Aussie Maths & Science Teachers: Save your time with SmarterEd
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?
`text(The smallest cube will have the)`
`text(smallest base:)`
`text(Base will have 12 blocks.)`
`text(Cube will have 12 stacked levels.)`
`:.\ text(Blocks needed for the smallest cube)`
`= 12 xx 12`
`= 144`
Igor was designing a shield using 10 identical isosceles triangles, as shown in the diagram below.
How many degrees in the angle marked `x`?
| degrees |
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 |
Write the answer to this division in the box.
| `11.66 ÷ 0.11 =` |
Damon bought 2 identical bags of salt for his swimming pool.
After he used `2/3` of one bag in the pool, he had a total of 20 kilograms of salt left.
How many kilograms of salt were in one full bag?
| kilograms |
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 |
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 |
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 |
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.
`w = sqrt m`
where `w` is the wingspan in metres and `m` is the mass in kilograms.
What is the difference in centimetres between the macaw's actual wingspan and the wingspan predicted by the rule?
| centimetres |
Trapeziums `ABCD` and `AEFG` are similar.
What is the distance from `E` to `F`?
| metres |
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 |
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 `x` days.
What is the value of `x`?
A wheelchair ramp is pictured below.
The ramp is in the shape of a triangular prism?
What is the volume of the ramp?
| `7.2\ text(m³)` | `3.6\ text(m³)` | `0.72\ text(m³)` | `0.36\ text(m³)` |
|
|
|
|
|
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?
| `70\ text(cm)` | `54\ text(cm)` | `50\ text(cm)` | `42\ text(cm)` |
|
|
|
|
|
A red blood cell and a white blood cell have a combined total mass of `1.3 xx 10^-10` grams.
If the red blood cell has a mass of `3 xx 10^-11` grams, what is the mass of the white blood cell?
|
|
`1 xx 10^-10\ text(grams)` |
|
|
`1 xx 10^-11\ text(grams)` |
|
|
`1.7 xx 10^-10\ text(grams)` |
|
|
`1.7 xx 10^-11\ text(grams)` |
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?
| $ |
`P`, `Q`, `R` and `S` are towns that lie on a straight train track as shown below.
The distance between `P` and `Q` is half the distance from `P` to `S`.
The distance from `R` to `S` is one-sixth the distance from `P` to `S`.
The distance from `Q` to `R` is 15 km.
What is the distance between `P` and `S`?
| kilometres |
The graph below can be used to approximately convert kilograms to pounds.
Using the graph, a mass of 6 kilograms is closest to
|
|
`11.8\ text(pounds)` |
|
|
`12.1\ text(pounds)` |
|
|
`12.2\ text(pounds)` |
|
|
`13.2\ text(pounds)` |
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?
What is the area of the shaded part of the figure?
| square centimetres |
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?
`x^2 > 5x`
What is the smallest positive whole number `x` can be that makes this expression correct?
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 |
Ian was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes.
The first temperature taken was `−2.6^@text(C)`.
The second temperature was `2.4^@text(C)`.
The third measurement showed that the temperature had increased one and a half times the previous increase.
What was the third temperature?
| `\ ^@text(C)` |
`1/4` of Riley's savings equals `1/3` of Cianna's savings.
Their total savings together is $63.
How much has Cianna saved?
| `$` |
Candy has read `3/16` of her new book.
If her new book has 400 pages, how many pages has she read?
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?
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?
| `text(7 cm)` | `text(9 cm)` | `text(12 cm)` | `text(14 cm)` | `text(15 cm)` |
|
|
|
|
|
|
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?
| `3 : 5` | `5 : 3` | `1 : 2` | `2 : 1` |
|
|
|
|
|
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 |
Mark had a small orchard on his farm.
`1/6` of his trees were lemon trees and `1/2` were orange trees.
Mark has `14` more orange trees than lemon trees.
How many trees does Mark have?
| `28` | `36` | `42` | `84` |
|
|
|
|
|
`4/45 = 3/40 + 1/x`
Find the value of `x?`
`ABCD` is a rhombus. `AC` is the same length as the rhombus sides.
What is the size of `/_ DCB?`
| `90^@` | `100^@` | `110^@` | `120^@` | `130^@` |
|
|
|
|
|
|
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?
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?
| $ |
The rule for the graph is
`h = d^2/k`
`h` is the height in metres, of a person's eyes above the ground.
`d` is the distance a person can see to the horizon.
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 `k.`
Ralph is `1/2` the age of Murray.
Peter is `1/3` the age of Murray.
Ralph is `8` years older than Peter.
How old is Murray in years?
| years |
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 |
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.
| `25\ text(m²)` | `100\ text(m²)` | `200\ text(m²)` | `300\ text(m²)` |
|
|
|
|
|
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 |
Mal drew the line `y = 4 - x` on a grid.
He then drew `y = x -2` on the same grid.
What are the coordinates of the intersection point of these two lines?
| `(−1,3)` | `(1,3)` | `(3,−1)` | `(3,1)` |
|
|
|
|
|
`text(Strategy one: graph each line and see the intercept.)`
`text(Strategy two:)`
`text(Testing each set of coordinates in both equations,)`
`text{consider the 4th option, (3,1).}`
`1=4-3\ \ text{(satisfies 1st equation)}`
`1=3-2\ \ text{(satisfies 2nd equation)}`
`=>\ (3,1)\ \ text(is the intersection point.)`
`x/3 = 5/13`
What is the value of `x`?
| `5/39` | `15/39` | `8/13` | `15/13` |
|
|
|
|
|
Sharon made a number pattern using this rule:
| next number = previous number × |  |
+ |  |
| |
and | |
are whole numbers. |
Her number pattern is:
`−2, −1, 1, 5, 13, …`
What is the next number in Sharon's pattern?
| `17` | `19` | `21` | `29` |
|
|
|
|
|
`text(Using the rule:)`
| `−1` | `= −2 xx` | |
`+` | |
`…\ (1)` |
| `1` | `= −1 xx` | |
`+` | |
`…\ (2)` |
`text(Subtract)\ \ (1) – (2),`
| `−2` | `= −` | |
|
`= 2` |
| `text(Substitute)\ ` | |
`text{= 2 into (1)}` |
| `−1` | `= −4\ +` | |
|
`= 3` |
| `:.\ text(Next number)` | `= 13 xx 2 + 3` |
| `= 29` |
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?
| hours |
Simplify: `(2 xx 4^3 xx 5^3)/(4 xx 5^2 xx 4^2 xx 2^2)`
| `10` | `5/2` | `1` | `1/4` |
|
|
|
|
|
Pedro cuts a sector from a circle so that `3/8` of the area of the circle remains.
If the circle's radius is 5 cm, what is the perimeter of the shape, to the nearest centimetre?
| cm |
The product of three different positive whole numbers is 40.
What is the largest possible sum of the three numbers?
In the diagram `AB` is a straight line.
What is the size of the angle marked `x^@?`
| degrees |
| `x` | `= 90 – 60` |
| `= 30^@` |
Which of these equations represents the line in the graph?
| `y = 11 - 2x` | `y = 11 + 5.5x` | `y = 11 - 5.5x` | `y = 11 + 2x` |
|
|
|
|
|
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?
| $ |
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?
| `text(2.5%)` | `text(12.5%)` | `text(27.5%)` | `text(32.5%)` | `text(35%)` |
|
|
|
|
|
|
Which statement is always true?
|
|
Scalene triangles have two angles that are equal. |
|
|
All angles in a parallelogram are equal. |
|
|
The opposite sides of a trapezium are equal in length. |
|
|
The diagonals of a rhombus are perpendicular to each other. |
Mike uses match sticks to make a pattern of houses.
When a shape consists of 7 houses, how many sticks will the shape have?
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 |
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?
| `10.3` | `21.1` | `31.7` | `47.5` |
|
|
|
|
|
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.
| `2:1` | `5:2` | `200:1` | `250:1` | `4000:1` |
|
|
|
|
|
|
Lee travels from `A` to `C` following the route `A -> B -> C` as shown in the diagram below.
How many metres less would Lee travel if he travelled directly from `A` to `C` as shown by the dotted line in the diagram?
| m |
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 $112.50.
What is the rental cost to drive 60 kilometres?
| `$` |
Leigh has a picnic blanket with an area of 5 square metres.
What is the area of her picnic blanket in square centimetres?
| `25\ text(cm²)` | `50\ text(cm²)` | `500\ text(cm²)` | `50\ 000\ text(cm²)` | `250\ 000\ text(cm²)` |
|
|
|
|
|
|
Angus bought a tennis racket which cost $22.50 before the Goods and Services Tax (GST) was added.
How much did Angus' tennis racket cost after adding the 10% GST?
| `$` |