Easy problems. E2 Calculate A -1 B 0 C 1 D 2 E 5 E3 Calculate A 8 B 9 C 10 D 12 E 24

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1 Easy problems E1 How many tadpoles are there in this picture? A 1B 3 C 6 D 12 E cannot tell E2 Calculate A -1 B 0 C 1 D 2 E 5 E3 Calculate A 8 B 9 C 10 D 12 E 24 E = A 10 B 1111 C 4321 D 1234 E E5 What is the value of 2 2 2? A 2 B 6 C 8 D 222 E none of these E6 Which has the answer 49? A 2 25B 4 12C 5 10D 6 8 E 7 7 E7 What are the missing numbers in this table? A 4 and 35 B 6 and 30 C 8 and D 6 and 35 E 8 and E8 How many of these fractions are more than 2 1? E9 What is 2 1 of 2 1? A 0 B 1 C 1 D 2 E E10 Which fraction has the largest value?

2 Harder problems H25 Boris the spider weaves a circular web of circumference 40 cm. The web is made of sections where the angle at the centre is exactly 45 degrees. If he travels around the edge of one of the sections of his web, how far will he have travelled? 45 A 5 cm B 8 cm C 10 cm D 15 cm E 24 cm H26 The diagram shows centimetre cubes arranged into a bigger cube with holes all the way through. How many centimetre cubes are there in the model? A 7 B 20 C 22 D 24 E 27 H27 Which of these solid shapes will not tessellate in three dimensions? A B C D E H28 How many lines of symmetry does a chess board have? H29 How many of these 11 letters have at least one line of symmetry? M E A S U R E M E N T A 0 B 6 C 7 D 8 E 9 H30 Suppose 2 5 of people are left-handed. How many left-handed people would you expect to find in a group of 55 people on a coach? A 2 B 11 C 22 D 25 E 30 8

3 P1 P2 Puzzling problems Jamal tried to work out on a calculator but he made a mistake and got the answer Which of these is most likely to have been his mistake? A He pressed instead of + B He pressed 21.7 instead of 12.7 C He pressed instead of + D He pressed 35.8 instead of 38.5 E He missed out one of the decimal points. Mick Sterbs the gardener plants 30 rows of beans, 20 rows of carrots and 15 rows of cabbages. Each row has 20 plants. How many plants has he planted altogether? A 600 B 700 C 900 D 1000 E 1300 P3 A group of four girls is having problems. J dislikes K and L. L dislikes J and M. K dislikes L and M, and M dislikes L. Which two girls get on well together? A J and M B L and M C J and K D K and L E L and J P4 European countries use the Indian/Arabic way of writing numbers, but our symbols look different now. In Arabic the number 427 is written and 742 is. Which of these represents the number 247? A B C D E P5 An extra large tub of mini-heroes chocolates weighs 1.5 kg including wrappings. The weight of the chocolates is 1.44 kg. How much do the wrappings weigh? A 6 g B 39 g C 60 g D 390 g E 600 g P6 A clock strikes only the hours. How many times does it strike altogether in twenty four hours? A 24 B 48 C 78 D 156 E

4 V9 Very challenging problems The ages of the three children in my family multiplied together come to How old is the oldest child? A 7 B 11 C 13 D 17 E 19 V10 Illtyd tried to use a calculator to add two 2-digit numbers. But he pressed instead of + and got the answer 325. What was the correct answer to the addition? A 25 B 32 C 38 D 70 E More information needed V11 I have four counters numbered 1, 2, 3 and 4. Using each counter only once, what is the largest number I can get if I make them into two 2-digit numbers and multiply them together? A 312 B 1302 C 1312 D 1849 E 1936 V12 Which set of numbers gives a mean of 7, a median of 6 and a mode of 5? A 4, 15, 5, 6, 6 B 5, 5, 7, 7, 11 C 4, 5, 6, 7, 8 D 7, 7, 7, 7, 7 E 7, 6, 5, 5, 12 V13 A set of four numbers has mode 7, median 10 and mean 15. What is the range of the four numbers? A 10 B 13 C 17 D 26 E more information is needed V14 The diagram shows a black and white cubic liquorice allsort with three layers of equal thickness. What fraction of the outside is coloured black? A 1 B 2 C 4 D 1 E V15 Which of these fractions gives when written as a decimal? A 4 B 4 C 4 D 4 E

5 The Primary Mathematics Challenge The problems in this book are taken from the Primary Mathematics Challenge (PMC) papers from November 2002 to February The PMC is aimed at school pupils aged 11 or less. In September and October, schools order packs of ten challenge papers (which include Answers and Notes and certificates for everyone). Pupils take the challenge at any time during the month of November. The top scoring pupils are then invited to take the PMC Finals in the following February. Questions from these finals are included in this book. For further information, visit the PMC pages on the MA website ( The problems set in the PMC Finals are very difficult for primary-aged pupils, and therefore will also challenge younger secondary pupils. PMC Live On-Line Two PMC papers can be taken live on line on the MA website. Primary Maths Problems On-Line There are also some more PMC problems live on the MA website. These can be accessed directly by pupils from school or home. Pupils select one of four levels, and are given five problems at that level from the problems bank. Their responses are marked and a certificate provided. 79