Aussie Maths & Science Teachers: Save your time with SmarterEd
The following graph with five vertices is a complete graph.
Edges are removed so that the graph will have the minimum number of edges to remain connected.
The number of edges that are removed is
`text(The minimum number of edges for)`
`text{a connected graph is 4 (spanning tree).}`
`:.\ text(Edges to be removed)`
`= 10 – 4`
`= 6`
`=> C`
Megan walks from her house to a shop that is 800 m away.
The equation for the relationship between the distance, in metres, that Megan is from her house `t` minutes after leaving is
`text(distance) = {(100t, 0 <= t <= 6),(\ 600, 6 < t <= a),(quadkt, a < t <= 10):}`
If Megan reaches the shop 10 minutes after leaving her house, the value of `a` is
The point (2, 12) lies on the graph of `y = kx^n`, as shown below.
Another graph that represents this relationship between `y` and `x` could be
The feasible region for a linear programming problem is shaded in the diagram below.
The equation of the objective function for this problem is of the form
`P = ax + by`, where `a > 0` and `b > 0`
The dotted line in the diagram has the same slope as the objective function for this problem.
The maximum value of the objective function can be determined by calculating its value at
A string of seven flags consisting of equilateral triangles in two sizes is hanging at the end of a racetrack, as shown in the diagram below.
The edge length of each black flag is twice the edge length of each white flag.
For this string of seven flags, the total area of the black flags would be
All towns in the state of Victoria are in the same time zone.
Mallacoota (38°S, 150°E) and Portland (38°S, 142°E) are two coastal towns in the state of Victoria.
On one day in January, the sun rose in Mallacoota at 6.03 am.
Assuming that 15° of longitude equates to a one-hour time difference, the time that the sun was expected to rise in Portland is
Mai invests in an annuity that earns interest at the rate of 5.2% per annum compounding monthly.
Monthly payments are received from the annuity.
The balance of the annuity will be $130 784.93 after five years.
The balance of the annuity will be $66 992.27 after 10 years.
The monthly payment that Mai receives from the annuity is closest to
A resort has 4 pools.
Which pool has the largest surface area?
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A shape, pictured below, is made with 5 rhombuses.
What is the perimeter of the shape?
| `10\ text(cm)` | `14\ text(cm)` | `12\ text(cm)` | `20\ text(cm)` |
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Daniel made this design by joining six tiles together.
Which of this could not be Daniel's design?
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Jude left the factory and turns left on Bop St.
He then turns left immediately and walks straight ahead.
What building does he pass?
| `text(school)` | `text(cinema)` | `text(shop)` | `text(cafe)` |
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Jane and five of her friends share 2 cakes.
If all six friends share equally, what fraction of one cake does each of them get?
| `1/2` | `1/3` | `1/6` | `1/12` |
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A group of soccer fans all go to a soccer game.
Entry to the game costs $3.
Altogether the group pay $156.
How many soccer fans are there in the group?
| `50` | `51` | `52` | `63` |
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5 boys win $3.
They share the money equally.
How much does each boy get?
| cents |
Percy buys a cricket ball and a set of stumps.
The total cost is $23.
The stumps cost $3 more than the ball.
What is the cost of the ball?
| $ |
There are 8 small boxes packed into the carton below.
How many small boxes can fit in the carton altogether?
Jeremy had these tiles.
He then turned each tile a quarter turn clockwise.
Which of these is his new design?
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Jeff went to the corner store to buy 4 kg of flour.
Approximately how much did Jeff pay?
| `$2` | `$3` | `$4` | `$6` |
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Kim started at 5 and made this number pattern
| `5, 6, 8, 11, 15, 20,` |
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What is the next number in the pattern?
| `21` | `25` | `26` | `30` |
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Bernard is putting tiles on a section of his toy room wall.
Altogether, how many tiles of the same size will be needed to fully cover this section of the wall?
How many quarters are there in three and a half apples?
| `7` | `8` | `13` | `14` |
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Iris needs 4 cups of raisins to make a fruit cake.
She measures `1/2` a cup each time.
How many `1/2` cups will she need?
| `1` | `2` | `4` | `8` |
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Kim is packing 27 plums into boxes to take to the market.
Each box can hold 5 plums.
What is the smallest number of boxes Kim needs to make sure all the plums are packed?
| `29 + 37` has the same value as `30 +` |
| `55 - 28 =` |
In 5 years time, Megan will be 16.
Brian will then be half Megan's age.
How old is Brian now?
| `3` | `6` | `8` | `11` |
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John left the police station and drove to the Law Courts.
What was the first building he passed on his left?
| `text(bank)` | `text(chemist)` | `text(newsagent)` | `text(cafe)` |
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Dinesh thought of a number.
He doubled the number and subtracted 4.
The answer was 14.
What number did Dinesh first think of?
Rachael draws around this tile.
She turns the tile a quarter turn.
She draws around the tile in its new position.
Which of these could show the two shapes that Rachael drew?
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At what time does the next train leave?
| `9:02` | `1:09` | `2:45` | `1:45` |
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Write a number in the box to make this number sentence correct.
| `33 -` | `= 17` |
Mandy is cutting out luggage tags from a plastic sheet.
Each luggage tag is identical and is pictured below.
Mandy throws away all pieces of plastic that are not complete tags.
What is the greatest number of luggage tags that Mandy can cut from the plastic sheet?
`text(10 luggage tags is the most that can be cut.)`
These clocks show two times in the afternoon.
How many minutes are there between the two times?
| minutes |
Domi had some money in her purse.
She spent $3.75 and had $2.55 left .
How much money did Domi start with?
| $ |
Peter travels a lot for work.
The table below shows the months when Peter visited different places.
During how many months did Peter visit Adelaide but not New Zealand?
| `4` | `5` | `6` | `7` | `9` |
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A shop sells eggs in small and large cartons.
A small carton holds 6 eggs.
A large carton holds 12 eggs.
Alice buys a total of 60 eggs.
She buys 3 large cartons and some small cartons.
How many small cartons does she buy?
Marcus hangs 2 pairs of pants on a line.
Any trousers next to each other share a peg.
He uses 3 pegs.
How many pegs would Marcus use to hang 5 pairs of pants?
Kylie cut this shape into rectangles with no pieces left over.
What is the smallest number of rectangles she could have cut it into?
This shoe print was found at a crime scene.
Which shoe below could have made the print?
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Damon had $1.40 in 5-cent coins in his piggy bank.
How many 5-cent coins does Damon have?
Anne went for a walk everyday.
This graph shows how far Anne went on her walk each day in a week.
On how many days in the week did Anne walk at least 5 kilometres?
| `3` | `4` | `5` | `6` |
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Tom has this picture of a panda on his phone.
He makes the picture twice as wide and half as high.
How will the picture look after he does that?
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This prism is made of cubes of the same size.
Some cubes have been taken out to form the object shown below.
How many cubes are in this new object?
An athletics club has 13 girls.
There are 6 more girls than boys.
How many people are in the club altogether?
Curly, Larry and Moe share a bag of oranges.
Curly and Larry get `1/5` of the oranges each.
What fraction of the bag of oranges does Moe get?
| `4/5` | `3/5` | `2/5` | `1/5` |
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Vivian wrote the number sentence
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`- 3 = 6` |
In which of these does the 
have the same value as above?
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Bennelong writes a number on a piece of paper and hides it.
He gives his friend the following clues about his number.
What is Bennelong's number?
| `30` | `34` | `300` | `304` |
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Clive is using a number line to show a pattern.
In Clive's pattern, what number comes before 35?
| `29` | `30` | `31` | `32` |
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Andrew kept 3 bird cages.
Each bird cage had 8 birds in it.
He then bought one more bird cage and spread the birds out evenly between the 4 cages.
How many birds were then in each cage?
| `5` | `6` | `8` | `9` |
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| `13 +` | `+ 12 = 53` |
5.31 is equal to
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`0.5 + 0.3 + 0.1` |
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`5.0 + 0.3 + 0.1` |
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`5 + 0.3 + 0.01` |
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`5 + 0.03 + 0.01` |
Renee made a pie graph of the cost of things she paid for using her credit card over a month.
Which information can be found using this pie graph?
The amount of money she spent using her credit card
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for going to the cinemas in the month. |
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on electricity each week. |
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on shopping each day. |
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on rent for the month. |
There are 8 small boxes packed into the carton below.
How many small boxes can fit in the carton altogether?
Manou held a dinner party for 24 people.
He planned on giving each guest 3 carrots in their baked dinner.
How many carrots did he need altogether?
Angelina takes 3 marbles out of the bag at the same time.
Which of these is impossible?
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2 striped marbles and 1 white marble. |
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2 white marbles and 1 grey marble. |
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2 grey marbles and 1 striped marble. |
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2 star marbles and 1 grey marble. |
This grid map shows the names of some places along a hiking track.
The distance between The Terrace and Karuah is about 40 km.
Which of these is closest to the distance from Rees to Janis along the track?
| `text(30 km)` | `text(40 km)` | `text(50 km)` | `text(70 km)` |
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Ivan and Novik receive pocket money each week.
Ivan gets $3 and Novik gets $7.
After 12 weeks, how much more pocket money has Novik received than Ivan?
| $ |
Using this table the distance from Byron to Eltham is 28 km.
What is the distance from Talofa to Clunes?
| `text(10 km)` | `text(18 km)` | `text(20 km)` | `text(24 km)` |
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4 angles are labelled on the triangle pictured below.
Which angle is closest in size to 45°?
| `A` | `B` | `C` | `D` |
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