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KS3MathsMMS 270044 Cover.qxp 11/1/06 Ma 11:01 am Page 1 Mathematics tests KEY STAGE 3 LOWER TIER & HIGHER TIERS 2006 2006 Mark schemes for Mental mathematics Tests A, B and C Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk First published in 2006 © Qualiﬁcations and Curriculum Authority 2006 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, provided full acknowledgement is given. Produced 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 270044_KS3_MenMaMS.indd 2 http://www.SATs-Papers.co.uk 23/12/05 2:01:30 pm Introduction This booklet contains the mark schemes for the lower tier test (Test C) and the higher tiers tests (Tests A and B). The pupil answer sheets will be marked by external markers who will follow the mark schemes in this booklet, which are provided here for teachers’ reference. 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 3 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 3 http://www.SATs-Papers.co.uk 23/12/05 2:01:30 pm 4 270044_KS3_MenMaMS.indd 4 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23/12/05 2:01:30 pm How many right angles does a rectangle have? Multiply eight by three. The height of the Statue of Liberty is one hundred and ﬁfty-one feet. What is this height to the nearest hundred feet? What number do I need to add to thirty-three to make one hundred? How many seconds are there in three minutes? Divide nine hundred and twenty by ten. What number is four less than minus seven? Look at the expression on your answer sheet. Write it as simply as possible. 2 3 4 5 6 7 8 9 ‘Now turn over your answer sheet.’ 17 Look at the diagram drawn on a square grid. What percentage of the diagram is shaded? 16 Look at the data on your answer sheet. Which number is the mode? 15 Look at the numbers on your answer sheet. Add them. 14 Look at the equation. What is the value of x? 13 For two adults to see a ﬁlm, the cost is eleven pounds altogether. How much does it cost for one adult to see the ﬁlm? 12 Subtract twenty-four from ﬁfty. 11 Look at the diagram on your answer sheet. Put a ring round the arrow that is pointing south-west. 10 A group of pupils share twenty-four pounds. They each get exactly six pounds. How many pupils are in the group? ‘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 seven hundred and three. 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 seconds feet Time: 5 seconds Practice question School Last name First name Mental mathematics 25 Total marks 920 33 151 feet Key stage 3 mathematics 2006 Pupil answer sheet 7 6 5 4 3 2 1 17 16 15 14 13 12 11 10 £ % 50 £6 7 5 0.5 6 8 8 3.7 16 + x = 23 £ 11 24 £ 24 3d – d –7 6 5 5 N pupils Time: 10 seconds 9 8 Time: 5 seconds continued 5 17 16 15 14 13 12 11 10 9 8 5 270044_KS3_MenMaMS.indd 5 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23/12/05 2:01:31 pm ‘Put your pens down. The test is ﬁnished.’ 30 A rectangle has a length of six centimetres and an area of thirty square centimetres. What is the width of the rectangle? 29 A birthday card costs one pound and forty-ﬁve pence. How much do three of these cards cost? 28 Look at the shape made from equilateral triangles. Shade two more triangles so that the shape has rotation symmetry of order three. 27 Your answer sheet shows the answer to one hundred and thirty-two divided by six. Use this information to help you work out the answer to one hundred and thirty-two divided by three. 26 Look at the diagram on the square grid. Draw the reﬂection of the shape in the mirror line. 25 Three pencils cost sixty pence. How much would four pencils cost? 24 The tally chart shows the number of pupils with and without a calculator. Altogether, how many pupils are there? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 23 What is the next prime number after seven? 22 Two angles ﬁt together to make a straight line. One angle is seventy-eight degrees. How many degrees are there in the other angle? 21 Look at the triangle drawn on the grid. Write down the coordinates of the point marked A. 20 I have a fair six-sided dice numbered one to six. I am going to roll the dice. What is the probability that I will roll an odd number? 19 Write a number that is a factor of both nine and twelve. 18 The diagram shows what some people had for breakfast. How many people had both cereal and toast, but not eggs? 23 22 21 20 19 18 –2 A 5 ( ° 2 Cereal –2 0 2 y , 0 Eggs 10 1 4 B C 9 7 78° ) 2 x 12 people 3 6 Toast Time: 10 seconds continued 23 22 21 20 19 18 30 29 28 27 26 25 24 £ 132 132 Mirror line cm ÷ ÷ Without a calculator With a calculator 3 6 Time: 15 seconds = = 6cm p 30cm2 £1.45 22 60p pupils 30 29 28 27 26 25 24 Key stage 3 mathematics 2006 2006 Key stage 3 mathematics Mental mathematics higher tiers tier Test C Mental mathematics lower Test A Time: 5 seconds continued 8 –11 9 2d Test C Test A Mark scheme Time: 10 seconds 10 4 pupils Accept embedded values, eg 4 × 6 11 N Accept any unambiguous indication 12 26 13 £ 5.50 14 7 Accept embedded values, eg 16 + 7 15 4.2 Accept equivalent fractions or decimals 16 5 Accept value indicated in list 17 25 % Do not accept equivalent fractions or decimals Time: 5 seconds 703 1 Do not accept responses given in words 4 2 24 3 4 200 feet 5 67 Accept embedded values, eg 33 + 67 6 180 seconds Do not accept amended units 7 92 6 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 6 http://www.SATs-Papers.co.uk 23/12/05 2:01:31 pm Time: 10 seconds continued 24 20 pupils 25 18 4 people Time: 15 seconds 80 p 26 19 1 or 3 20 1 2 21 Accept equivalent probabilities Mirror line ( –2 , 1 ) Accept lines not drawn accurately, provided the pupil’s intention is clear 27 44 28 22 102 ° 29 23 11 £ 4.35 30 5 cm 7 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 7 http://www.SATs-Papers.co.uk 23/12/05 2:01:32 pm 8 270044_KS3_MenMaMS.indd 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23/12/05 2:01:33 pm Divide three hundred by ten. Multiply six by nine. How many millimetres are there in eight centimetres? What number is six less than minus two? Write in ﬁgures the number that is one less than one million. Round three point six eight to one decimal place. Look at the expression on your answer sheet. Write it as simply as possible. 2 3 4 5 6 7 8 In a quiz, pupils were asked a question. The pictogram shows how many pupils were right and how many were wrong. Eight pupils were right. How many pupils were wrong? ‘Now turn over your answer sheet.’ 16 What is ﬁve per cent of three hundred pounds? 15 I have a fair six-sided dice, numbered one to six. I roll the dice. What is the probability that I roll a number greater than two? 14 The scale on a map is ten centimetres to two kilometres. On the map the distance between two points is ﬁfteen centimetres. How many kilometres are there between the two points? 13 Look at the expression on your answer sheet. When x is nine, what is the value of the expression? 12 AB is a straight line. Work out the size of angle w. 11 In a class of twenty-eight pupils, thirteen are boys. About what fraction of the class are boys? Put a ring round the fraction that is closest. 10 The perimeter of a square is twenty centimetres. What is the length of one side of the square? 9 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ What number is the arrow pointing to on the number line? 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 6 5 4 3 2 1 0 10 Test A mm Time: 5 seconds Practice question School Last name First name Mental mathematics Key stage 3 mathematics 2006 Pupil answer sheet –2 9 300 37 20 Total marks 6 5 4 3 2 1 16 15 14 13 12 11 10 9 £ 1 8 ° 1 4 A 50° 1 3 13 cm 10cm : 2km Wrong Right Time: 10 seconds 8 7 5% 3 4 B £300 km 15cm 2x – 8 w 1 2 pupils 10 y2 – 3y2 3.68 Time: 5 seconds continued 16 15 14 13 12 11 10 9 8 7 9 270044_KS3_MenMaMS.indd 9 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23/12/05 2:01:33 pm ‘Put your pens down. The test is ﬁnished.’ 30 Nine multiplied by nine has the same value as three to the power what? 29 Look at the grid. What is the equation of the line marked B? 28 Look at the right-angled triangle. Work out the height of the triangle. 27 What is the square root of forty thousand? 26 The table on your answer sheet shows the number of milk bottles ordered for twenty different houses. Altogether, how many milk bottles were ordered? 25 The diagram shows an arrow of height three centimetres. I enlarge it by a scale factor of two and a half. What is the height of the enlarged arrow? 24 A machine copies exactly ﬁfty pages a minute. How many pages can it copy in half an hour? 23 In a survey, some people were asked if they use a library. The pie chart shows the results. Twelve people said no. How many people were asked altogether? 22 Your answer sheet shows the answer to twenty-seven multiplied by thirty-two. Use this information to help you work out the answer to twenty-seven multiplied by sixteen. ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 21 Look at the expression. When y is six, work out the value of the expression. 20 Jake and Sarjun share some money in the ratio one to three. Sarjun’s share is one hundred and ﬁfty pounds. Altogether, how much money did they share? 19 Using three as an approximation for pi, ﬁnd the circumference of a circle with diameter eight centimetres. 18 Material costs four pounds ﬁfty per metre. How many metres of this material can I buy with twenty-seven pounds? 17 Find the volume of a cuboid measuring two centimetres by eight centimetres by four centimetres. £ m 25 24 23 22 × × 27 27 cm 16 32 = = 1:3 cm £150 8cm £27 3 cm 50 Yes No 864 y( y – 3) £4.50 cm 3 2cm by 8cm by 4cm Time: 15 seconds 21 20 19 18 17 Time: 10 seconds continued 25 24 23 22 21 20 19 18 17 30 29 28 27 26 0 2 4 6 y 0 height B 2 3 4 10 1 2 9×9 6 x 40000 2 8 1 4 3 0 8 Frequency 6 Number of milk bottles Time: 15 seconds continued 30 29 28 27 26 Key stage 3 mathematics 2006 Mental mathematics higher tiers Test A Time: 5 seconds continued 7 8 Test A Do not accept equivalent fractions or decimals 3.7 7y 2 Time: 10 seconds Mark scheme 9 3 pupils 10 5 cm 11 1 8 1 4 1 3 1 2 3 4 Time: 5 seconds 12 130 ° 13 10 14 3 km 15 2 3 Accept equivalent probabilities, including 0.66, 0.67 or better, or their percentage equivalents 16 £ 15 Do not accept incorrect % signs 8 1 2 30 3 54 4 80 mm 5 –8 6 999 999 Do not accept responses given in words 10 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 10 http://www.SATs-Papers.co.uk 23/12/05 2:01:34 pm Time: 10 seconds continued 17 64 cm3 18 6 m 19 24 cm 20 £ 200 21 18 Time: 15 seconds continued 26 30 27 200 Accept –200 with 200 or alone 28 6 Ignore units given 29 x=2 Accept unconventional notation, eg 1x = 2, x1 – 2 = 0 30 4 Accept embedded values, eg 34 Time: 15 seconds 22 432 23 60 24 1500 25 7 1 cm 2 Accept equivalent fractions or decimals 11 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 11 http://www.SATs-Papers.co.uk 23/12/05 2:01:34 pm 12 270044_KS3_MenMaMS.indd 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23/12/05 2:01:35 pm Write eighty-eight thousand in ﬁgures. Write the number that is halfway between a half and one. What is the area of a rectangle with a width of six centimetres and a length of seven centimetres? Ninety-seven per cent of the Earth’s water is salt water. The rest is fresh water. What percentage of the Earth’s water is fresh water? Divide twenty-four by minus six. To the nearest metre the height of a building is twelve metres. What is the least value the height of the building could be? 2 3 4 5 6 7 A lesson starts at two forty-ﬁve and ﬁnishes at three twenty. How long is the lesson in minutes? 9 ‘Now turn over your answer sheet.’ 15 There are thirty cubes in a bag. I am going to take out one cube at random. The probability that it will be blue is two-ﬁfths. How many blue cubes are in the bag? 14 A sunﬂower is one hundred and ﬁfty centimetres tall. How tall will it be if its height increases by ten per cent? 13 Look at the numbers on your answer sheet. What is their mean? 12 Look at the expression on your answer sheet. Write it as simply as possible. 11 Look at the diagram. Work out the size of angle x. 10 Look at the triangle on the grid. Write the coordinates of the point marked A. A teacher asked some pupils which ﬂavour drink they preferred. The bar chart shows the results. Twenty pupils said orange. About how many said lime? 8 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ A teacher divides a class of thirty pupils into six equal groups. How many pupils are in each group? 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 7 6 5 4 3 2 1 m % cm2 Time: 5 seconds Practice question School Last name First name Mental mathematics Test B 1 2 Key stage 3 mathematics 2006 Pupil answer sheet –6 97% 30 37 1 Total marks 7 6 5 4 3 2 1 15 14 13 12 11 10 9 8 0 C B ( 20 cm , x ° 4 A 2:45 ) x 3:20 pupils 30 150cm 2 5 10% 22 18 10 30 5k + 2m + 3m + 4k 2 minutes 335° 0 2 4 y 0 orange lime Time: 10 seconds 15 14 13 12 11 10 9 8 13 270044_KS3_MenMaMS.indd 13 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23/12/05 2:01:35 pm Write down the two possible values of m plus ﬁfteen. m squared equals one hundred. ‘Put your pens down. The test is ﬁnished.’ 30 29 Some people were asked which colour car they preferred. The pie chart shows the results. What percentage of the people said blue? 28 What is the square root of nine twenty-ﬁfths? 27 On the grid, sketch the straight line with equation y equals x plus two. 26 In a box of pens, one half are black, one sixth are red and the rest are blue. What fraction of the pens is blue? 25 Forty-four people paid twenty-ﬁve pence each to go into a book sale. How much money is that altogether? 24 Your answer sheet shows the answer to seven multiplied by ﬁfty-eight. Use this information to help you work out the answer to three and a half multiplied by ﬁfty-eight. 23 Look at the pattern on the square grid. Shade two more squares so that the grid has two lines of symmetry. 22 Write a multiple of nine that is bigger than seventy and smaller than eighty. and 0.2 1 2 y 2 cm 19 18 17 20 km/h cm 16 23 22 70 80 23 22 21 Time: 15 seconds 21 2km 5 minutes 20 19 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 2cm 3cm 3:5 3 4 18 17 16 Time: 10 seconds continued 21 A car travelled two kilometres in ﬁve minutes. What was the car’s average speed in kilometres per hour? 20 From three-quarters, subtract nought point two. 19 A 3-D shape has exactly six faces. All six faces are rectangles. What is the name of the 3-D shape? 18 Look at the expression on your answer sheet. What is the value of this expression when y is four? 17 The rectangle on your answer sheet has been enlarged by a scale factor of two. Write down the dimensions of the rectangle before the enlargement. 16 The ratio of boys to girls in a class is three to ﬁve. There are twelve boys. How many girls are there? 30 29 28 27 26 25 24 £ = 0 2 4 y 0 Red and 1 2 44 406 4 m2 = 100 m + 15 Blue 72° 2 = × 58 1 3 × 58 2 7 x 1 6 25p % 9 25 Time: 15 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2006 2006 Key stage 3 mathematics Mental mathematics higher tiers tiers A Mental mathematics higher Test Test B Time: 10 seconds 8 Test B Test A 25 answer 35 Do not accept incorrect % signs Mark scheme 9 35 minutes 10 ( 4 , 1 ) 11 25 ° Time: 5 seconds 5 1 2 88 000 Do not accept responses given in words 3 3 4 Accept equivalent fractions or decimals 4 42 cm2 12 9k + 5m 5 3 % 13 20 6 –4 14 165 cm 7 11.5 m 15 12 Accept equivalent fractions or decimals Accept embedded values, eg 12 30 14 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 14 http://www.SATs-Papers.co.uk 23/12/05 2:01:36 pm Time: 10 seconds continued Do not accept 12 : 20 20 Time: 15 seconds continued 17 1 cm and 1 Cuboid £ 11 26 1 3 27 y Accept equivalent fractions but do not accept equivalent decimals 8 19 203 1 cm 2 Accept pair in either order Accept equivalent fractions or decimals 18 24 25 16 20 0.55 21 Accept ‘rectangular prism’ Condone ‘cube’ or ‘square prism’ 4 Accept equivalent fractions or decimals 24 km/h 2 0 0 2 x 4 Accept line at least two diagonals in length, and line not drawn accurately, provided the pupil’s intention is clear 28 Time: 15 seconds 22 3 5 Accept – 3 with 3 or alone Do not accept 8×9 72 Accept equivalent fractions or decimals 5 5 29 20 % Do not accept equivalent fractions or decimals 30 23 5 and 25 Accept pair in either order or 15 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 15 http://www.SATs-Papers.co.uk 23/12/05 2:01:36 pm EARLY YEARS NATIONAL CURRICULUM 5–16 GCSE GNVQ GCE A LEVEL NVQ OTHER VOCATIONAL QUALIFICATIONS Further teacher packs may be purchased (for any purpose other than statutory assessment) by contacting: QCA Orderline, PO Box 29, Norwich NR3 1GN tel: 08700 606015; fax: 08700 606017 email: orderline@qca.org.uk Order ref: QCA/06/1923 Sourced from SATs-Papers.co.uk 270044_KS3_MenMaMS.indd 16 270044 http://www.SATs-Papers.co.uk 23/12/05 2:01:37 pm