Welcome To The Mathematics Challenge Click button to start quiz 50:50 Stop 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 Click button to start quiz Note: You can use the 50:50, Telephone and Group icons if you need assistance, but only one time each. 1 $100

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $64,000 10 $32,000 If - 15 + 5 - 7 = 3 then what does equal 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 17 B: 20 D: 24 C: 22

15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 95 B: 105 C: 115 D: 125

15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 152 B: 158 C: 164 D: 170

15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 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 $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 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 1/2 B: 1/3 C: 1/4 D: 2/3

15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 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 $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 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 21 B: 28 C: 32 D: 34

Click button to continue Stop Previous Congratulations! Congratulations! You’ve Reached the $1,000 Milestone!

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $64,000 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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 525 B: 675 C: 750 D: 875

A: More than half the students either walk or cycle. 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $64,000 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 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $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

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 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 $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 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: Purple B: Red C: Green D: Blue

15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 11 B: 12 C: 13 D: 14

15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $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 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 4 B: 5 C: 6 D: 7

Click button to continue Stop Previous Congratulations! Congratulations! You’ve Reached the $32,000 Milestone!

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $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 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: Jane B: Ayse C: Omar D: Anne

A: Melbourne won by 2 goals B: Newcastle won by 2 goals 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $64,000 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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $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

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $125,000 11 $64,000 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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 B: 720 degrees A: 360 degrees C: 900 degrees D: 1080 degrees

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $250,000 12 $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 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 16 B: 18 C: 20 D: 22

Remember - click on one of these lifelines if you need assistance 15 $1 Million 14 $500,000 Stop Previous See Solution 13 $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 $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 50:50 Remember - click on one of these lifelines if you need assistance 1 $100 A: 6 B: 7 C: 8 D: 9

Stop Previous Congratulations! Congratulations! YOU WIN

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

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 50 + 75 = 125km Return

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 Return

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 Return

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 242 - 210 = 32 Return

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

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

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 Return

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 20 - 7 = 13 chairs Return

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

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

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

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

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 = 10 + 22 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

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 – 3 - 5 + 7 or a minimum of 4 days movement Vertically – you can’t get zero from 2 & 4 but you can from 2 + 4 – 6 or a minimum of 3 days. So the least number of days to get back to zero is 3 + 4 = 7 Return

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