Primary Maths Challenge 2010 Primary Mathematics Challenge Semi

Primary Maths Challenge 2010

Primary Mathematics Challenge Semi -final round 1 Question no. 1 You are allowed only one attempt at this question. It is worth a total of 10 marks Amy adds the three numbers between 5 and 9 together What is her total? Answer 2010 Mark

Primary Mathematics Challenge Semi -final round 1 Question no. 2 Amy buys 3 pencils and a sharpener. 40 p 90 p How much change does she have from £ 5? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi -final round 1 Question no. 3 You are allowed only one attempt at this question. It is worth a total of 20 marks Jack calculates 4 x 15 x 3 instead of 5 x 3 x 4 What is the difference between his two answers? ANSWER 2010 Total marks

N Primary Mathematics Challenge Semi-final round 1 Question no. 4 Jamie is travelling north-west when he realises he should be travelling east. He turns anti-clockwise. How many degrees does he turn through to make sure he is travelling in the right direction? Try 1 2 3 2010 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 5 The numbers in the boxes are found by adding together the two numbers in the boxes immediately below. Complete the drawing so that all boxes are filled correctly 50 20 15 50 30 20 10 15 1 st try for 10 marks 20 15 10 2 nd try for 5 marks 50 2010 30 30 10 3 rd try for 5 marks

You are allowed only one attempt at this question. It is worth a total of 20 marks Primary Mathematics Challenge Semi -final round 1 Question no. 6 The names of four mathematical shapes are hidden in this circle. The letters in pairs of sectors will together make the name of one shape. Write the shapes correctly in the answer boxes Find all four shapes – each one is worth five marks each Ans. In any order E X A L Y N C O G S U 2010 H D I M R R A B P R N I E D M O H Y Total marks Mark

Primary Mathematics Challenge Semi-final round 1 Question no. 7 Look at this sentence: ALL CHILDREN SHOULD HAVE THREE HOURS MATHEMATICS HOMEWORK EVERY NIGHT What is the average number of letters per word? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 8 James Connolly of the USA won the triple jump in the Olympic Games of 1896 with a distance of 13. 71 m. Nelson Evora of Portugal won the Beijing event in 2008 with a distance of 17. 44 m. How much further did Evora jump? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 9 You are allowed only one attempt at this question. It is worth a total of 20 marks A rocket travels 5 metres using 25 grams of gunpowder. Jack’s rocket weighs 500 grams. The casing and stick weigh 125 grams and the stars inside the rocket weigh 75 grams. The rest is gunpowder. Jack fires his rocket from the bottle shown below. Put a cross where you think the rocket lands – the cross must be accurate 40 -50 m 51 -55 m 2010 56 -60 m 61 -65 m Total marks

Primary Mathematics Challenge Semi -final round 1 Question no. 10 Pringles tubes are packed in larger boxes of 16 A shopkeeper buys 8 larger boxes. How many Pringles tubes does the shopkeeper have altogether? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 11 Beth is on a calorie controlled diet. She eats 1800 calories each day. How many calories does she eat in one week? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi -final round 1 Question no. 12 You are allowed only one attempt at this question. It is worth a total of 20 marks Each of these questions is worth five marks. Ans. 1. How many degrees are there in a triangle? 2. 40 is the total of 12, 17 and which number? 3. What is a quarter of 96? 4. How many millimetres in 4. 7 cm? Total marks 2010 Mark

Primary Mathematics Challenge Semi -final round 1 Question no. 13 Jack has a tank containing 15 litres of water. He transfers some of his water to two bottles. He puts a third in the first bottle and 20% in the other bottle. How much water is left in his tank? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 14 Jack works five days from Monday to Friday. On Monday he earns £ 1. 25. Each day that he works his pay doubles from the previous day. How much does he earn altogether during the five days? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 15 You are allowed only one attempt at this question. It is worth a total of 20 marks Del Boy buys 20 Martian reject DVD players for £ 15. 50 each. He sells them all for a total of £ 550 Answer How much did he pay in total for the DVD players? (10 marks) How much profit did he make on each DVD player? (10 marks) Total marks 2010 Marks

Primary Mathematics Challenge Semi -final round 1 Question no. 16 Beth uses circles to continue the pattern How many circles will she draw to show the next item in the sequence? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 1 Question no. 17 You are allowed only one attempt at this question. It is worth a total of 20 marks A captain sails the shortest route between Fish Island Ghost island. The scale on his map is 10 mm to every 2 km Ports Grid size Round Island Ghost Island Fish Island Bird Island How far does the captain sail between the islands? 2010 ANSWER km Marks 2 cm

Primary Mathematics Challenge Semi-final round 1 Question no. 18 Each square on the co-ordinate grid is 1 unit long and 1 unit wide Co-ordinate ( , ) Marks You are allowed only one attempt at this question. It is worth a total of 20 marks The circle intersects with the triangle and the rectangle on the grid at four different points Write the four co-ordinates (in any order) for 5 marks each Total marks 0 2010

Primary Mathematics Challenge Semi -final round 2 Question no. 1 You are allowed only one attempt at this question. It is worth a total of 10 marks Two odd numbers with a difference of 2 when multiplied together make 35 Writer the two numbers in the answer box Answer 2010 Mark

Primary Mathematics Challenge Semi-final round 1 Question no. 2 Identify one thing that is the same about all six of these numbers 1412 2010 233 53 Try 1 2 3 20006 Answer 35 80 Mark 10 5 5

Primary Mathematics Challenge Semi-final round 2 Question no. 3 You are allowed only one attempt at this question. It is worth a total of 20 marks In Maths Challenge semi-final round 1 there were 16 schools competing and in semi-final round 2 there were 14 schools competing. After each semi-final half the teams from each round went through to the final. Teams have four children each. How many children went to the final? ANSWER 2010 Total marks

Primary Mathematics Challenge Semi -final round 2 Question no. 4 The perimeter of the equilateral triangle is 60 cm. What is the area of the square? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi -final round 2 Question no. 5 Millie doubles a number and doubles it again. Her outcome is 0. 5 What number did she start with? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi -final round 2 Question no. 6 The bar graph shows the amount of money collected by five children in a charity swim John Beth Lucy Peter Amy 0 10 20 Money in £s 30 1. How much money did Amy raise? 2. How much more money did Peter raise than Beth? 2010 Try 1 1 2 1 3 1 Answer 2 2 2 Mark 10 5 5

Primary Mathematics Challenge Semi-final round 2 Question no. 7 10 cm This shape is made up from four squares the same size. A shaded square is made from the diagonals of the four squares. The sides of the smaller squares are each 10 cm 2010 What is the area of the grey square? Try 1 2 3 Answer cm 2 Mark 10 5 5

Primary Mathematics Challenge Semi-final round 2 Question no. 8 You are allowed only one attempt at this question. It is worth a total of 20 marks Each of these true or false statements is worth five marks T or F 1. You cannot make two squares by folding a rectangle in half 2. All even numbers are divisible by both 2 and 4 without a remainder 3. A regular shape must have all its sides equal and all its angles equal 4. 45 mm is twice the length of 2. 25 cm Total marks 2010 Marks

Primary Mathematics Challenge Semi -final round 2 Question no. 9 You are allowed only one attempt at this question. It is worth a total of 20 marks There are six judges in a gymnastics competition. The maximum score each judge can award is 10. Jane’s five scores on the bar are 8. 5 8. 275 8. 4 8. 175 8. 45 The highest and lowest marks are not counted and the remaining scores are added together. What is Jane’s final total Answer Total marks 2010

Primary Mathematics Challenge Semi-final round 2 Question no. 10 Millie rounds two, 2 -digit numbers to the nearest ten. Her answer in both cases is 50. Both her numbers are prime numbers. What are her two numbers and what is the total of the two numbers? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi -final round 2 Question no. 11 Look carefully at the sketch. How many different squares can you find in the drawing? 2010 Try 1 2 3 Answer Mark 10 5 5

You are allowed only one attempt at this question. Semi-final round 2 Question no. 12 It is worth a total of 20 marks Which of these numbers is the odd one out according to the information given? Primary Mathematics Challenge Ans. There are 5 marks for each answer 49 39 27 19 29 69 1. The only prime number that is 30 when rounded to the nearest 10 2. The only square number 3. The only multiple of three where the sum of the digits is a multiple of five 4. The only number that is a cube number (e. g. 1 is a cube number because it is 1 x 1) Total marks 2010 Mark

Primary Mathematics Challenge Semi -final round 2 Question no. 13 Beccy goes on a bicycle journey. She travels for 1½ hours at 18 k. p. h. and for 45 minutes at 20 k. p. h. How far does she travel altogether? 2010 Try 1 2 3 Answer Mark 10 5 5 k. p. h. means kilometres per hour

Primary Mathematics Challenge Semi-final round 2 Question no. 14 Three-fifths of a number is 15. Two thirds of another number is 6. Find the product of the two numbers. 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Semi -final round 2 Question no. 15 Here is a number function machine. It uses two processes in the rule. What is the rule used to change the input number to the output number? Input Try 1 2 3 2010 Function Output 15 9 27 13 30 14 Answer Mark 10 5 5

Primary Mathematics Challenge Semi-final round 2 Question no. 16 A B C D Each cube is 1. 5 times smaller than the cube to its right. Cube B has a volume of 36 cm 3 What are the volumes of the other three cubes 2010 Try 1 A 2 A 3 A Answer C D C D Mark 10 5 5

Primary Mathematics Challenge Semi-final round 2 Question no. 17 There are 240 children in a school. The chart shows the percentage of children who like best the subjects shown. Science Games Mathematics English How many children like mathematics? How many children like English? 2010 Try 1 Maths 2 Maths 3 Maths Answer science Mark 10 5 5

Primary Mathematics Challenge Semi-final round 2 Question no. 18 You are allowed only one attempt at this question. It is worth a total of 20 marks This question is a real challenge!!! A Think what you know about isosceles triangles and it will become easier 250 B Triangle ABC is isosceles. 900 Angle DAC is 250 Calculate angles BAC and BCD 900 D C 2010 Answer: angle BAC is 0 10 marks Answer: angle BCD is 0 10 marks Total marks

Primary Mathematics Challenge Final round 1 Question no. 1 You are allowed only one attempt at this question. It is worth a total of 10 marks Tom shares 40 sweets equally between himself and three friends. How many sweets do they each have? Answer 2010 Mark

Primary Mathematics Challenge Final round 1 Question no. 2 Beth buys a birthday present and has £ 9. 51 change from £ 20 How much did the present cost? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 3 You are allowed only one attempt at this question. It is worth a total of 20 marks Sophie’s house number is between forty and sixty-one. Her house number is an odd number. Rounded to the nearest 100 it is 100. What are all the possibilities her house number could be? ANSWER 2010 Total marks

Primary Mathematics Challenge Final round 1 Question no. 4 In this row of numbers Amy halves the even numbers and doubles the odd numbers. She the rewrites them in order starting with the smallest 11 24 10 7 19 14 8 21 Rewrite her new numbers in order in the try boxes below 1 st try 10 marks 2 nd try 5 marks 3 rd try 5 marks 2010

Primary Mathematics Challenge Final round 1 Question no. 5 Find the average height in cm of the three children below. 2 m 1 m 0 m 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 6 You are allowed only one attempt at this question. It is worth a total of 20 marks The rule for this function machine is double the input number and subtract 4 For five marks each, write the missing numbers in the spaces INPUT FUNCTION OUTPUT 45 18 3. 25 8. 8 TOTAL MARKS 2010 MARKS

Primary Mathematics Challenge Final round 1 Question no. 7 What is the difference in area between the square and the triangle? Each square in the drawing is 1 cm long and 1 cm wide Try 1 2 3 2010 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 8 In the first modern Olympic games in Athens in 1896 the 100 m was won by Francis Lane of the USA in a time of 12. 20 sec. In Beijing 2008 Usain Bolt was quicker by 2. 51 sec. in the same event. What was Usain Bolt’s time? 2010 Try 1 2 3 Answer Mark 10 5 5

You are allowed only one attempt at this question. It is worth a total of 20 marks Primary Mathematics Challenge Final round 1 Question no. 9 Each of these wheels is a mathematical process, item or term. Work out each one and write the answer – correctly - in the boxes below Each answer is worth five marks A E T C E L N G R C S E I O L E S S I O T P R T N A I Total marks 2010 U T M O N R E A R

Primary Mathematics Challenge Final round 1 Question no. 10 In a Sudoku puzzle there are nine large squares, each with nine smaller squares containing each of the numbers 1 -9. What is the total of all the digits used when the whole puzzle is completed? Sample 2 3 9 8 5 8 6 2010 1 7 1 4 6 1 9 5 4 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 11 Three of these drawings show three-fifths shaded grey Write the letters of these drawings in the answer box A 2010 B C D Try 1 2 3 E Answer F Mark 10 5 5

You are allowed only one attempt at this question. It is worth a total of 20 marks Primary Mathematics Challenge Final round 1 Question no. 12 Each of the single digit numbers in the list can be added to a 2 -digit number to make a square number. Each pair and correct solution are worth 5 marks Write each pair in the answer boxes along with the square number you have made. 10 2010 9 29 8 16 Pair no 1 = Pair no 2 = Pair no 3 = Pair no 4 = 6 Total marks 7 56

Primary Mathematics Challenge Final round 1 Question no. 13 In the early days of making cartoon films the animator had to draw a minimum of 12 pictures for every second of film. What was the minimum number of pictures drawn for two minutes of cartoon? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 14 Jack works five days from Monday to Friday. Each day that he works his total pay is double the previous day. At the end of five days he has earned £ 192 How much did he earn on Monday? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 15 Jack has three numbers, they are 3, 5 and 7 Calculate the difference between their product and their total 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 16 A sports shop reduces all prices by 20% in a sale. What was the old price of a cricket bat? Now £ 120 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 1 Question no. 17 You are allowed only one attempt at this question. It is worth a total of 20 marks Jack has a five digit combination lock. No two digits are the same. Each box contains a single digit Using the clues below work out Jack’s combination. The first and last digits total 5 The middle digit is even and a prime number The first three digits are even, odd, even The second digit is a square number greater than one The fourth digit is the sum of three of the other digits Jack’s combination is: 2010 Total marks

Primary Mathematics Challenge Final round 1 Question no. 18 You are allowed only one attempt at this question. It is worth a total of 20 marks Tom calculates the area of each of these rectangles. He then writes them in order starting with the largest at the top. Calculate each area and write the letters of each rectangle in order of size in the answer column. 5 marks for each correct answer in the right place 9 cm 6 cm Shape A 12 cm Each square is 0. 5 cm The width is half the length B D 2010 C 140 mm Total marks 5 cm Mark

You are allowed only one attempt at this question. It is worth a total of 10 marks Primary Mathematics Challenge Final round 2 Question no. 1 Lucy looks at this part of a 1 -100 number square. She subtracts the two missing numbers. What is her answer? 44 45 65 Answer 2010 Mark

Primary Mathematics Challenge Final round 2 Question no. 2 In each 480 gram box of chocolates there are two identical layers of chocolates. In each layer there are 12 chocolates. What is the average weight of each chocolate? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 3 You are allowed only one attempt at this question. It is worth a total of 20 marks A double-decker bus has the following passenger spaces: Lower deck 24, upper deck 36, 8 standing. How many people are on the moving bus altogether when it is full? (think very carefully before you answer!!) ANSWER 2010 Total marks

Primary Mathematics Challenge Semi-final round 2 Question no. 4 The sequence is made from two alternating sequences. 1 0 4 2 7 4 10 6 13 8 Which two numbers come next? 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 5 Lisa starts in the grey box. When she moves to a circle she adds 5 to the number she has just left. When she moves to a square she subtracts 2 from the number she has just left. What number does Lisa finish with in the grey circle? 50 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 6 You are allowed only one attempt at this question. It is worth a total of 20 marks How many cubes have been used to make this shape. Circle the answer you think is correct 18 19 20 21 22 23 24 2010 Total marks

Primary Mathematics Challenge Final round 2 Question no. 7 0 cm 10 cm 20 cm 30 cm 40 cm Tom uses the gauge to measure the width of his octagon in mm How wide is Tom’s octagon in mm? 2010 Try 1 2 3 Answer mm mm mm Mark 10 5 5

Primary Mathematics Challenge This question is worth 20 marks. Final round 2 Question no. 8 You will have only one attempt to complete your answer The 24 -hour digital clock display shows the time Sally’s train leaves the station. Her journey takes 2 hours and 52 minutes. Shade in the bars on the 24 -hour digital clock below to show her arrival time. 2010 Total marks

Primary Mathematics Challenge Final round 2 Question no. 9 Sarah produces a tally chart of stickers collected by her friends Number of stickers 20 Number of stickers Jack Lucy Tom Amy Ben She makes it into a graph but it is not complete Your tasks 10 0 2010 You are allowed only one attempt at this question. It is worth a total of 20 marks 1. Use the tally chart information to write the 5 children’s names in the correct place on the vertical boxes on the horizontal axis. (10 marks) 2. Complete the tally chart by putting in Tom’s tally. (10 marks) Total marks

Primary Mathematics Challenge Final round 2 Question no. 10 Jack and Amy agree to share the cost of a skateboard. Jack pays 40% of the cost and Amy the rest. £ 140 How much do they each pay? 2010 Try 1 Amy 2 Amy 3 Amy Answer Jack Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 11 How many of the linked shapes below are pentagons? Write the letters of the identified shapes in the answer box B A 2010 C F D G H E Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 12 You are allowed only one attempt at this question. It is worth a total of 20 marks Each correct answer is worth five marks 1. Identify this 3 -d shape 2. Which regular 2 -d shape has 3 lines of symmetry? 3. The net of a cylinder is made from two circles and which other shape? 4. A hexagonal prism has how many faces? 2010 Ans. Total marks Mark

Primary Mathematics Challenge Final round 2 Question no. 13 The chart shows the number of books read by five children during a school year. How many books did they read altogether? Jack Amy Lucy Tom Ben Four books 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 14 6 18 8 16 19 15 11 23 47 21 14 17 Tom adds 19 to each of these numbers Write the numbers from the list that will give him an answer between 25 and 35 2010 Try 1 2 3 Answer Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 15 Jack finds ¾ of a number, Amy finds ½ of the same number, Ben finds 2/3 of the same number and Lucy finds 3/8 of the same number. Ben’s answer is 16. What were the answers found by the other three children? 2010 Try 1 Jack 2 Jack 3 Jack Answer Amy Amy Lucy Mark 10 5 5

Primary Mathematics Challenge Final round 2 Question no. 16 Which two criteria have been used to sort this Venn Diagram? 1 st try A. B. 81 4 36 64 75 25 9 10 marks 101 13 2 nd try A. B. 5 marks 3 rd try A. B. 5 marks 2010

Primary Mathematics Challenge Final round 2 Question no. 17 You are allowed only one attempt at this question. It is worth a total of 20 marks 8 cm 16 cm Lucy uses squares and rectangles like those above to make shape below 2010 What is the perimeter of Lucy’s new shape? Answer Total marks

Primary Mathematics Challenge Final round 2 Question no. 18 Each square on the co-ordinate grid is 1 unit long and 1 unit wide You are allowed only one attempt at this question. It is worth a total of 20 marks The kite shape is translated to a new position on the grid. Two of the new lines have been drawn for you. Complete the shape in its new position on the grid. 0 Write the four new co-ordinates (in any order) for 5 marks each Co-ordinate 2010 ( , ) Total marks Marks

Primary Mathematics Challenge Tie break question How many right-angle triangles are there in the drawing? School 2010 Answer