The Aliens Have Landed and 174 other problems PDF
Preview The Aliens Have Landed and 174 other problems
The Aliens Have Landed and 174 other problems Mary Ellis Published by: The Mathematical Association 259 London Road Leicester LE2 3BE United Kingdom Telephone: Book sales 0014 (44) (0) 116 221 Membership 0013 Conference 0013 Email: Book sales sales@m -a.org.uk Membership office@m -a.org.uk Web: www.m-a.org.uk © The Mathematical Association, 2017 ISBN: 978-0-906588-92-5 978-0-906588-92-5 Printed and bound in Great Britain: DON@T KNOW Contents Introduction Dedication Problems 6 1 60 66 Answers 67 1 6 0 110 Appendix 1 111 Appendix 2 114 978-0-906588-92-5 Introduction This is a book of 175 problems, together with full solutions rather than just answers. The problems are all aimed at pupils in secondary schools, although many of the problems are accessible to bright ten year olds. The collection contains some original problems but many are adapted from ones I have come across over the years. The problems can be used in a variety of ways. I have set each page of problems as a weekly challenge to my pupils in Years 6, 7 and 8, posting an A4 copy on the Maths Board and photocopying A5 copies for pupils to work on in their own time. Pupils in Year 6 only have to answer one of the questions and pupils in Year 7 and 8 have to answer at least two questions. All the correct answers are then drawn out of a “Maths Hat” during our Friday assembly and three lucky winners each receive Crunchies! The problems are often explained in assembly too, either by Year 8 pupils or by me. The majority of the pages contain three problems and one of the problems on each page is deliberately easier than the other two, although it is not necessarily the first problem! The idea behind this is for students to at least read through all the problems before deciding which one to tackle first. The problems could also form the basis of a student competition or students could be encouraged to work through the problems on their own as Extension work to the standard curriculum. It is intended that the problems and solutions should be photocopied to allow their use to be as flexible as possible. Permission is given by The Mathematical Association for purchasers to make photocopies for use in their institutions. Mary Ellis Head of Mathematics Westminster Under School February 2017 To Martha Lucy Jacob Poppy Archie Toby Beatrix & Kate Katie Fraser Pippa Sam Hannah and Lottie & my parents. The Aliens have landed 1 IVOR Hoe is a fanatical gardener. He has to plant his daisies in rows, which form a perfect square. After forming a large square, he finds that he has 46 more seeds, which are still unplanted. He thinks hard and then buys 13 more seeds. He plants these seeds to increase the size of his original square and manages to make a slightly larger bigger square. How many daisies has he planted? I VOR Pain (tooth hurty …!) had toothache and he arranged to see his dentist at the very appropriate time of two thirty in the afternoon. What is the angle between the two hands at two thirty? I VOR Pot grew so many flowers that he decided to sell them! He sold 200 flowers altogether. He sold carnations at £1.50 each, roses at £5.75 each, and his daisies at £2.60 each. He actually sold mostly carnations, and 20 fewer roses than daisies. The total takings came to £589.50. How many of each type of flower did he sell? 6 and 174 other problems 2 C AN you find five consecutive square numbers e.g. 1, 4, 9, 16, and 25 such that the sum of the first three squares equals the sum of the last two squares? 2 2 2 2 2 a + b + c = d + e A cylindrical can contains three tennis balls, stacked one above the other. What is the ratio of the height of the can to the circumference of the can? EV ERYDAY Archie brings countless copies of the Metro newspaper into school for his classmates to read. One day I asked him to put all the copies into the recycling bin before the next lesson. But in his hurry to get to French, he left one copy of the paper scattered all around the classroom … I picked up one sheet and I noticed that the left hand page was page 20, and the right hand page was page 5. How many sheets of paper had been left lying round the classroom in total?! 7 The Aliens have landed 3 D ID you know? 11 × 11 = 121 111 × 111 = 12 321 1 111 × 1 111 = 1 234 321 So, what is the value of 1 111 111 111 × 1 111 111 111 TH E square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number? A garden pond, full of gold fish, is shaped as a polygon with 12 equal sides each at right angles to its adjacent side. The pond also has rotational symmetry of order 4. Draw a plan of the pond. The perimeter of the pond in metres is equal to its area in square metres. Find its area. 8 and 174 other problems 4 IT takes 10 minutes for Toby to run through a two-mile long tunnel and then, as he is rather tired, 20 minutes to run back through the tunnel. What is his average speed? J ACOB has some very strange but colourful sheep. Some are green, some are orange and others are even purple! He has 60 sheep in total. If Jacob painted 35 of them with a yellow dye, 43 of them with a blue dye and 42 of them with a red dye, how many of them are green, orange and purple? yellow + blue = green Hint yellow + red = orange red + blue = purple A bat and a ball costs £4.20, the bat costs £3 more than the ball. How much does the ball cost? 9
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