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Ma Mathematics tests KEY STAGE 3 for Mental mathematics tests A, B and C 2009 ALL TIERS Mark scheme National curriculum assessments Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk QCA wishes to make its publications widely accessible. Please contact us if you have any specific accessibility requirements. First published 2009 © Qualifications and Curriculum Authority 2009 ISBN 1-84721-699-1 Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced for the purpose of research, private study, criticism or review, or by educational institutions solely for educational purposes, without permission, providing full acknowledgement is given. Printed in Great Britain by the Qualifications and Curriculum Authority under the authority and superintendence of the Controller of Her Majesty’s Stationery Office and Queen’s Printer of Acts of Parliament. The Qualifications and Curriculum Authority is an exempt charity under Schedule 2 of the Charities Act 1993. Qualifications and Curriculum Authority 83 Piccadilly London W1J 8QA www.qca.org.uk Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2009 KS3 Mathematics test mark scheme: Mental mathematics Introduction Introduction This booklet contains the mark schemes for the lower tier test (test C) and the higher tiers tests (tests A and B). General guidance for markers Please note that pupils should not be penalised if they record any information given in the question or show their working. Ignore any annotation, even if in the answer space, and mark only the answer. Accept an unambiguous answer written in the stimulus box, or elsewhere on the page, but clearly attributable to the relevant question. General guidance for marking the written tests also applies to marking the mental mathematics tests. In addition, please apply the following principles unless speciﬁc instructions to the contrary are given in the mark scheme: accept responses in words and/or ﬁgures, eg 7 point 3, 4 hundred accept any unambiguous indication of the correct response from a given list, eg circling, ticking, underlining accept unambiguous misspellings accept units that have been correctly converted to a different unit provided the new unit is indicated. Where units have been given on the answer sheet, do not penalise pupils for writing the units again accept responses with commas as spacers, eg 50,000 but do not accept a point used as a spacer, eg 50.000 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 3 4 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk How many minutes are there in two hours? What is twenty-six pounds ﬁfty-eight pence rounded to the nearest pound? What number do I need to add to sixty-three to make one hundred? Multiply two hundred and six by ten. How many faces does a triangular prism have? I am thinking of a number. I call it b. I subtract two from my number. Write an expression to show the result. Add eight to minus three. 2 3 4 5 6 7 8 The tally chart shows the number of silver and red cars a shop sold in one week. How many more red cars were sold than silver cars? ‘Now turn over your answer sheet.’ 16 Look at the numbers on your answer sheet. Add them. 15 Look at the equation on your answer sheet. When a is thirty-four, what is the value of b? 14 The sequence of numbers on your answer sheet goes down in steps of four. Write the next two numbers in the sequence. 13 Look at the number on your answer sheet. Round it to the nearest hundred. 12 I am counting up in nought point twos. Two point three, two point ﬁve, two point seven, … Write down the next two numbers. 11 A radio programme starts at six forty-ﬁve pm and lasts for forty-ﬁve minutes. At what time does the programme ﬁnish? 10 Look at the number line on your answer sheet. What number is the arrow pointing to? 9 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ Write in ﬁgures the number eight hundred and one. 1 For the ﬁrst group of questions you will have 5 seconds to work out each answer and write it down.’ ‘Now we are ready to start the test. Lower tier test C questions 7 6 5 4 3 2 1 £ Test C minutes Time: 5 seconds Practice question School Last name First name Mental mathematics 24 Total marks b 206 63 £ 26.58 Key stage 3 mathematics 2009 Pupil answer sheet 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9 16, 2.3 6.45 pm 0 Red Silver , , 100 –3 4 2.6 0.8 a – b = 14 8, 9343 2.7 pm 45 minutes 2.5 12, Time: 10 seconds 8 Time: 5 seconds continued 16 15 14 13 12 11 10 9 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 5 ‘Put your pens down. The test is ﬁnished.’ 30 Look at the numbers on your answer sheet. Put a ring round the number that is prime. 29 Four point three multiplied by six equals twenty-ﬁve point eight. What does four point three multiplied by twelve equal? 28 Look at the names of shapes on your answer sheet. Put a ring round the name of the shape that has only one pair of parallel sides. 27 Your answer sheet shows the coins Jack has in his pocket. He is going to take a coin from his pocket at random. What is the probability he will take a two pence coin? 26 Look at the shaded triangle drawn on a centimetre square grid. What is the area of the triangle? 25 Lisa did a survey to ﬁnd out the type of books pupils in her class preferred. The bar chart shows her results. How many more pupils chose story books than poetry books? 24 Your answer sheet shows how Ella spent all her pocket money one month. What percentage did she spend on clothes? 23 Paul was born on the ﬁrst of August in nineteen ninety-eight. How old will he be on the ﬁrst of August in two thousand and nine? 22 Look at the number machine on your answer sheet. I put in the number two. What number should come out? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 21 What is twenty per cent of ﬁfty pounds? 20 Each side of a pentagon is eight centimetres long. What is its perimeter? 19 Halve the expression on your answer sheet. 18 One hundred people were asked whether they used a gym or not. The pie chart shows the results. How many people said no? 17 Look at the dial on your answer sheet. The arrow turns from ‘off’ to ‘rinse’. Through how many degrees does the arrow turn? £ Spin cm 24 23 22 in magazines food clothes ×4 Yes No Rinse Off Time: 15 seconds 21 20 19 18 17 +6 % 25% 40% 2009 out £ 50 8 cm 8pq people ° Wash Time: 10 seconds continued 24 23 22 21 20 19 18 17 30 29 28 27 26 25 2 cm2 4 21 square 6 8 rhombus 10 12 23 25 4.3 × 6 = 25.8 27 trapezium parallelogram rectangle 0 Story Reference Poetry Time: 15 seconds continued 30 29 28 27 26 25 2009 Key stage 3 mathematics 2006 Mental mathematics lower tier Test C A higher tiers Test Time: 5 seconds continued 8 Test C Test A 5 Time: 10 seconds 801 2 12 £ 27 4 37 5 6 b–2 14 0 and –4 Accept pair in either order 15 20 Accept embedded values, eg 34 – 20 = 14 16 3.4 Accept equivalent fractions or decimals Condone answers of £27.00 Accept embedded values, eg 63 + 37 = 100 5 7 9300 Accept pair in either order Accept equivalent fractions or decimals 2060 6 2.9 and 3.1 Do not accept responses given in words 120 minutes 3 7:30 pm 13 1 60 11 Time: 5 seconds 6 10 Mark scheme 9 Do not accept unconventional notation, eg 1b – 2 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 10 seconds continued 17 180 ° 18 75 Time: 15 seconds continued 4 pq 20 26 6 cm2 1 5 Do not accept unconventional notation, eg 4 × p × q 40 cm 21 7 27 19 25 £ 10 Accept equivalent probabilities Time: 15 seconds 28 22 14 rectangle rhombus parallelogram square 23 51.6 Accept equivalent fractions or decimals 11 29 24 trapezium 35 % Do not accept equivalent fractions or decimals 30 Sourced from SATs-Papers.co.uk 21 23 25 27 http://www.SATs-Papers.co.uk 7 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Subtract thirty-six from two hundred. Write in ﬁgures the number ten thousand and ten. Look at the numbers on your answer sheet. Add them. Look at the number on your answer sheet. Round it to two decimal places. Look at the expression. Write it as simply as possible. To the nearest centimetre the length of a shelf is ﬁfty-eight centimetres. What is the smallest value the length of the shelf could be? 2 3 4 5 6 7 I started a train journey at three twenty pm. The journey lasted for forty-ﬁve minutes. At what time did I arrive? 9 Practice question School Last name First name Mental mathematics 15 On my desk I have three blue pens, one red pen and four black pens. I am going to pick up one of the pens at random. What is the probability that I will pick up a black pen? ‘Now turn over your answer sheet.’ 14 A football team won ﬁfty-ﬁve per cent of their games and lost thirty per cent. The rest ended in a draw. What percentage of their games ended in a draw? 13 Draw an arrow on the scale to show two point two kilograms. 5 4 3 2 11 What is ﬁfty per cent of one hundred and ten pounds? 12 Write down a multiple of four that is greater than one thousand. 1 10 Some pupils were asked how they had travelled to school that day. The pie chart shows the results. Which form of transport is the mode? m Test A 39 Total marks 0.576 –9 36 5 600 cm Key stage 3 mathematics 2009 Pupil answer sheet Time: 5 seconds Look at the equation. What is the value of x? 8 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ How many metres are six hundred centimetres? 1 For the ﬁrst group of questions you will have 5 seconds to work out each answer and write it down.’ ‘Now we are ready to start the test. Higher tiers test A questions 5 4 3 2 1 cm 14 13 12 11 10 9 8 £ 2 kg % Car Train Walk pm Time: 10 seconds 7 6 lost 30% won 55% 3 kg 50% Bus Bike 45 minutes x + 7 = 22 58 cm 8 p2 – p2 Time: 5 seconds continued 14 13 12 11 10 9 8 7 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 9 ‘Put your pens down. The test is ﬁnished.’ 30 Write down the three consecutive whole numbers that add up to forty-ﬁve. 29 The diagram shows three lines meeting at a point. Work out the value of k. 28 The mean of three numbers is ten. Two of the numbers are eight. What is the third number? 27 I can make a three-digit number using the digits one, two and three in six different ways. How many of these three-digit numbers are even? 26 Look at the regular decagon. The exterior angle marked a is thirty-six degrees. What is the size of an interior angle? 25 I eat one half of a pizza. My friend eats one third of the pizza. What fraction of the pizza is left? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 24 What is the square root of one ninth? 23 Look at the equation. What is the value of y when x equals three? 22 A bird ﬂies at an average speed of thirty-six kilometres per hour. At this speed, how far would it ﬂy in ten minutes? 21 Twelve people in a group are left-handed. Twenty per cent of the group are left-handed. How many people are in the group? 20 Your answer sheet shows a diagram of a 3-D shape. What is the mathematical name of this shape? 19 There are ninety seats in a train carriage. How many seats are there in twelve of these carriages? 18 Look at the expression. When m is eight, what is the value of the expression? 17 Write down a prime number between ten and twenty. 16 A rectangular football pitch is sixty-ﬁve metres by one hundred metres. A footballer runs once around the perimeter of the pitch. How far does he run? 23 22 21 20 19 18 17 16 65m 20 12 90 y = 4 x2 km 20% 12 4( m – 3 ) 10 m 36 km per hour people 100m 23 22 21 20 19 18 17 16 30 29 28 27 26 25 1 , ° k° 2 a , 7k° 4k° Time: 15 seconds 3 1 9 1 3 45 Mean = 10 1 2 24 3 blue, 1 red, 4 black 15 15 Time: 10 seconds continued Time: 10 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2009 Mental mathematics higher tiers Time: 5 seconds continued Test A 6 7p2 Do not accept unconventional notation, eg 7 × p2 or 7pp 7 57.5 cm Accept equivalent fractions or decimals Test A Mark scheme Time: 10 seconds Accept embedded values, eg 15 + 7 = 22 8 15 9 4:05 pm 10 Bus 11 £ 55 12 Time: 5 seconds 1 6 m 2 13 –4 5 0.58 2.2kg marked on the scale, ie 10 010 4 Any multiple of 4 greater than 1000, eg 1004, 5064 Note that any number is a multiple of 4 where the last two digits constitute a number that is a multiple of four Do not accept amended units 164 3 Accept unambiguous indication, eg Bu 10 2kg Do not accept equivalent fractions or decimals Sourced from SATs-Papers.co.uk 14 15 % 3kg Do not accept equivalent fractions or decimals http://www.SATs-Papers.co.uk Time: 10 seconds continued 15 1 2 16 Accept equivalent probabilities 330 m Time: 10 seconds continued 24 Accept – 1 with 1 or alone 3 3 Accept 0.33 or better 1 3 Time: 15 seconds 25 26 144 ° 27 2 28 14 29 17 1 6 30 Accept 30° 30 14, 15, 16 Accept values in any order Accept equivalent fractions Do not accept equivalent decimals One of 11, 13, 17 or 19 18 20 19 1080 20 cylinder 21 6 km 23 Accept ‘circular prism’ 60 people 22 Accept both even numbers given, ie 132 and 312 36 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 11 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Look at the expression. Write it as simply as possible. Write the number that is three less than six thousand. Multiply seven point eight by two. What number is three cubed? The probability that I will have toast for breakfast is nought point three. What is the probability that I will not have toast for breakfast? Write nought point nought nine as a fraction. Multiply minus six by minus eight. 2 3 4 5 6 7 8 A carton of orange drink costs twenty-ﬁve pence. How many cartons can I buy for two pounds ﬁfty? ‘Now turn over your answer sheet.’ 15 Put a cross on the grid to show the point with coordinates minus two, one. 14 Look at the rectangle drawn on a square grid. What percentage of the rectangle is shaded? 13 At ten pm, the temperature was eight degrees Celsius. By midnight the temperature had dropped by ten degrees. What was the temperature at midnight? 12 Pupils in a class were asked if they would prefer an apple or a banana. The pictogram shows the results. How many pupils were in the class? 11 Look at the numbers on your answer sheet. Add them. 10 I was delayed in trafﬁc from quarter to six to twenty past six one evening. For how many minutes was I delayed? 9 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ Look at the units of length on your answer sheet. Put a ring round the one that is best used for the distance between two towns. 1 For the ﬁrst group of questions you will have 5 seconds to work out each answer and write it down.’ ‘Now we are ready to start the test. Higher tiers test B questions metres 8y + 3y inches kilometres 39 Total marks 6000 centimetres millimetres Test B 6 0.3 4 5 7.8 3 2 1 Time: 5 seconds Practice question School Last name First name Mental mathematics Key stage 3 mathematics 2009 Pupil answer sheet 6 5 4 3 2 1 15 14 13 12 11 10 9 Key: –2 % Banana Apple 25p °C 0 –2 0 2 y 14 2 x 8°C pupils = 3 pupils 13 minutes 15 £2.50 0.09 Quarter to six Time: 10 seconds 8 7 Time: 5 seconds continued 15 14 13 12 11 10 9 8 7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 13 ‘Put your pens down. The test is ﬁnished.’ 30 The diagram shows a right-angled triangle. Which value under the triangle shows the length of the hypotenuse? Put a ring round the correct value. 29 The angles in a triangle are in the ratio two to three to four. What are the sizes of the three angles? 28 The table shows the number of children in ten families. How many children are there altogether? 27 Look at the expression. When b is seven, work out the value of the expression. 26 One hundred pupils study French, German or both languages. Sixty-ﬁve pupils study French and eighty-three pupils study German. How many study both languages? 25 The scale of a map is one centimetre to two kilometres. On the map two places are seven and a half centimetres apart. What is the actual distance between the two places? 24 I am thinking of two numbers that add to twelve. One number is two more than the other. What are my two numbers? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 23 Look at the expression. Multiply out the brackets. 22 A rectangular photograph measures eight centimetres by ten centimetres. I enlarge the photograph so that the shorter side is twelve centimetres. What is the length of the longer side? 21 Look at the equation. What is the value of x when y is twenty? 20 The prices of meals in a canteen are increased by ﬁve per cent. What is the new price if the old price was two pounds? 19 On a sponsored walk, I walked four miles in each hour. How long did it take me to walk eighteen miles? 18 Look at the isosceles triangle. What is the size of angle x? 17 A regular pentagon has a side length of four centimetres. What is its perimeter? 16 A teacher asked pupils in a class ‘Do you have a pet?’ The percentage bar chart shows the results. Estimate the percentage of pupils who said no. 23 22 21 20 19 18 17 16 £ ° 8 cm 0% No x 10 cm hours cm £2 3y (5 – y ) cm y = 3x – 7 18 30° 4 cm % 100% 5% Yes Time: 10 seconds continued 23 22 21 20 19 18 17 16 30 29 28 27 26 25 24 6 3 cm °, 18 1 1 4 3 1 27 12 children °, 3 cm 9 83 ( 3 + b )2 5 65 km 1 7 cm 2 Frequency 2:3:4 Number of children 0 1 2 3 4 1cm : 2km and Time: 15 seconds ° 30 29 28 27 26 25 24 Key stage 3 mathematics 2009 Mental mathematics higher tiers Time: 5 seconds continued Test B 7 9 100 Accept equivalent decimals Do not accept equivalent fractions Test B Mark scheme 8 48 Time: 10 seconds 9 10 millimetres kilometres 42 12 21 pupils 13 –2 °C 14 1 35 minutes 11 Time: 5 seconds 10 75 % metres centimetres 2 3 11y inches Do not accept unconventional notation, eg 11 × y Do not accept equivalent fractions or decimals 5997 y 15 4 15.6 5 27 6 0.7 Accept equivalent fractions or decimals 14 2 –2 Accept equivalent probabilities Sourced from SATs-Papers.co.uk 0 0 2 x –2 http://www.SATs-Papers.co.uk Time: 10 seconds continued answer 40 % Accept pair in either order 25 15 km 48 20 28 22 children 29 17 5 and 7 27 Do not accept equivalent fractions or decimals 24 26 16 30 % Time: 15 seconds 40 °, 20 cm 18 75 ° 19 1 4 2 hours 20 £ 2.10 21 9 22 15 cm Accept equivalent fractions or decimals Accept 4 hours 30 minutes 60 °, 80 ° Accept values in any order 23 15y – 3y2 Accept unconventional notation, eg 15 × y – 3y × y Do not accept incomplete processing, eg 5 × 3y – 3y 2 Sourced from SATs-Papers.co.uk 30 6 9 18 12 27 http://www.SATs-Papers.co.uk 15 29 Bolton Street London W1J 8BT Telephone: 08700 60 60 40 Minicom: 020 7509 6546 Fax: 020 7509 5908 Email: tests@naa.org.uk Website: www.naa.org.uk/tests Sourced from SATs-Papers.co.uk For more copies: QCA Orderline, PO Box 29, Norwich NR3 1GN www.qca.org.uk/orderline email: orderline@qca.org.uk Tel: 08700 60 60 15 Fax: 08700 60 60 17 QCA/09/3783 http://www.SATs-Papers.co.uk 290026