ST ALBANS SCHOOL 11 PLUS MATHEMATICS ENTRANCE EXAM PAPER – 2 by smoothmaths | Jul 4, 2020 | 0 comments Welcome to your ST ALBANS SCHOOL 11 PLUS MATHEMATICS ENTRANCE EXAM PAPER - 2 SECTION A: MATHEMATICAL SKILS 1. Fill in the three missing numbers to make these four fractions equivalent. \[\frac{24}{5}\] \[\frac{8}{25}\] \[\frac{3}{25}\] \[\frac{14}{25}\] \[\frac{20}{25}\] None 2 (a) Given that Write down the answer to \[\frac{1}{3}\] \[\frac{1}{6}\] \[\frac{3}{7}\] \[\frac{2}{3}\] \[\frac{3}{5}\] None (b) Given thatwrite down the answer to \[\frac{11}{15}\] \[\frac{4}{5}\] \[\frac{11}{12}\] \[\frac{13}{16}\] \[\frac{17}{19}\] None 3. (a) Calculate 27 × 36 732 932 772 972 672 None (b) Use your answer to part (a) to write down the answer to 27 × 18 = 486 432 476 496 456 None (c) Use your answer to part (a) to write down the answer to 2.7 × 3.6 = 9.72 97.2 9.32 7.72 7.32 None 4. Given that 352 × 48 = 16896Work out 16896 ÷ 24 = 504 604 704 804 904 None 5. (a) Write 0.427 as a fraction \[\frac{427}{100}\] \[\frac{427}{1000}\] \[\frac{427}{10000}\] \[\frac{427}{10}\] \[\frac{427}{100000}\] None (b) Write 6/20 as a percentage. 20% 40% 30% 50% 60% None 6. (a) How many centimetres are there in five kilometres? 5000cm 5000000cm 50000cm 500000cm 50000000cm None (b) How many times does two hundred go into one million? 5000 50000 4000 40000 3000 None 7. Write in words the answer to one hundred thousand subtract one hundred and eleven. Eighty nine thousand eight hundred and eighty nine Ninety nine thousand eight hundred and eighty nine Ninety nine thousand nine hundred and eighty nine Ninety nine thousand eight hundred and ninety nine Ninety nine thousand nine hundred and ninety nine None 8. In this number pyramid, the number in each block is found by adding together the numbers in the two blocks immediately below. Fill in the missing numbers. 4,-2,-4 -4,-1, 4 -2,-1,4 -4,2,4 -3,-1,4 None 9. Decide whether for each of the following is correct or not. Write Y for 'yes' and N for 'no'.(a) 15 - 3 × 7 = -6 might be 84 N Y might be 6 none of the above None (b) 3 + 5 × 4 = 32 might be -23 Y might be 32 N none of the above None (c) 6 × 3 + 2 = 20 Y N might be-20 might be 30 none of the above None 10. Calculate 28.3 - 1.64 + 0.57 might be-20 N 27.3 might be 30 none of the above None 11. Work out the answer to the following, giving your answer as a decimal. 26.23 27.33 28.23 9.61 28.33 None 12. What is half of 1.1 ? 0.55 0.61 1.92 1.69 1.06 None 13. Look at the following four numbers, each of which represents a digit in a four-digit number. 9, 2, 8, 3Using each number once only:(a) Write down the largest number you can make. 2983 9283 9832 3892 3829 None (b) Write down the smallest even number you can make. 3982 2398 9382 9328 9238 None 14. (a) An aeroplane leaves Heathrow at 21:26 and arrives at Atlanta at 10:45 on the following day. How long does this journey take, in hours and minutes ? 6 hrs 19 min 14 hrs 29min 13 hrs 19 min 3 hrs 19 min 2 hrs 19 min None (b) In fact, the times were given as local times. The time in Atlanta is five hours behind U.K. time. What is the actual length of the journey ? 4hrs 15mins 23hrs 11mins 22hrs 19mins 18hrs 19mins 11hrs 30mins None 15. One cube has each of its faces covered by one face of an identical cube, making a solid as shown.The total volume of the solid is 56 cm³.(a) Find the width of one cube, in cm. 6cm 3cm 4cm 5cm 2cm None (b) Find the total surface of the solid, in cm². 130\[cm^{2}\] 100\[cm^{2}\] 120\[cm^{2}\] 140\[cm^{2}\] 160\[cm^{2}\] None 16. Write + or - in each space to make the calculation correct. 123 45 67 89 = 100 -,-+ -,+,- -,-,- +,+,- +,-,+ None 17. What fraction of this shape is shaded ? \[\frac{5}{16}\] \[\frac{5}{32}\] \[\frac{1}{4}\] \[\frac{1}{3}\] \[\frac{5}{6}\] None 18. A factor tree can be used to write any number as a product of prime factors.We can say that180 = 2 × 2 × 3 × 3 × 5(The order of the numbers does not matter)Use a factor tree, or any other method you know, to write 420 as a product of prime factors. 2x2x5x5x7 2x3x3x5x7 2x2x3x5x7 2x3x7x5x7 2x5x5x7x7 None 19. Year 6 were playing a number gameEmily said, 'If I multiply my number by 4 and then subtract 5, I get the same answer as multiplying my number by 2 and then adding 1'.(a) Faye called Emily's number x and formed the following equation:4x - 5 = 2x + 1Solve this equation and write down the value of x, showing your working clearly. 6 4 5 3 2 None Gemma said, ' Multiplying my number by 2 and then adding 5 gives the same answer as subtracting my number from 23'.(b) Find Gemma's number, showing your working clearly. 7 6 8 9 5 None 20. The equilateral triangle ADF is split into four equally sized smaller equilateral triangles.(a) Two of the four small triangles are to be painted black and the other two are to be painted white. In how many different ways can this be done ? 9 7 8 6 5 None Ben thinks that he can draw a copy of the of triangles without taking his pencil off the page and without going over the same line twice. He begins at A and then travels to B.(b) Complete the list below showing the order that Ben's pencil visits the corners of the triangles.A, B,.......... D,E,B,C,E,F,C,A D,E,F,C,E,B,C,A D,F,B,C,E,F,C,A D,E,B,C,E,F,C,D A,E,B,C,E,B,C,F None 21. Farmer John has 14 horses and farmer Paul has 27.John buys some horses from Paul and then has 3 more horses than Paul.How many did John buy? 22 8 9 16 5 None 22. What is 6 7 8 9 5 None 23. Mongle birds can be either pink or green. Some of them eat insects, but the rest prefer seeds.In a particular flock of Mongle birds, there are 17 green birds int otal and 12 birds which eat seeds.9 of the pink birds eat insects and 2 of the green ones eat seeds.How many birds are there in the flock?(You can use the table tohelp you) 56 46 27 36 34 None 24. Each number in this sequence is half of the number before. Write in the missing numbers. , , , 12, 6, 3, , 96,48,24,1.5,0.75 86,48,24,1.5,0.75 96,38,24,1.5,0.75 96,48,18,1.5,0.75 96,48,24,1.25,0.625 None 25. I am counting up the money from the tombola at the end of the school fair.(a) There are twenty four £1 coins, seven £2 coins, six £5 notes, fourteen £10 notes, three £20 notes and one £50 note.How much money is there in total? £ 290 £ 304 £ 318 £ 270 £ 250 None (b) I exchange all of the money for as many £20 notes as possible. How many £20 notes do I have now? 15 12 13 14 20 None 26. Two of the angles in a quadrilateral are right angles. One of the others is five times larger than the fourth angle.What is the size of the largest angle? 100 120 180 160 150 None 27. The front row of a theatre has 48 seats and each other row has four more seats than the row in front. There are 80 seats in the last row. How many seats are there altogether in the theatre? 500 516 496 520 576 None 28. Martha and Sally each have the same amount of money.If Martha spends £10 and Sally spends £20, then Martha has three times as much as Sally.If Martha spends £15 and Sally spends €20, then Martha has twice as much as Sally.How much money do they have altogether? 50 60 25 40 30 None 29. The sum of two whole numbers is 30 and their difference is 20.What are the two numbers? 4.26 5,25 3,27 2,28 6,24 None 30.Use the information in the table above to answer the following questions.(a) Explain how the table shows that 49 x 343 = 16 807 \[7^{2}\] x \[7^{3}\] = \[7^{5}\] \[7^{2}\] x \[7^{3}\] = \[7^{6}\] \[7^{3}\] x \[7^{3}\] = \[7^{6}\] \[7^{2}\] x \[7^{2}\] = \[7^{6}\] \[7^{4}\] x \[7^{3}\] = \[7^{6}\] None (b) Use the table to help you work out the value of 8 \[7^{2}\] \[7^{3}\] 7 1 None (c) Use the table to help you work out the value of 49 28 35 21 56 None (d) 3 2 1 4 5 None 31. In this multiplication each letter stands for a different digit. What digit does D represent? 5 4 3 6 2 None 32. On each of the cards below, n can be any positive number. The answers given by the cards are all positive numbers.(a) Which card (s) will always give an answer less than n ? 0.8n \[\frac{n}{0.8}\] \[n^{2}\] \[n^{1/2}\] \[\frac{1}{n}\] None (b) When n = 1, which card(s) will give an answer of one? \[n^{2}\] , √ n, 0.8n \[n^{2}\] , √ n , \[\frac{1}{0.8}\] 0.8n,\[\frac{1}{n}\] , \[\frac{0.8}{n}\] \[n^{2}\] , √ 0.8 , \[\frac{1}{0.8}\] \[n^{2}\] , √ n , \[\frac{1}{n}\] None (c) When n = 4, which card(s) will give an answer of less than 4? 0.8n , √ n , \[\frac{1}{n}\] 0.8n , \[\frac{n}{0.8}\] , \[\frac{1}{n}\] 0.8n , √ n, \[\frac{n}{0.8}\] \[n^{2}\] , √ n , \[\frac{1}{n}\] 0.8n , √ n , \[\frac{n}{0.8}\] None 33. ‘Yummy’ chocolate bars are packed in either boxes of 5 or boxes of 12.What is the smallest number of full boxes required to pack exactly 2019 ‘Yummy’ bars? 110 120 130 170 180 None Time's up
