City of london school paper 1 by smoothmaths | Jun 19, 2020 | 0 comments Welcome to your City of London school 11+ paper Specimen Entrance Examination Mathematics 1. For this question you can do rough working on the left hand side of the page if required. Put answers only in the spaces on the right. 2740027000273002074027200 2.74 × 10,000 =2740027000273002074027200 1.(b)\[13^{2}\] =16914412181196 1.(c)The square root of 49 is —————78965 1.(c) The cube root of 125 is —————57689 1.(d) \[4^{3}\] = —————64164981none of the above 1.(e) \[\frac{240}{300}\] in its simplest form is ————\[\frac{4}{5}\]\[\frac{5}{4}\]\[\frac{3}{4}\]\[\frac{4}{3}\]\[\frac{1}{2}\] 1.(f) 25% of 68 = ———————1720251510 1.(g) 43 × 38 = —————16341600162016101590 2. The calculator display below shows\[\frac{2}{9}\] as a decimal.Complete the empty box to show how the calculator would display the answer to \[\frac{2}{900}\] . You do not need to write your digits in the same style, but you should use 10 digits. 0.0022222220.022222220.2222222220.00222none of the above 3. I buy 7 drinks at 72p each, and 9 sandwiches at £1.21 each. How much change do I get from a £20 note? £4.07£3.07£1.07£2.07£5.07 4. Reflect the letters in the mirror line below. Three letters have been done for you. 5. Martin is given £240. He gives \[\frac{1}{8}\] to his sister and \[\frac{1}{5}\] of what remains to his little brother. How much does he keep himself?168138178210200 6. The thermometers below show the temperature recorded at midday yesterday and midnight last night. 5450354044 (i) What was the temperature midday yesterday in °F? ———— °F5444405035 6.(ii) What was the temperature midnight last night in °C? —–——— °C-6-5-80-3 6.(iii) What was the difference in temperature between midday yesterday and midnight last night in °C? ————°C1816201012 7. How many minutes are there between 9.23 am and 1.06 pm? ——————minutes223200215186217 8. (i) What fraction of the above design is shaded? Give your fraction in its simplest form. \[\frac{1}{3}\]\[\frac{3}{4}\]\[\frac{1}{2}\]\[\frac{3}{2}\]\[\frac{1}{4}\] 8.(ii) How many more of the hexagons need to be shaded so that \[\frac{3}{4}\] of the design is shaded? 54321 8.(iii) What fraction of the large rectangle below is shaded? \[\frac{11}{6}\] or \[\frac{5}{8}\]\[\frac{8}{9}\]\[\frac{11}{10}\]\[\frac{5}{8}\]\[\frac{9}{16}\] 9. (i) Write 15% as a fraction in its simplest form. \[\frac{3}{20}\]\[\frac{5}{20}\]\[\frac{1}{20}\]\[\frac{1}{10}\]\[\frac{3}{10}\] 9.(ii) Rowan sends 7 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. ————days2318102021 10. In a sponsored walk: Adam took 4 hours, 39 minutes; Billy took 274 minutes and Charlie took 4\[\frac{3}{5}\] hours. Who was quickest and who was the slowest? Quickest———— Slowest————Billy Quickest, Adam SlowestBilly slowest, Adam QuickestBoth are SlowestBoth are Qucikestboth a & b 11. The diagram below shows two overlapping rectangles. 11.(i) Calculate the area of the larger rectangle only. 360 \[cm^{2}\]300\[cm^{2}\]350\[cm^{2}\]340\[cm^{2}\]310\[cm^{2}\] 11.(ii) Calculate the total shaded area that the rectangles cover. ———— \[cm^{2}\]448 \[cm^{2}\]438 \[cm^{2}\]450 \[cm^{2}\]470 \[cm^{2}\]468 \[cm^{2}\] 12. The diagram below shows a rectangle and a square. The diagrams are not drawn to scale. If they have equal perimeters, what is the difference in their area? ———— \[cm^{2}\]400 \[cm^{2}\]500 \[cm^{2}\]600 \[cm^{2}\]300 \[cm^{2}\]200 \[cm^{2}\] 13. Calculate the size of the missing angle in this triangle. The diagram is not drawn to scale. —————°6272786470 14.(a) Find the size of angle 'a' in the diagram below. a=—————°20304560None of the above 14.(b) Would you describe 100°? Acute, obtuse or reflexObtuseBilatteralAcuteRightIsosceleous 15. A right angled triangle is shown below. It is not drawn to scale. 15.(i) Calculate the perimeter of the triangle. —————cm13.8 cm10.8 cm12.8 cm8.8None of the above 15.(ii) Calculate the area of the triangle. —————\[cm^{2}\]7.56.554.53.8 16. The diagram above is not drawn to scale. 16.(i) A box measures 20cm by 11cm by 15cm. Calculate the volume of the box. —————\[cm^{3}\]3300\[cm^{3}\]3000\[cm^{3}\]3200 \[cm^{3}\]3100 \[cm^{3}\]3400 \[cm^{3}\] 16.(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 8 cm, calculate the total length of string used. —————cm130 cm132 cm122 cm78 cm120 cm 17. (ii) Cube numbers? %BLANK%2728252123 17.(iii) Square numbers? 2522242628 17.(iv) Fibonacci numbers? The Fibonacci numbers follow the sequence 1, 1, 2, 3, 5, 8, 13…2122242327 17.(v) Triangular numbers? The triangular numbers follow the sequence 1, 3, 6, 10, 15, … 212828 or 212223 17.(vi) Perfect numbers?A perfect number is a number whose factors (not including itself) add up to itself. e.g. 6 is a perfect number because 1 + 2 + 3 = 6. 2821222324 17.(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 2 and 22 are factors. 25 or 2725272829 18. What is 4 − ((4 + 4) ÷ 4)? 24869 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 =————a = 7,b = 11, c = 13a = 8,b = 12, c = 14a = 10,b = 13, c = 16a = 6,b = 10, c = 12a = 4,b = 8, c = 10 20. Given that 2357 × 99 = 233 343, find: (i) 233 343 ÷ 99 23572537135753277325 20.(ii) 235∙7 × 99 23334.333324.33.23344333.233342 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 × (4+2) =4 × 6 =24 21.(a) Work out 4 ⟴ 5 3632252824 21.(b) Work out 4 ⟴ (3 ⟴ 2) 7672786460 21.(c) Work out the value of p such that 6 ⟴ p =78 p=————76549 22. Four bells ring at intervals of 2, 8, 7 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. ———— seconds616416516510610 Time is Up! Time's up
