Aussie Maths & Science Teachers: Save your time with SmarterEd
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 |
Sisko keeps a tin of lollipops on his desk at home.
His son Tardis takes 1 lollipop out every 4 days.
Sisko adds a new lollipop to the tin every 5 days.
The lollipops in Sisko's tin are decreasing by 1 lollipop every `x` days.
What is the value of `x`?
`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-fifth the distance from `P` to `S`.
The distance from `Q` to `R` is 21 km.
What is the distance between `P` and `S`?
| kilometres |
Ranch is tiling his bathroom.
He follows this pattern to make a line of tiles that is 60 cm long.
How many tiles are in this line?
What is the area of the shaded part of the figure?
| square centimetres |
Chandler, Ross and Joey are picking grapes to earn money.
Their pay is based on the number of tonnes of grapes they pick.
Their total pay is $1080.
How much does Chandler earn?
| `$` |
The object below is a prism.
How many edges does the object have?
It takes Kate 6 seconds to place a brochure in an envelope and seal it.
How many minutes will it take her to pack and seal 65 envelopes?
| minutes |
`8x > x^2`
What is the largest whole number `x` can be that makes this expression correct?
Sue and Belinda have total combined savings of $32.
If `1/5` of Sue's savings equals `1/3` of Belinda's savings, how much has Belinda saved?
| $ |
An ancient civilisation created the following pattern in a large square field.
What is the area shaded grey in the pattern?
| square metres |
Three identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.
If the prism has a volume of 1029 cubic centimetres, what it its height?
| centimetres |
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 trout fish is 16.9 kilograms.
It's length is 1.24 metres.
A rule that can be used to approximately predict the length of a trout from its mass is
`l = sqrt(m/10)`
where `l` is the length of the trout in metres and `m` is the mass in kilograms.
What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
| centimetres |
Six identical triangles are used to make the figure below.
What is the size of the angle marked `x^@`?
| degrees |
`text(Consider the centre angles of each triangle,)\ c°`
| `6 xx c^@` | `= 180^@` |
| `c^@` | `= 30^@` |
| `:. x^@` | `= 180 – (90 + 30)` |
| `= 60^@` |
Towns `A, B` and `C` are marked on the scale diagram below.
The distance from Town `A` to Town `B` is 11 km.
What is the distance from Town `B` to Town `C?`
| kilometres |
Blart bought a second hand bike at a cost of $440.
He had to spend 55% of his savings to buy the bike.
How much did Blart have in his savings after buying the bike?
| $ |
A new museum records the number of visitors over 5 days.
The cost of entry for each visitor was $12.
What was the mean amount of entry fee money collected per day?
| $ |
Daniel is in a 2-day rally car race.
On day 1, Daniel takes 1 hour and 20 minutes to travel 115 km.
On day 2, Daniel takes 2 hours to travel 175 km.
What is Daniel's average speed over the 2 days.
| kilometres per hour |
Manou was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes.
The first temperature taken was − 8.2°C.
The second temperature was 4.2°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)` |
Krol has read `7/16` of his new science fiction book.
If the book has 400 pages, how many pages has he read?
The edges of a `4 xx 4 xx 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 6 × 6 × 6 cube in the same way?
The table below shows the relationship between the width of a tree's trunk in centimetres and how old it is in months.
If this pattern continues, how old would you expect a tree with a 7 cm wide trunk to be?
| months |
`text(Continuing the pattern:)`
`:.\ text(Expected age = 27 months)`
Lux is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
Lux keeps the larger piece of wood which is in the shape of a trapezoidal prism.
What is the volume of the larger piece of wood in cubic metres?
Give your answer to 2 decimal places.
| m³ |
`2/55 = 2/50 + 1/x`
Find the value of `x?`
On a weekend, Abbey works 6 hours at her normal pay rate, 6 hours at time and a half of her normal pay rate, and 3 hours at double her normal pay rate.
Abbey was paid $495.60 in total for this work.
What is her normal pay rate per hour?
| $ |
The rule for the graph is
`A = c^2/k`
`A` is the area of bushland in square kilometres.
`c` is the estimated population of feral cats.
The graph shows that a 40 km² area of bushland is estimated to have a feral cat population of 80.
Use this to calculate the value of `k.`
| `90 - sqrt (18^2 + 80^2)/4 =` |
Jerry cut a golf ball into two halves.
The following calculation gives the approximate volume of one half of the ball in cm³.
`text(Volume) = 1/2 xx 4/3 pi xx r^3`
What volume does the calculation give, to the nearest cm³, where `r` is the radius of the ball?
| cm³ |
Albus measured the diameter of two coins and recorded his results in the table below.
One inch equals 25.4 millimetres.
What is the difference in millimetres between the diameters of the two coins?
Give your answer to three decimal places.
| millimetres |
Joe is `3/4` the age of Nick.
Kevin is `2/3` the age of Nick.
Joe is `3` years older than Kevin.
How old is Nick in years?
| years |
Matilda 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 a shape with a perimeter of 24 cm.
What is the total number of triangles and squares combined that Matilda has used?
A dog bath is in the shape of a rectangular prism.
Its measurements can be seen below:
One cubic metre holds 1000 litres of water.
How many litres of water will fill the dog bath?
| litres |
It takes 5 clowns 6 hours to blow up 600 balloons.
At the same rate, how many hours should it take for 4 clowns to blow up 240 balloons?
| hours |
Luigi packs boxes with packets of different types of pasta. He packs one box at a time.
Each box contains 5 packets of spaghetti, 2 packets of fettucini and 1 packet of penne pasta.
Every hour Luigi packs 400 packets of pasta in total.
How many packets of spaghetti does he pack into boxes in one hour.
The product of three different whole numbers is 72.
What is the smallest possible sum of the three numbers?
In the diagram `PQ` is a straight line.
What is the size of the angle marked `a^@?`
| degrees |
`text(The bottom left triangle is equilateral.)`
| `:. a^@` | `= 180 – (90 + 30)` |
| `= 60^@` |
A cement slab is laid in Yvette's backyard that forms an 8 m × 4 m rectangle.
Yvette is going to lay plastic tiles around the edge of her slab using one row of 250 mm × 250 mm tiles.
She will use 50% black tiles costing $6 per tile and 50% white tiles costing $7 per tile.
What is the total cost of the tiles she used?
| $ |
Rodin makes a large sculpture in the shape of a cube.
The total length of all of its edges is 72 metres.
What is the area of one of the cube's faces?
| m² |
Pearl uses matchsticks to make a pattern of figures.
How many sticks will the shape number 6 have?
Candy is saving her money to buy some new riding boots.
After 1 week, she had saved 35% of the cost of the boots.
After 2 weeks, she had saved another $60 and now had 65% of the cost of the boots.
How much do the riding boots cost?
| $ |
Ona drew a diagram of a skeleton.
The actual length of the skeleton is 180 centimetres.
What is the actual shoulder width of the skeleton?
| centimetres |
The number of registered vehicles in five countries are recorded in the table below.
How many more registered vehicles are there in the USA than Australia and Norway combined?
Shanti travels directly from from `P` to `R` as shown in the diagram below.
If she takes the route `P -> Q -> R`, how far extra does she travel?
| m |
Ziggy rents a hang glider from a hire company.
The cost to rent the hang glider is directly proportional to the number of minutes between the original hire time and when it is returned.
Ziggy's rental cost for 3 hours and 20 minutes is $92.50.
What will be Ziggy's rental cost if he returns the hang glider after 60 minutes?
| `$` |
Joplin bought a hat that cost $27.50 before the Goods and Services Tax (GST) was added.
How much did Joplin pay for the hat after adding the 10% GST?
| `$` |
Korin is saving to buy a Spiderman suit.
He created a table to keep track of his savings.
Complete the rule for the linear relationship between the amount of money in Korin's savings account and the number of months of saving.
| `y = ` | `x + 160` |
Holly picks a 2 digit number at random.
She can give the following clues about her number:
What is Holly's number?
A plan of Petal's garden is shown below.
Petal wants to irrigate her garden and needs to know the total area.
What is the total area of Petal's garden, in square metres?
| m² |
| `text(Area)` | `=\ text(square + triangle)` |
| `= (6 xx 5) + (1/2 xx 6 xx 3)` | |
| `= 30 + 9` | |
| `= 39\ text(m²)` |
Paul and Simon are saving money so they can visit their grandmother on a holiday.
Paul has $200 and plans to save $50 each week.
Simon has $300 and plans to save $25 each week.
After how many weeks will Paul and Simon have saved the same amount?
| weeks |
Manuel chooses a positive whole number under 5 and Basil has to guess what number it is.
The probability that Basil chooses the right number is 25%.
What is the probability that Basil chooses the wrong whole number?
| % |
A miniature engine contains two types of ball bearings.
There are two times as many small ball bearings as large ball bearings.
The mass of a small ball bearing is 190 milligrams and the mass of a large ball bearing is 300 milligrams.
The total mass of all the ball bearings in the engine is 239 grams.
How many ball bearings in total are used in the engine?
What is the value of `x` given `7/2 x + 7 = 4x - 5?`
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.
Each smaller triangular prism is 78 cm³ in size.
What is the maximum number of smaller triangular prisms that can fit inside the box?
An archery target has the following dimensions.
What is the area of the entire target?
Round your answer to the nearest square centimetre.
| cm² |
Mr. Soros put $2000 into a simple interest account for a year.
He did not take any money out or add any money to the account.
At the end of the year he had $2080 in the account.
What was the annual percentage interest rate?
| % |
A museum has a glass entrance that is made up of four triangles and a square, as shown in the diagram below.
Belou is hired to clean the interior sides of the entrance, not including the floor.
What is the area that Belou will need to clean? Answer to the nearest square metre.
| m² |
A regular pentagon can be divided into three triangles from one vertex, as shown below.
What is the size of the internal angle `x°`?
| degrees |
A fruit platter contains the following pieces of fruit:
How many pieces of fruit are in the platter?
