Billy followed these instructions to create a drawing:
- Draw a rectangle.
- Use one of the sides of this shape to draw a triangle with 2 equal sides.
- Draw a line of symmetry through your completed drawing.
Which of these did he draw?
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Aussie Maths & Science Teachers: Save your time with SmarterEd
Billy followed these instructions to create a drawing:
Which of these did he draw?
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Valerie looked at the calendar on 23 March.
She plans to go to the theatre on 15 April and circled this on the calendar below.
What day of the week is 23 March?
Wednesday | Friday | Saturday | Sunday | Monday |
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`text(Sunday)`
`text(Working backwards:)`
`text{1 April → Tuesday (from calendar)}`
`text{31 March → Monday (31 days in March)}`
`text(24 March → Monday)`
`:. 23\ text(March is a Sunday)`
Gerome thinks of a number that follows the rules below.
Which of the below could be the number that Gerome is thinking of.
`5404` | `6117` | `6051` | `5602` | `5413` | `6223` |
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`5413`
`text(By trial and error,)`
`text(Consider 5413:)`
`=>\ text(5413 is odd)`
`=>\ text(lies between 5400 and 6200)`
`=> 5+4+1+3 = 13`
`:.\ text(5413 satisfies all the rules.)`
Gillian has 84 brochures to give out at a conference.
She puts an equal number of brochures onto each table at the conference and has none left over.
Select the option that shows the number of tables that could not be at the conference.
`6` | `7` | `14` | `16` | `21` |
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`16`
`text(Consider the options and factors of 84:)`
`6 xx 7 xx 2 = 84`
`14 xx 6 = 84`
`21 xx 4 = 84`
`16\ text(is not a factor of 84.)`
`:. 16\ text(tables could not be at the conference.)`
This graph shows the number of men and women that registered to vote before a council election on different days of the week.
On which day is the difference between the number of men and women registering closest to 55?
Monday | Tuesday | Wednesday | Thursday | Friday |
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`text(Monday)`
`text(Each interval = 20 people)`
`text(Difference needs to be slightly smaller than 3 intervals.)`
`=>\ text(Monday is closest)`
Torvil has 18 scarves.
Dean has 5 less scarves than Torvil.
Which of these shows how to work out the total number of scarves they have altogether?
`18 - 5` | `18 + 5` | `2 xx 18 - 5` | `2 xx 18 + 5` |
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`2 xx 18 – 5`
`text(Torvil’s scarves) = 18`
`text(Dean’s scarves) = 18 – 5`
`:.\ text(Total scarves)` | `= 18 + 18 – 5` |
`= 2 xx 18 – 5` |
Bilbo has 14 rings.
Gandalf has 7 more rings than Bilbo.
Which of these shows how to work out the total number of rings they have altogether?
`14 xx 2 - 7` | `14 xx 2 + 7` | `14 - 7` | `14 + 7` |
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`14 xx 2 + 7`
`text(Bilbo’s rings) = 14`
`text(Gandalf’s rings) = 14 + 7`
`:.\ text(Total rings)` | `= 14 + 14 + 7` |
`= 14 xx 2 + 7` |
Melvin is writing a number pattern.
`23, 27, 31, 35, text(__, __, )` |
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He continues this pattern until he has written 7 numbers.
Select the option that will give the 7th number in Melvin's pattern.
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`35 xx (4 + 4)` |
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`35 + 3 + 3 + 3` |
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`35 + (4 xx 3)` |
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`35 + (4 + 3)` |
`35 + (4 xx 3)`
`text(5th number) = 35 + 4 = 39`
`text(6th number) = 39 + 4 = 43`
`text(7th number) = 43 + 4 = 47`
`35 + (4 xx 3)` | `= 35 + 12` |
`= 47` |
Wilson is at an ice cream shop.
He can choose an ice cream flavour, a topping and one candy mix.
Which of these show a way to calculate the number of different combinations that Wilson can order?
`3 + 2 + 4` | `3 xx 2 + 4` | `4 xx 3 + 2` | `3 xx 4 xx 2` |
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`3 xx 4 xx 2`
`text(Total different combinations)`
`= 3\ text(flavours)\ xx 2\ text(toppings)\ xx 4\ text(candy mixes)`
`= 3 xx2 xx 4`
`= 3 xx 4 xx 2`
Gordon buys `1/5` of a kilogram of grapes.
Which is another way to write `1/5` of a kilogram?
0.02 kilogram | 2 kilogram | 20 kilogram | 0.2 kilogram |
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`text(0.2 kilogram)`
`1/5\ \ text(kilogram) =\ text(0.2 kilogram)`
Carrie purchases `7/10` of a kilogram of gold.
Which is another way to write `7/10` of a kilogram?
0.07 kilogram | 0.7 kilogram | 7 kilogram | 70 kilogram |
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`text(0.7 kilogram)`
`7/10\ \ text(kilogram) =\ text(0.7 kilogram)`
A farmer has 6054 sheep on her property.
Another 425 sheep are added to the flock.
Which of these could be used to calculate the exact number of sheep the farmer now has?
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6000 + 4000 + 500 + 200 + 4 + 5 |
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6000 + 400 + 500 + 40 + 20 + 5 |
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6000 + 400 + 50 + 20 + 4 + 5 |
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6000 + 500 + 400 + 20 + 4 + 5 |
`6000 + 400 + 50 + 20 + 4 + 5`
`6054 + 425`
`= (6000 + 50 + 4) + (400 + 20 + 5)`
`= 6000 + 400 + 50 + 20 + 4 + 5`
A company has 3208 exercise books in a warehouse.
Another 731 exercise books are delivered to the warehouse.
Which of these could be used to calculate the correct number of exercise books in the warehouse?
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3000 + 200 + 700 + 80 + 30 + 8 + 1 |
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3000 + 200 + 700 + 30 + 8 + 1 |
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3000 + 7000 + 200 + 300 + 8 + 1 |
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3000 + 200 + 700 + 80 + 30 + 1 |
`3000 + 200 + 700 + 30 + 8 + 1`
`3208 + 731`
`= (3000 + 200 + 8) + (700 + 30 + 1)`
`= 3000 + 200 + 700 + 30 + 8 + 1`
In one month, a factory makes two thousand, nine hundred and eight tennis balls.
Write this as a numbers in the box below:
tennis balls |
`2908`
`2908`
Mr Newman asked his class a question and recorded the results in the table below.
Which question could Mr Newman have asked?
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How many times did you do play each sport last month? |
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What year did you first play each sport? |
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Do you play two of the following sports? |
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What is your favourite Summer sport? |
`text(What is your favourite Summer sport?)`
`text(What is your favourite Summer sport?)`
Which set of coins shows the same amount of money as the coins above?
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`text(Coins need to add up to:)`
`$1 + 50¢ + 20¢ + 5¢ = $1.75`
`text(Consider the 2nd option:)`
`50¢ + 10¢ + 10¢ + 50¢ + 50¢ + 5¢`
`= 175\ text(c)`
`= $1.75`
Which set of coins shows the same amount of money as the coins above?
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`text(Coins need to add up to:)`
`$1 + 50¢ + 10¢ + 20¢ = $1.80`
`text(Consider the last option:)`
`10¢ + 10¢ + 50¢ + 50¢ + 50¢`
`= 180\ text(c)`
`= $1.80`
Marco is travelling from Dubbo to Adelaide.
He must take two flights, one from Dubbo to Sydney and one from Sydney to Adelaide.
Marco's flight schedule is shown.
What is Marco's total flying time?
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1 hour 40 minutes |
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1 hour 50 minutes |
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3 hours 30 minutes |
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3 hours 50 minutes |
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4 hours 5 minutes |
`text(3 hours 30 minutes)`
`text(Dubbo → Sydney)`
`text(7:00 am − 8:40 am = 1 hr 40 mins)`
`text(Sydney → Adelaide)`
`text(9:15 am − 11:05 am = 1 hr 50 mins)`
`:.\ text(Total flying time)`
`= 1:40 + 1:50`
`= 3\ text(hours 30 minutes)`
Daisy is travelling from Ballina to Hobart.
She must take two flights, one from Ballina to Melbourne and one from Melbourne to Hobart.
Daisy's flight schedule is shown.
What is Daisy's total flying time?
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1 hour 55 minutes |
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2 hours 15 minutes |
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4 hours |
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4 hours 10 minutes |
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6 hours 15 minutes |
`text(4 hours 10 minutes)`
`text(Ballina → Melbourne)`
`text(6:10 am − 8:25 am = 2 hr 15 mins)`
`text(Melbourne → Hobart)`
`text(10:30 am − 12:25 pm = 1 hr 55 mins)`
`:.\ text(Total flying time)`
`= 2:15 + 1:55`
`= 4\ text(hours 10 minutes)`
Tuxedo tosses a coin 5 times and it lands on heads each time.
If he tosses the coin a 6th time, the most likely result is:
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a head |
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a tail |
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both heads and tails have the same chance |
`text(both heads and tails have the same chance)`
`text(A coin toss has the same chance)`
`text(of a head or tail each time.)`
Shelly rolls a three for her first roll of a standard dice.
Shelly rolls a second dice.
Which of the following results is most likely?
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Shelly rolls a 3. |
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Shelly rolls a number less than 3. |
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Shelly rolls an odd number. |
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Shelly rolls an even number above 3. |
`text(Shelly rolls an odd number)`
`text(Consider the number of possibilities of each option:)`
`text(Roll a 3 – 1 possibility)`
`text(Roll a number less than 3 – 2 possibilities)`
`text(Roll odd number – 3 possibilities)`
`text(Roll even number above 3 – 2 possibilities)`
`:.\ text(Rolling an odd number is the most likely.)`
Roderick rolls a standard dice once.
Which of the following results is least likely?
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Roderick rolls an odd number. |
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Roderick rolls a 2 or a 4. |
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Roderick rolls an even number. |
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Roderick rolls a 6. |
`text(Roderick rolls a 6)`
`text(Consider the chance of each option:)`
`text{Pr (rolling an odd number)} = 3/6`
`text{Pr (rolling an even number)} = 3/6`
`text{Pr (rolling a 2 or 4)} = 2/6`
`text{Pr (rolling a 6)} = 1/6`
`:.\ text(Roderick rolls a 6 is the least likely.)`
Anne is making a green cordial.
It is made by mixing water with green concentrate.
Anne adds 5 litres (L) of water to 90 millilitres (mL) of concentrate.
How much cordial did Anne make?
`59\ text(mL)` | `509\ text(mL)` | `590\ text(mL)` | `5090\ text(mL)` |
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`5090\ text(mL)`
`text(Converting to mL:)`
`5\ text(L) = 5000\ text(mL)`
`:.\ text(Total cordial)` | `= 5000 + 90` |
`= 5090\ text(mL)` |
Miles is making a juice cordial.
It is made by mixing juice extract with water.
Miles adds 85 millilitres (mL) of juice extract to 1 litre (L) of water.
How much juice cordial did Miles make?
`185\ text(mL)` | `1085\ text(mL)` | `1850\ text(mL)` | `10\ 850\ text(mL)` |
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`1085\ text(mL)`
`text(Converting to mL:)`
`1\ text(L) = 1000\ text(mL)`
`:.\ text(Total juice cordial)` | `= 1000 + 85` |
`= 1085\ text(mL)` |
Veronica is making green cordial.
It is made by mixing water with green concentrate.
Veronica adds 2 litre (L) of water to 60 millilitres (mL) of green concentrate.
How much cordial did Veronica make?
`20\ 060\ text(mL)` | `2060\ text(mL)` | `260\ text(mL)` | `26\ text(mL)` |
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`2060\ text(mL)`
`text(Converting to mL:)`
`2\ text(L) = 2000\ text(mL)`
`:.\ text(Total cordial)` | `= 2000 + 60` |
`= 2060\ text(mL)` |
A hot air balloon is 26.5 metres high.
The length of the balloon section is 21.75 metres.
What is the height of the basket section?
4.25 metres | 4.75 metres | 5.25 metres | 5.70 metres |
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`4.75`
`:.\ text(Height of the basket section)`
`= 26.50 – 21.75`
`= 26.50 – 21.00 – 0.75`
`= 5.50 – 0.75`
`= 4.75\ text(metres)`
A netball club receives 6 boxes containing 42 netballs each.
It then gives 7 balls to every team in the club and there are no balls left over.
How many teams are in the club?
32 | 36 | 42 | 49 |
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`36`
`text{One box (42 balls) supplies 6 teams with 7 balls each.}`
`:.\ text(Teams supplied by 6 boxes)`
`= 6 xx 6`
`= 36`
An AFL club receives 9 boxes containing 36 AFL balls each.
It then gives 12 balls to every team in the club and there are no balls left over.
How many teams are in the club?
27 | 30 | 32 | 48 |
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`27`
`text{One box (36 balls) supplies 3 teams with 12 balls each.`
`:.\ text(Teams supplied by 9 boxes)`
`= 9 xx 3`
`= 27`
A soccer club receives 7 boxes containing 32 soccer balls each.
It then gives 8 soccer balls to every team in the club and there are no balls left over.
How many teams are in the club?
24 | 28 | 30 | 35 |
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`28`
`text{One box (32 balls) supplies 4 teams with}`
`text(8 balls each)`
`:.\ text(Teams supplied by 7 boxes)`
`= 7 xx 4`
`= 28`
Brian has poured water into some measuring cups.
He makes them all exactly one-sixth full.
Brian counts by sixths to find out, in total, how many full cups of water he has.
Which number does Brian count next?
`6` | `1` | `1 1/6` | `1 1/3` | `5/6` |
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`5/6`
`text(The amount of water increases by)\ \ 1/6\ \ text(each time.)`
`2/3 + 1/6` | `= 4/6 + 1/6` |
`= 5/6` |
Mischa has poured cordial into some measuring cups.
She makes them all exactly one quarter full.
Mischa counts by quarters to find out, in total, how many full cups of cordial she has.
Which number does Mischa count next?
`7` | `2` | `2 1/2` | `2 1/4` | `1 3/4` |
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`1 3/4`
`text(The amount of cordial increase by)\ \ 1/4\ \ text(each time.)`
`1 1/2 + 1/4` | `= 1 2/4 + 1 1/4` |
`= 1 3/4` |
Grant has 95 cents in 5-cent pieces.
How many 5-cent pieces does she have?
`17` | `475` | `19` | `100` |
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`19`
`95 ÷ 5 = 19\ text(pieces)`
How many months are there in 2 years?
12 months | 15 months | 20 months | 24 months |
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`24`
`text(Months in 2 years)`
`= 2 xx 12`
`= 24\ text(months)`
How many months are there in 3 years?
12 months | 15 months | 30 months | 36 months |
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`36`
`text(Months in 3 years)`
`= 3 xx 12`
`= 36\ text(months)`
How many days are there in 5 weeks?
7 days | 12 days | 25 days | 35 days |
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`35`
`text(Number of days)`
`= 5 xx 7`
`= 35\ text(days)`
Four friends were asked what pets they owned.
Who had both a horse and a turtle as pets?
Joey | Ross | Rachel | Monica |
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`text(Rachel)`
`text(Rachel)`
Four friends were asked what pets they owned.
Who had both a cat and a budgie as pets?
Chandler | Ross | Phoebe | Monica |
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`text(Monica)`
`text(Monica)`
Which one of these gives an answer of 84?
70 + 14 | 8 + 4 | 80 + 14 | 70 + 4 |
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`70 + 14`
`70 + 14 = 84`
Which one of these gives an answer of 63?
60 + 13 | 6 + 3 | 50 + 3 | 50 + 13 |
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`50 + 13`
`50 + 13 = 63`
Bob lays pavers on his back deck, as shown below.
What is the area of his back deck in square metres?
`70` | `180` | `195` | `300` |
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`195\ text(m²)`
`text(Area)` | `= (20 xx 7) + (8 xx 5)` |
`= 140 + 40` | |
`= 180\ text(m²)` |
Chakra has a toy horse that is 4 cm high.
His father Dinesh has a real horse that is 2 metres high.
How many times as high as Chakra's toy horse is Dinesh's real horse?
`1` | `50` | `75` | `125` | `200` |
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`50`
`text(Height of Dinesh’s horse)`
`= 2 xx 100`
`= 200\ text(cm)`
`:.\ text(Number of times higher)`
`= 200 ÷ 4`
`= 50`
Which one of these shapes has the longest perimeter?
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`text{Perimeter of 18 units (largest).}`