Your Name Candidate Number 2 Specimen Entrance Examination to join First Form MATHEMATICS Do not open this booklet until you are told to do so INSTRUCTIONS • This paper is indicative of entrance exami[.]
Your Name: Candidate Number: Specimen Entrance Examination to join First Form MATHEMATICS Do not open this booklet until you are told to so INSTRUCTIONS • • • • • This paper is indicative of entrance examination content Answer as many questions as you can in the spaces provided Show all your working clearly Be careful not to spend too long on any one question Calculators are not allowed Leave blank % Score Total Marker 60 For this question you can rough working on the left hand side of the page if required Put answers only in the spaces on the right 2.74 × 10,000 = …… ……… 132 = …… ……… The square root of 49 is …… ……… The cube root of 125 is …… ……… 43 = …… ……… 240 300 in its simplest form is …… ……… 25% of 68 = …… ……… 43 × 38 = …… ……… (8) The calculator display below shows as a decimal Complete the empty box to show how the calculator would display the answer to 900 You not need to write your digits in the same style, but you should use 10 digits (1) I buy drinks at 72p each, and sandwiches at £1.21 each How much change I get from a £20 note? £…………………….…………… (2) City of London School Reflect the letters in the mirror line below Three letters have been done for you QUEEN U V I C T OR I A O STREET T mirror line (2) 1 Martin is given £240 He gives to his sister and of what remains to his little brother How much does he keep himself? £…………………….…………… (2) City of London School The thermometers below show the temperature recorded at midday yesterday and midnight last night Midnight Midday o F 90 o o C F 90 30 o C 30 70 20 70 20 50 10 50 10 30 30 –10 –10 (i) What was the temperature midday yesterday in °F? (ii) What was the temperature midnight last night in °C? (iii) …………………….……………°C What was the difference in temperature between midday yesterday and midnight last night in °C? …………………….……………°F …………………….……………°C (3) How many minutes are there between 9.23 am and 1.06 pm? …………………….……………minutes (2) City of London School (i) What fraction of the above design is shaded? Give your fraction in its simplest form (ii) …………………….…………… How many more of the hexagons need to be shaded so that of the design is shaded? …………………….…………… (iii) What fraction of the large rectangle below is shaded? …………………….…………… (3) (i) Write 15% as a fraction in its simplest form …………………….…………… (ii) Rowan sends text messages each day A £5 credit buys him 140 text messages Today he received an extra 15% free text messages when he bought his £5 credit How many days should the credit last? Show your working …………………….……………days (3) 10 In a sponsored walk: Adam took hours, 39 minutes; Billy took 274 minutes and Charlie took hours Who was quickest and who was the slowest? Quickest …………………….…………… Slowest…………………….…………… (1) City of London School 11 The diagram below shows two overlapping rectangles 12cm 5cm 9cm Diagram not drawn to scale 13cm 7cm 20cm i) Calculate the area of the larger rectangle only …………………….……………cm2 ii) Calculate the total shaded area that the rectangles cover …………………….……………cm2 (4) 12 The diagram below shows a rectangle and a square The diagrams are not drawn to scale 70cm 30cm If they have equal perimeters, what is the difference in their area? …………………….……………cm2 (2) City of London School 13 Calculate the size of the missing angle in this triangle The diagram is not drawn to scale 33° 85° …………………….……………° (1) 14 (a) Find the size of angle ‘𝑎’ in the diagram below 19° 72° 𝑎 17° 𝑎 = ….……………° (b) Would you describe 100°? Acute, obtuse or reflex? …………………….…………… (3) City of London School 15 A right angled triangle is shown below It is not drawn to scale 5∙8 cm cm cm (i) Calculate the perimeter of the triangle (ii) Calculate the area of the triangle …………………….……………cm …………………….……………cm2 (2) 16 15 cm 11 cm 20 cm The diagram above is not drawn to scale (i) A box measures 20cm by 11cm by 15cm Calculate the volume of the box …………………….……………cm3 (ii) A string is tied around the box with a bow at the top as shown in the diagram If the length of the bow is cm, calculate the total length of string used …………………….……………cm (4) City of London School 20, 21, 22, 23, 24, 25, 26, 27, 28, 17 Write one number from 20 to 30 that satisfies the descriptions below Some numbers are used more than once (i) Prime? (ii) Cube numbers? (iii) Square numbers? (iv) ………………………………………………………………………… Fibonacci numbers? The Fibonacci numbers follow the sequence 1, 1, 2, 3, 5, 8, 13… (v) ………………………………………………………………………… Triangular numbers? The triangular numbers follow the sequence 1, 3, 6, 10, 15, … ………………………………………………………………………… ………………………………………………………………………… (vi) ………………………………………………………………………… Perfect numbers? A perfect number is a number whose factors (not including itself) add up to itself e.g is a perfect number because + + = ………………………………………………………………………… (vii) Powerful numbers? A powerful number has the property that for every prime number which divides into it, that prime number squared also divides into it e.g 16 is a powerful number because both and 22 are factors ………………………………………………………………………… (7) City of London School 18 What is − ((4 + 4) ÷ 4)? …………………….…………… (1) 19 1001 = 𝑎 × 𝑏 × 𝑐, where a, b and c are prime numbers, with c is bigger than b, and b bigger than a Find a, b and c a = ………., b = ………., c = ……… (2) 20 Given that 2357 × 99 = 233 343, find: (i) 233 343 ữ 99 . (ii) 2357 ì 99 …………………….…………… (2) City of London School 10 21 The symbol ⟴ has a special meaning in arithmetic 𝑎 ⟴ 𝑏 means add 𝑎 and 𝑏 and then multiply by 𝑎 For example: ⟴ = × (4 + 2) =4×6 = 24 (a) Work out ⟴ …………………….…………… (b) Work out ⟴ (3 ⟴ 2) …………………….…………… (c) Work out the value of 𝑝 such that ⟴ 𝑝 = 78 𝑝 = …………………….…………… (3) City of London School 11 22 Four bells ring at intervals of 2, 8, and 11 seconds If they are all rung at the same time, how many seconds will pass before they all ring at the same time again? You should show some justification for your answer …………………….…………… seconds (2) END OF EXAM Now go back and check your work! City of London School 12 11+ Specimen Paper Mark Scheme Answers 27400 169 64 Notes (cao) (cao) (cao) (cao) (cao) Answers 15 (i) 13.8 (ii) 7.5 16 (i) 3300 (ii) 130 4/5 (cao) 17 17 1634 0.002222222 £4.07 (cao) (cao) (0.00222 digits at least) (award for £15.93) 6 (i) 54 (ii) –6 (iii) 18 223 (allow 3hrs 43) (i) 1/3 (ii) (iii) 11/16 (i) 3/20 (ii) 23 10 Billy ; Adam 11 (i) 360 (20 × 18) (ii) 448 (468 − 20) 12 400 (502 − 30 × 70) 13 62 14 (a) 𝑎 = 20° (b) obtuse (award if see 42 or 3/10 or 7/10) (cao) (cao) (cao) (award for last digits 23) (cao) (cao) in question (vii) 18 19 complete words correct or one letter wrong throughout) 168 (i) 23 (or 29) mistake (cao) (ii) (iii) (iv) (v) (vi) 11 (award if any two (15 × 11 × 20) Notes (cao) (cao) (award if see 220, 300 or 165) (award if see ‘122’) 20 (i) (ii) 21 (a) (b) (c) 22 27 25 21 21 or 28 28 25 or 27 𝑎=7 𝑏 = 11 𝑐 = 13 2357 23334.3 36 76 LCM (2, 7, 8, 11) 616 (7 × × 11) (cao) (cao) (cao) (cao) (cao) (cao) (cao) (award if two of a,b,c correct or if 143 seen) (cao) (cao) (cao) (cao) (cao) (good attempt at LCM) (award for 1232) 1 (accept 5.5 𝑜𝑟 ) 8 (cao) (award if see ‘161’) (cao in that order) (award if see ‘18’) (award if see ‘468’) (award if see ‘2100’ or 2500) (cao) (award if see 18 & 143 on diagram, or 71 in bottom left) (cao) Total: 60 marks Mark % Mark % 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2% 3% 5% 7% 8% 10% 12% 13% 15% 17% 18% 20% 22% 23% 25% 27% 28% 30% 32% 33% 35% 37% 38% 40% 42% 43% 45% 47% 48% 50% 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 52% 53% 55% 57% 58% 60% 62% 63% 65% 67% 68% 70% 72% 73% 75% 77% 78% 80% 82% 83% 85% 87% 88% 90% 92% 93% 95% 97% 98% 100% ... …………………….…………… seconds (2) END OF EXAM Now go back and check your work! City of London School 12 11+ Specimen Paper Mark Scheme Answers 27400 169 64 Notes (cao) (cao) (cao) (cao) (cao) Answers 15 (i) 13.8... …………………….…………… (c) Work out the value of