive 60 kilometres?
Measurement, NAP-I4-NC29
Leigh has a picnic blanket with an area of 5 square metres.
What is the area of her picnic blanket in square centimetres?
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Number, NAP-I4-NC28 SA
Angus bought a tennis racket which cost $22.50 before the Goods and Services Tax (GST) was added.
How much did Angus' tennis racket cost after adding the 10% GST?