1. Welcome To The Mathematics Challenge Click button to start quiz
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Welcome To The Mathematics Challenge 15
$1 Million 14
$500,000 13
$250,000 12
$125,000
How good are you at Maths?
The questions in this quiz have all been taken from publications by the Australian Mathematical Trust (in association with The Mathematical Association of Victoria).
Click on the correct answer to each question to move to the next level. If you choose the wrong answer you will get a message. Be warned – the questions get harder the further you go.
See how much your knowledge of Maths could gain you. 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
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$100

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$1 Million 14
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$64,000 10
$32,000
If = 3
then
what does equal 9
$16,000 8
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$4,000 6
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$100
A: 17
B: 20
D: 24
C: 22

3. 15
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While driving from the city to the lake, Amal passes a road sign shown in the diagram.
About an hour later she notices a sign indicating that she has only 5 km to go to the lake.
How many kilometres has she travelled from the city? 11
$64,000
City 50km
Lake 80km 10
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$100
A: 95
B: 105
C: 115
D: 125

4. 15
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20 cm 11
$64,000
A rectangular wire grid is made up of 15 equal squares as shown.
If the length of the grid is 20 centimetres, what is the total length, in centimetres, of all the wire in the grid? 10
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$100
A: 152
B: 158
C: 164
D: 170

5. 15
$1 Million 14
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Jane is given a large block of chocolate which is made up of squares and is 6 pieces wide and 8 pieces long.
She eats all the outside pieces.
What fraction of the block is left? 11
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$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
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$100
A: 1/2
B: 1/3
C: 1/4
D: 2/3

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The average age of 11 players in the Australian soccer team is 22.
During a match one player got a red card and had to leave the field. The average of the 10 remaining players on the field was then 21.
How old was the player who got the red card? 11
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$100
A: 21
B: 28
C: 32
D: 34

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$1 Million 14
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This picture graph shows the number of people at the zoo for these days.
If each figure of a whole person represents 50 people attending what is the total number of people who attended for the three days? 10
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$100
A: 525
B: 675
C: 750
D: 875

9. A: More than half the students either walk or cycle. 15
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Cycle 10
$32,000
From the information presented in the chart which statement is true? 9
$16,000
Walk
Bus 8
$8,000 7
$4,000
Car 6
$2,000 5
$1,000 4
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$100
A: More than half the students either walk or cycle.
B: More than a quarter of the students walk to school
C: More students walk to school than come by car.
D: More than half the students either take the bus or cycle to school

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There are five blocks of different colours stacked on top of each other. If:
the red block is above the purple block,
the blue block is underneath the orange block
the green block is below the blue and above the red.
what colour is the bottom block? 11
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$100
A: Purple
B: Red
C: Green
D: Blue

11. 15
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A carpenter made 20 chairs and stools with a total number of 73 legs.
If the chairs each have 4 legs, and the stools have 3 legs, how many chairs did she make?
$64,000 10
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$16,000 8
$8,000 7
$4,000 6
$2,000 5
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$100
A: 11
B: 12
C: 13
D: 14

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$64,000
Five towns are joined by a system of roads as shown.
How many different ways are there of travelling from town P to town T if, on any particular journey, no road is used more than once? 10
$32,000 9
$16,000 P Q T 8
$8,000 7
$4,000 R S 6
$2,000 5
$1,000 4
$500 3
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$100
A: 4
B: 5
C: 6
D: 7

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You’ve Reached
the $32,000
Milestone!

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$250,000 12
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$64,000
Ayse
If ‘Anne Jane’ means ‘Anne is taller than Jane’ then according to the diagram who is the second tallest person in the group? 10
$32,000 9
$16,000
Anne 8
$8,000
Omar 7
$4,000 6
$2,000
Jane
Tran 5
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$100
A: Jane
B: Ayse
C: Omar
D: Anne

15. A: Melbourne won by 2 goals B: Newcastle won by 2 goals15
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At half time in a soccer match between Newcastle and Melbourne, the score was Newcastle 1, and Melbourne 0.
Three goals were scored in the second half.
Which of the following could NOT be the result of the match? 10
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$100
A: Melbourne won by 2 goals
B: Newcastle won by 2 goals
C: Newcastle won by 1 goal
D: Newcastle won by 4 goals

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$250,000 12
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Four coins of the same size lie on a table as shown. Keeping in contact with the other three coins, the shaded (red) coin is rolled around the other three coins until it returns to its starting place.
Through what angle does the shaded coin turn, on its axis, in rolling once round the other three coins? 10
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$100
B: 720 degrees
A: 360 degrees
C: 900 degrees
D: degrees

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$125,000
Anne designs a dart board as shown, where she scores P points in the centre circle, Q points in the next ring and R points in the outer ring. She throws three darts in each turn
In her first turn, she gets two darts in ring Q and one dart in ring R and scores 10 points.
In her second turn, she gets two in circle P and one in ring R and scores 22 points.
In her next turn she gets one dart in each of the three rings. How many points does she score? 11
$64,000 P Q R 10
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$100
A: 16
B: 18
C: 20
D: 22

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$250,000 12
$125,000
A beetle sets out on a journey. On the first day, it crawls 1m in a straight line. On the second day it makes a right-angled turn (in either direction) and crawls 2m in a straight line. On the third day it makes a right-angled turn (in either direction) and crawls 3m in a straight line. This continues each day with the bug making a right-angled turn (in either direction) and crawling 1m further than it did the day before. What is the least number of days before the beetle could find itself stopped at its starting point? 11
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$32,000 9
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$8,000 7
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$2,000 5
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$100
A: 6
B: 7
C: 8
D: 9

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Congratulations!
Congratulations!
YOU WIN

20. Return If - 15 + 5 - 7 = 3 then what does equal
This can be rearranged so that: =
= 20
Return

21. This means she has travelled a total of 50 + 75 = 125km
While driving from the city to the lake, Amal passes a road sign shown in the diagram.
About an hour later she notices a sign indicating that she has only 5 km to go to the lake.
How many kilometres has she travelled from the city?
City 50km
Lake 80km
The sign is 80km from the lake so when Karen is 5km from the lake she has travelled 75km past the sign.
This means she has travelled a total of = 125km
Return

22. A rectangular wire grid is made up of 15 equal squares as shown.
20 cm
A rectangular wire grid is made up of 15 equal squares as shown.
If the length of the grid is 20 centimetres, what is the total length, in centimetres, of all the wire in the grid?
The 20cm long rectangle is made up of 5 squares, so the side length of each square must be 4cm (20/5)
This means that the grid consists of 4 rows of 20cm and 6 columns of 12cm giving a total length of
(4 * 20) + (6 * 12) = 152cm
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23. Jane is given a large block of chocolate which is made up of squares and is 6 pieces wide and 8 pieces long.
She eats all the outside pieces.
What fraction of the block is left?
There were originally 8 * 6 = 48 pieces of chocolate.
When Jane eats the outside pieces the block is then 4 pieces wide and 6 pieces long
Therefore, there are 24 pieces left and she has eaten 24 pieces.
The fraction left is 24/48 = 1/2
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24. The average age of 11 players in the Australian soccer team is 22.
During a match one player got a red card and had to leave the field. The average of the 10 remaining players on the field was then 21.
How old was the player who got the red card?
The average age of 11 players is 22, so the total of their ages is 11 * 22 = 242
When one player leaves the field the average age of the remaining 10 players is 21, so the total age is 10 * 21 = 210
Therefore, the age of the player who left the field is the difference between the two combined sets of ages and is = 32
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25. This picture graph shows the number of people at the zoo for these days.
If each figure of a whole person represents 50 people attending what is the total number of people who attended for the three days?
Each figure represents 50 people and there is a total of
13½ figures
Therefore there are a total of 13 ½ * 50 = 675
Return

26. From the information presented in the chart which statement is true?
Cycle
From the information presented in the chart which statement is true?
Walk
Bus
Car
It can be seen that:
Walk plus Cycle are less than a semicircle so A is False
Walk is less than a quarter of a circle so B is False
The Walk sector is less than the Car sector so C is False
This leaves D as the only correct alternative
Return

27. There are five blocks of different colours stacked on top of each other. If:
the red block is above the purple block,
the blue block is underneath the orange block
the green block is below the blue and above the red.
what colour is the bottom block?
The Green block is above the Red and so also above the Purple. It is also below the Blue and hence also the Orange. This means the Green block is in the middle and the order from the top is:
Orange
Blue
Green
Red
Purple
…… so the bottom block is Purple
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28. A carpenter made 20 chairs and stools with a total number of 73 legs.
If the chairs each have 4 legs, and the stools have 3 legs, how many chairs did she make?
The carpenter made 20 chairs and stools. If she had made 20 chairs, the number of legs these would have had is 4 * 20 = 80 which is 7 more legs than there actually are.
This means there must have been 7 stools in the total of 20 (since each stool has one less leg than a chair) and therefore she must have made = 13 chairs
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29. The seven possible routes are:
Five towns are joined by a system of roads as shown.
How many different ways are there of travelling from town P to town T if, on any particular journey, no road is used more than once? P Q T R S
The seven possible routes are:
PQT
PRST
PRQT
PRQST
PQRST
PRSQT
Return

30. Return Ayse Anne Omar Jane Tran
If ‘Anne Jane’ means ‘Anne is taller than Jane’ then according to the diagram who is the second tallest person in the group?
Anne
Omar
Jane
Tran
From the diagram:
Ayse is taller than Omar, Anne and Jane
Also, Tran is taller than Ayse
So Ayse must be the second tallest
Return

31. At half time in a soccer match between Newcastle and Melbourne, the score was Newcastle 1, and Melbourne 0.
Three goals were scored in the second half.
Which of the following could NOT be the result of the match?
The possible fulltime scores are:
Newcastle 4 – Melbourne 0
Newcastle 3 – Melbourne 1
Newcastle 2 – Melbourne 2
Newcastle 1 – Melbourne 3
Therefore it is not possible for Newcastle to win by 1 goal
Return

32. Therefore, in total, it will roll 3 * 360 = 1080 degrees
Four coins of the same size lie on a table as shown. Keeping in contact with the other three coins, the shaded (red) coin is rolled around the other three coins until it returns to its starting place.
Through what angle does the shaded coin turn, on its axis, in rolling once round the other three coins?
The shaded coin will rotate 360 degrees when it rolls around the first coin. It will roll another 360 degrees when it rolls around the second coin and a further 360 degrees going around the third coin.
Therefore, in total, it will roll 3 * 360 = 1080 degrees
Return

33. Anne designs a dart board as shown, where she scores P points in the centre circle, Q points in the next ring and R points in the outer ring. She throws three darts in each turn
In her first turn, she gets two darts in ring Q and one dart in ring R and scores 10 points.
In her second turn, she gets two in circle P and one in ring R and scores 22 points.
In her next turn she gets one dart in each of the three rings. How many points does she score? P Q R
On the first throw Anne gets 2Q + R = 10
On the second throw the result is 2P + R = 22
If these two results are combined then 2Q + R + 2P + R =
or 2Q + 2P + 2R = 32
This is twice the result of Anne’s final throw which was
Q + P + R
which therefore must be = 16 (32 / 2)
Return

34. So the least number of days to get back to zero is 3 + 4 = 7
A beetle sets out on a journey. On the first day, it crawls 1m in a straight line. On the second day it makes a right-angled turn (in either direction) and crawls 2m in a straight line. On the third day it makes a right-angled turn (in either direction) and crawls 3m in a straight line. This continues each day with the bug making a right-angled turn (in either direction) and crawling 1m further than it did the day before. What is the least number of days before the beetle could find itself stopped at its starting point?
Assume that on Day 1 the beetle moves in a horizontal direction. Then all moves in a horizontal direction must be an odd number of metres and all movements in the vertical direction are an even number of metres.
To come to rest at the starting position the beetle must be at zero for both the horizontal and vertical positions
Horizontally – you can’t get zero from 1 & 3 or 1 & 3 & 5 but you can get zero from 1 – or a minimum of 4 days movement
Vertically – you can’t get zero from 2 & 4 but you can from – 6 or a minimum of 3 days.
So the least number of days to get back to zero is = 7
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35. Bad Luck
Try Again!
Try Again!
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