City of London School Group 2 by smoothmaths | Jun 17, 2020 | 0 comments Welcome to your City of London School Mathematics Entrance Examination for entry in September 2008 Group 2 1. Look at these number cards. : Write the letter of the card that is ten times as big as 73 ——–— one thousand times as big as 73——–— one hundredth of 73 %BLANK% Write one number at the end of each equation to make it correct.Example26 + 34 = 16 + 44(a) 38 + 17 = 28 + ——–— 27 44 36 55 14 (b) 38 – 17 = 28 – ——–— 7 6 8 5 3 (c) 40 × 10 = 4 × ——–— 100 1000 10 40 50 (d) 7000 ÷ 100 = 700 ÷ ——–— 10 100 1000 70 700 2. The graph shows the average heights of young children. (a) What is the average height of girls aged 30 months? 90cm 95cm 89cm 85cm 87cm (b) What is the average height of boys aged 36 months? 96cm 95cm 98cm 97cm 94cm (c) Jane is average height for her age. Her height is 80cm. Use the graph to find Jane's age. 18 months 15 months 12 months 17 months 16 months (d) This formula tells you how tall a boy is likely to be when he grows up. . Marc's mother is 168cm tall. His father is 194cm tall.What is the greatest height Marc is likely to be when he grows up? Show your working. 198cm 194cm 178cm 188cm 168cm 3. (a) P is the midpoint of line AB. What are the coordinates of point P? P is (——–— , ——–— ) (60,60) (50,50) (40,40) (30,30) (70,70) (b) Q is the midpoint of line MN.The coordinates of Q are ( 30, 50 ) What are the c-oordinates of points M and N? M is (——–— , ——–— ) N is (——–— , ——–— ) M=(0,100),N=(60,0) M=(0,50),N=(60,0) M=(0,100),N=(30,0) M=(0,50),N=(40,0) M=(0,60),N=(100,0) 4. Andrew went on a cycling holiday. The table shows how far he cycled each day. Monday Tuesday Wednesday Thursday 32.3 km 38.7 km 43.5 km 45.1 km He claimed; 'On average, I cycled over 40 km a day'. Show that Andrew is wrong. 39.9<40 41>40 38<40 42>40 37<40 5. Which two numbers have a mean of 10 and a range of 8? The numbers are——–— and ——–— 14&6 12&5 14&7 13&6 14&8 6. A ruler costs k pence, and a pen costs m pence. Match each statement with the correct expression for the amount in pence. The ﬁrst one is done for you. 7. (a) A football club is planning a trip.The club hires 234 coaches. Each coach holds 52 passengers. How many passengers is that altogether? Show your working. ——–— passengers 12168 10968 11168 12968 11198 (b) The club wants to put one first aid kit into each of the 234 coaches.These first aid kits are sold in boxes of 18 How many boxes does the club need? ——–—boxes 13 boxes 15 boxes 18 boxes 11 boxes 20 boxes 8. You can buy a new calculator for £1.25 In 1979 the same type of calculator cost 22 times as much as it costs now.How much did the same type of calculator cost in 1979? Show your working. £ ——–— £27.50 £ 25.50 £ 27.40 £ 26.50 £ 24.50 9. Here are some number cards: You can use each card once to make the number 1735, like this: (a) What is the biggest number you can make with the four cards? 7531 7351 7513 7153 7135 (b) Explain why you cannot make an even number with the four cards. there is no 2multiple there is no even number there is no odd number there is no prime number both a&b (c) Use some of the four number cards to make numbers that are as close as possible to the numbers written below. Examples You must not use the same card more than once in each answer. 50 ……………... %BLANK%%BLANK% 60 ……………… %BLANK%%BLANK% 4000 ……………... %BLANK%%BLANK%%BLANK%%BLANK% 1500 ……………… %BLANK%%BLANK%%BLANK%%BLANK% 1600 ……...……... %BLANK%%BLANK%%BLANK%%BLANK% 10. (a) The diagram shows part of a number line. What number is the arrow pointing to? Write your answer in the box. 5.2 5.1 5.3 5.4 5.5 10.(b) Now draw an arrow on the number line above to show the number that is 1.2 less than 7 %BLANK% 10.(c) Work out the answer to 6.7 – 0.8 %BLANK% 5.9 6.1 5.5 5.8 5.6 11. a) Find the surface area of a cuboid which measures 2 cm by 3 cm by 7 cm. Include the units in your answer. 82\[cm^{2}\] 41\[cm^{2}\] 84\[cm^{2}\] 80\[cm^{2}\] 45\[cm^{2}\] b) Find the volume of the cubo. 42\[cm^{3}\] 14\[cm^{3}\] 6\[cm^{3}\] 21\[cm^{3}\] 32\[cm^{3}\] 12. Below is a map of the area surrounding City of London School drawn to a scale of 1 cm : 125 metres. a) Estimate how far it is, in metres, from City of London School to Bank Station by following the path shown. Give your answer to the nearest 10 metres. 880m 840m 780m 875m 770m b) If the walking distance form City of London School to Guildhall is 1500 metres, and I walk at 5km/h, find how long it takes, in minutes, to walk from Guildhall to the school. 18mins 180mins 60mins 30mins 0.3mins 13. Reflect the word MATHEMATICS in the given line. M A T HEMATICS 14. Look at the three by three table. Fill in the missing numbers so that each row adds up to 3, each column adds up to 3 and each diagonal adds up to 3 2 %BLANK% %BLANK% 3 1 %BLANK% 2 %BLANK% 4 5,0,-1,-3 5,-1,0,-3 -1,0,-3,5 0,-1,-3,5 '-1,-3,0,5 15. How many triangles are there in this diagram? 7 6 8 5 9 16. I have four identical square tiles. (a) Shade in the diagram below to show how the four tiles can fit together to make a pattern with 4 lines of symmetry. (b) Now shade in the next diagram to show how the four tiles can fit together to make a pattern with no lines of symmetry. (c) Show how the four tiles can fit together to make a pattern with rotation symmetry of order 2 . 17. I travel 1 mile at 60 m.p.h. and then 1 mile at 30 m.p.h. What is my average speed in miles per hour? 40mph 50mph 30mph 60mph 20mph 18. Find the sum of the prime numbers between 50 and 60. 112 102 115 122 130 19. What percentage of the integers 1 – 100 inclusive are not a multiple of 10? 90% 80% 70% 10% 60% 20. Even though the method of cancelling shown below is incorrect, the student has got the correct answer by chance. Can you find a similar fraction which will cancel down to give 2 5 ? \[\frac{26}{65}\] \[\frac{32}{35}\] \[\frac{22}{25}\] \[\frac{44}{45}\] \[\frac{27}{75}\] 21. What is the size of the angle labelled x in the diagram? The diagram is not drawn to scale. x = ——–— x=75 x=65 x=55 x=85 x=70 22. If you add up the digits of 14 you get 5 i.e. 1 + 4 = 5. How many 2-digit numbers are there altogether (including 14) which add up to a multiple of 5? 18 28 38 19 20 23. Find the sum of the smallest multiple of 11 greater than 100 and the largest multiple of 11 less than 300. 407 400 307 300 410 24. ≈ means approximately equal to. Given that 1 kilogram (kg) ≈ 2·2 pounds (lb), convert 154 lb to kg. 70kg 80kg 90kg 60kg 50kg 25. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 from the sequence of numbers above: (a) Which numbers are square numbers? 1144 2,89 1233 5,55 8,34 (b) Which number is the cube of 2? 8 5 13 24 11 (c) Which number is the cube root of 125? 5 2 1 3 4 (d) How many prime numbers are there in the list? 6 7 5 4 8 (e) The sequence of numbers above is called the Fibonacci sequence. 89 is the 11th Fibonacci number. Find the first 6 decimal places of 89 1 by finding 1 ÷ 89. 0,1,1,2,3,5 0,1,2,3,1,5 0,1,2,2,1,5 0,1,5,3,4,5 0,2,2,3,2,5 26. A palindromic number is the same whether read from left to right or right to left. For example 41514 is a palindromic number. Find as many whole numbers as you can which are: i) greater than 1 and less than 500 and ii) palindromic and iii) either a square number or a cube number. Do your working below the answer line. Answers: 121,484,343 121,216,225 484,125,216 289,400,256 196,169,343 Time's up