ALDENHAM SCHOOL 13+ Paper 2 by smoothmaths | Aug 9, 2020 | 0 comments Welcome to your ALDENHAM SCHOOL 13 + Entrance Paper SAMPLE PAPER 2 1.(a) What is the square root of 81?931881Both a & b (b) Work out 596 x 231370812608136081270813798 2. Emiliano asked 10 of his friends how many hours they spent using a computer each week. The results are as follows. 8 14 20 5 0 14 9 17 3 10 (a) Find the median of these numbers.9.5191054.5 (b) Find the range of these numbers20101714None of the Above 3. Write 0.5, 48% and \[\frac{9}{20}\] in order of size starting with the smallest. You must show your working.9/20, 48%, 0.50.5, 48%, 9/2048%, 0.5, 9/209/20, 0.5, 48%None of the Above 4. The diagram represents a solid made from 9 small cubes. The view of the solid from direction A is shown below. On the grid below, draw the view of the solid from direction B. 5. Square tiles are used to make patterns on a grid (a) The pattern continues in the same way. Draw Pattern 4 (b) (i) Complete this table. Pattern Number (n) 1 2 3 4 5 Number of tiles (N) 5 8 (ii) How many tiles are in Pattern 12?38343648None of the Above (c) There are 317 tiles in Pattern 105. How many tiles are in Pattern 104?314311317320None of the Above (d) Find a rule linking the pattern number (n) and the number of tiles (N).3n + 23n2n + 3n + 2n + 3 6.(a) Work out the size of angle x. x =138o148o142o132o144o (b) Xavier says that if this diagram was drawn accurately then ABC would be a straight line. Is he right? You must explain your answer.Xavier is not rightXavier is rightXavier is not rightXavier is not rightXavier is not right 7.(a) Share £320 in the ratio 2 : 3£128 : £192£160 : £106£800: £533£64 : £64All of the Above except 'a' (b) Work out: 3 \[\frac{2}{5}\] + 4\[\frac{3}{10}\]7 7/107 1/31 1/38 3/7Both b & c (c) Work out and simplify. \[\frac{3}{4}\] x \[\frac{2}{7}\]3/143/87/114/7Both a & b (d) A bracelet is made using only silver and gold, in the ratio is 5 : 3. What fraction of the bracelet is composed of gold?3/83/41/41/33/3 or 1 8. Solve the equations: (a) 5n + 7 = 52 n =96108None of the above (b) 5p - 6 = 2p + 18 p =842069 9. A game is played with two spinners. You multiply the two numbers on which the spinners land to get a final score. The final score is 4 x 2 = 8 ( a) Complete the table to show all the possible final scores (one score has been done for you). X 1 2 3 4 1 2 8 3 (b) Work out the probability of getting a final score of 3.1/61/41/3126 (c) Work out the probability of getting a final score which is an odd number.1/33/431/4Both a & b (d) If I were to spin the spinner 60 times, how many times would I expected to get an odd number.20151018None of the above 10. (a) Simplify 5c + 4c – c8c9c6cNone of the aboveAll of the Above except 'a' (b) Simplify 7x + 2y – 3x – 5y4x - 3y9x - 8y7x - 3y4x + 3yNone of the above 11. This shape is made up of rectangles. (a) Write down an expression, in terms of x and y, for the perimeter of the shape.2(3x + 5y)5(x + 2y)3(2x + 3y)4(x + 2y)None of the above (b) If x = 2 cm and y = 5 cm, find the area of the shape70403020None of the above 12. The table shows the school year and the reaction time of eight people who took part in the same test. School year 5 7 8 9 10 11 12 13 Reaction time (seconds) 6 5 4.8 4.5 4 4.2 3.5 3 (a) Draw a scatter graph of these data. (b) Draw a line of best fit on your scatter graph. (c) Describe the relationship shown by your scatter graph. 13. Here is a formula relating the quantities A, x and y. A = \[y^{3}\] + 4x (a) Work out the value of A when y = 5 and x = −10. A =85165125Both a & bNone of the above (b) Work out the value of x if A = 20 and y = 2 x =37124Both a & b 14. The diagram shows two parallel lines with a straight line crossing them diagonally. Work out the value of: (a) angle x°, giving your reason35o45o60o30oNone of the above (b) angle y°, giving your reason145o125o120o150oNone of the above (15) Factorise the expression 4x + 102(2x + 5)2(x + 5)4(x + 5)Both a & bNone of the above 16.(a) (i) Describe fully the single transformation that takes the shaded triangle to triangle A. (ii) On the grid above translate the shaded triangle by 2 squares to the right and 4 squares down. (b) Triangle P is an enlargement of the shaded triangle. (i) What is the scale factor of the enlargement?1/221/43/4None of the above (ii) What is the centre of enlargement?(-2,-1)(-2,1)(2,-1)(0,-2)None of the above 17. On her way to work Mrs Shah passes through three sets of traffic lights. She records the number of times she stops at traffic lights each day. Number of stops each day Frequency(number of days) 0 2 1 11 2 12 3 15 What is the mean number of stops per day? 28346 18.(a) Complete the table below for y = 3x + 2.. x -1 0 1 2 y 2 8 (b) Draw the graph of y = 3x + 2. (c) On the same grid, draw the line y = 6. 19.(a) A bike costs £130. Its price is reduced by 15% in a sale. Find the sale price.£110.5£149.5£100.5£120.5£115.5 (b) Dany, Claire and Ollie are having a debate. Dany says that if you increase an amount by 20% and then decrease it by 20% that you will end up with your original amount. Ollie says that it will be less. Claire says that it will be more. Who is correct? Explain your answer.Ollie is correctClaire is correctOllie is not correctClaire is not correctNone of the above 20. (a) 30 students from Year 7 are asked how they travel to school. Their replies, walk (W), bus (B) or car (C), are shown below. C C B W B W C B W C B B W W W C W C B B W W B W B W B W W C (i) Complete the tally column and the frequency column in the table Tally Frequency Walk (W) Bus (B) Car (C) Total 30 ||||| ||||| ||| & 13||||| |||| & 9||||| ||||| || & 12||||| ||||| & 10None of the above (ii) Which reply is the most common?WalkBusCarBoth a & bNone of the above (iii) What fraction of the students travel by bus?1/32/37/3013/30None of the above (b) 30 students from Year 11 are also asked how they travel to school. Their results are shown in the table. Frequency Walk (W) 13 Bus (B) 14 Car (C) 3 Total 30 More People from year11 travel in BusLess People from year7 travel in BusLess People from year11 travel in BusMore People from year 7 travel in BusBoth a & b Compare how Year 7 and Year 11 travel to school.(i) Write down one difference.More People from year11 travel in BusLess People from year7 travel in BusLess People from year11 travel in BusMore People from year 7 travel in BusBoth a & b (ii) Write down one similarity.Equall Number of People go by WalkEquall Number of People go by BusEquall Number of People go by CarEquall Number of People go by VanNone of the above (c) Draw a fully labelled pie chart for the Year 11 data. 21. 40 pupils were asked about their lunch one day. The table gives some information about their answers. (a) Complete the table. School Dinners Sandwiches Other Total Boys 15 5 22 Girls 8 7 Total 40 (b) Estimate the probability of a girl chosen at random eating sandwiches for lunch.3/115/401/5 or 8/407/11/20 or 2/40 22. Calculate the length of the side x. 1312511None of the above 23. Susan completes a journey in two stages. In stage 1 of her journey, she drives at an average speed of 80 km/h and takes 1 hour 45 minutes. (a) How far does Susan travel in stage 1 of her journey?140km60km100km80km120km (b) Altogether, Susan drives 190 km and takes a total time of 2 hours 15 minutes. What is her average speed, in km/h, in stage 2 of her journey?100km180km60km80km120km 24. Two families go to a pantomime. The James family of two adults and one child pay £36. The Irish family of three adults and three children pay £66. Work out the cost of an adult ticket and the cost of a child ticket. Adult ticket £Adult Ticket = £14Adult Ticket = £10Adult Ticket = £16Adult Ticket = £12Adult Ticket = £8 Child ticket £Child Ticket = £8Child Ticket = £2Child Ticket = £9Child Ticket = £6Child Ticket = £14 25. A local bike shop is having a 20% off sale on all of its bikes. Ben buys a bike for £432 in the sale. (a) How much would his bike have cost without the discount?£540£480£450£640£650 (b) Ben’s new bike has a wheel diameter of 40cm. Roughly how many revolutions will each wheel make if he cycles for 1 km?796.11591.51256.6125.6None of the Above Time is Up!