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Ma Mathematics tests KEY STAGE 3 for Mental mathematics tests A, B and C 2008 LOWER TIER & HIGHER TIERS Mark scheme National curriculum assessments Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 1 http://www.SATs-Papers.co.uk 3/12/07 11:35:19 am QCA wishes to make its publications widely accessible. Please contact us if you have any specific accessibility requirements. First published 2008 © Qualifications and Curriculum Authority 2008 ISBN 1-84721-491-6 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 282686_mmMs04.indd 2 http://www.SATs-Papers.co.uk 3/12/07 11:35:21 am 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 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 3 http://www.SATs-Papers.co.uk 3 3/12/07 11:35:21 am 4 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 4 http://www.SATs-Papers.co.uk 3/12/07 11:35:22 am How many sides does an octagon have? Double nineteen. Round four thousand two hundred and sixty-six to the nearest ten. Multiply six by seven. Look at the expression. Write it as simply as possible. Write one quarter as a decimal. What is nought point eight multiplied by ﬁve? 2 3 4 5 6 7 8 Look at the numbers on your answer sheet. Put a ring round the largest number. ‘Now turn over your answer sheet.’ 16 Sam is facing North. He turns clockwise to face North-East. Through how many degrees does he turn? 15 Subtract three from three squared. 14 The chart shows the number of men and women who work at a factory. One symbol represents twenty-ﬁve people. How many more men than women work at the factory? 13 John went to France on the twenty-ﬁfth of July and returned exactly one week later. On what date did John return? 12 The table shows the price of a journey by train or bus. How much will it cost two adults and one child to make the journey by bus? 11 Look at the coins. How much money is shown altogether? 10 Add together fourteen, ﬁfteen and sixteen. 9 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ Add sixty-seven and fourteen. 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 67 49 14 Total marks 0.8 5 1 4 7 8 7k – 4 k 6 7 6 4 5 4266 3 2 1 19 Time: 5 seconds Practice question School Last name First name Mental mathematics Test C Key stage 3 mathematics 2008 Pupil answer sheet 8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9 2110 train 14 2001 £2.00 ° women men W bus 3 S N 32 25th July 40p E 16 2100 £1.20 15 2101 = 25 people child £ £1.00 adult £ 2010 Time: 10 seconds 16 15 14 13 12 11 10 9 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 5 http://www.SATs-Papers.co.uk 5 3/12/07 11:35:22 am ‘Put your pens down. The test is ﬁnished.’ 30 Look at the diagram. Work out the size of angle a. 29 Twenty-nine multiplied by thirty-four is nine hundred and eighty-six. What is nought point two nine multiplied by thirty-four? 28 Look at the information on your answer sheet. The total mass of the three boxes is two kilograms. What is the mass of box C? 27 Ben has one red marble, one green marble and three blue marbles in his pocket. He is going to take one of the marbles out of his pocket without looking. What is the probability it will be green? 26 Look at the sequence of triangular numbers: one, three, six, ten, ﬁfteen. What is the next number in the sequence? 25 Look at the triangle and the square. The perimeter of the triangle is the same as the perimeter of the square. What is the side length of the square? 24 The bar chart shows how Pete spent some of his day. How many more hours did he spend sleeping than working? 23 I am thinking of a number. The number can be divided by three with no remainder. It can also be divided by four with no remainder. What could my number be? 22 Your answer sheet shows the cost of three tins of cat food. How much would six of these tins cost? ‘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. I subtract three from the expression. Write the new expression as simply as possible. 20 What is the square root of eighty-one? 19 Look at the triangle drawn on the grid. Write the coordinates of the point marked A. 18 Eight kilometres is about ﬁve miles. About how many miles is twenty-four kilometres? 17 Look at the temperature shown on the thermometer. The temperature drops by ﬁve degrees Celsius. What is the new temperature? ( C –2 8 km –2 0 2 y 23 22 £ B 2 °C 4 A 5b + 3 √81 ) 2 miles 5 miles 0 3 tins for 99p , 0 –6 – 4 – 2 °C Time: 15 seconds 21 20 19 18 17 Time: 10 seconds continued x 23 22 21 20 19 18 17 30 29 28 27 26 25 24 10, 34 ° 34 0.29 × = = 950g B 1 green 6, 6cm g C 3 blue cm 10 170° a 986 15, 4 6 8 Time (hours ) 29 × 450g A 2 8cm 3, 1 red 1, 6cm 0 working eating sleeping Time: 15 seconds continued 30 29 28 27 26 25 24 2008 Key stage 3 mathematics 2006 lower tiers Test Mental mathematics highertier Test C A Time: 10 seconds 9 2010 2001 2110 Test C Test A 10 £ 1.13 12 £ 2.80 13 1st August 14 75 15 6 16 45 ° 2101 45 11 2100 Mark scheme Time: 5 seconds 81 1 2 8 3 38 4 4270 5 42 6 3k 7 0.25 Accept any unambiguous or commonly used indication of the date, eg 1 Aug, 1/8 or 8/1 [US notation] Ignore years given Accept equivalent decimals Accept 45 + any multiple of 360 Do not accept equivalent fractions 4 (.0) 8 6 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 6 http://www.SATs-Papers.co.uk 3/12/07 11:35:23 am Time: 10 seconds continued – 3 °C Time: 15 seconds continued 5 cm 21 27 1 5 28 600 g 29 9.86 30 answer 3 26 14.9 18 24 25 17 100 ° 15.1 miles (1, –2) 19 9 20 Accept –9 with 9 or alone Accept equivalent probabilities Accept embedded values eg 9 × 9 5b 21 Time: 15 seconds Accept equivalent fractions or decimals £ 1.98 22 Any multiple of 12 23 Accept zero or negative multiples of 12 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 7 http://www.SATs-Papers.co.uk 7 3/12/07 11:35:23 am 8 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 8 http://www.SATs-Papers.co.uk 3/12/07 11:35:24 am Look at the numbers on your answer sheet. Write down the number that is the mode. Look at the expression. Write it as simply as possible. Subtract nought point one from four. What number is eight more than minus two? Look at the number on your answer sheet. Round it to one decimal place. What is the gradient of the line with equation y equals three x plus two? 2 3 4 5 6 7 Look at the shaded triangle drawn on a centimetre square grid. What is the area of the triangle? 9 3 2 1 ‘Now turn over your answer sheet.’ 17 Look at the number on your answer sheet. Halve it. 16 Look at the expression. Multiply out the brackets. 15 On average I take twenty breaths in one minute. How many breaths is that in one hour? 4.875 6 0.1 4 4 b + 5b 9 7 –2 4 4 42 99 Total marks 5 4 14 I travel at a constant speed of forty miles per hour. How far do I travel in two and a half hours? 8 Time: 5 seconds Practice question School Last name First name Mental mathematics Test A Key stage 3 mathematics 2008 Pupil answer sheet 13 Twenty per cent of a number is six. What is the number? 12 Look at the equation on your answer sheet. When b is three, what is the value of a? 11 Look at the triangle. Work out the size of angle p. 10 Write down the multiple of twelve between forty and ﬁfty. There are three hundred people at a concert. One hundred and ﬁfty-ﬁve of them are male. How many are female? 8 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ How many sixes are there in forty-two? 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 17 16 15 14 13 12 11 10 9 8 p 55° miles Time: 10 seconds 7 ° 50 6 5.7 3( a – 5 ) 20 40 mph 20% a = 5b – 4 25° 40 cm2 300 y = 3x + 2 Time: 5 seconds continued 17 16 15 14 13 12 11 10 9 8 7 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 9 http://www.SATs-Papers.co.uk 9 3/12/07 11:35:24 am ‘Put your pens down. The test is ﬁnished.’ 30 Eight squared is the same as two to the power what? 29 Look at the rhombus. Work out its area. 28 Look at the numbers on your answer sheet. Add them. 27 A pyramid has ﬁve faces. How many sides does the base of the pyramid have? 26 The frequency table shows the number of televisions owned by thirty families. Altogether how many televisions did they own? 25 Look at the cuboid. It has a volume of one hundred cubic centimetres. Work out length a. 24 Thirty-two people were asked if they travelled to work by bus one morning. The pie chart shows the results. How many people said yes? 24 23 22 21 × × 20 21 No 38 38 Time: 15 seconds 23 Look at the square grid. Shade one more square to give a shape with rotation symmetry of order two. £ 20 19 blue green = people Yes = 760 m3 m £1.20 0.3 0.4 red 24 23 22 21 20 19 30 29 28 27 26 a cm 3 2 1 0 Televisions 2cm 3 3 4 4 2 82 0.3 5 faces 8 10 10 2 Frequency cm 10cm 25 Probability Colour 18 18 Time: 15 seconds continued Time: 10 seconds continued 22 Twenty multiplied by thirty-eight is seven hundred and sixty. What is twenty-one multiplied by thirty-eight? 21 One of the shapes on your answer sheet is the net of a cuboid. Put a ring round the correct shape. ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 20 Look at the expression. Write down the value of the expression when m is six. 19 In a sale, the price of a notebook is decreased by ten per cent. What is the new price if the old price was one pound twenty? 18 In a bag, there are only red, green and blue balls. Complete the table to show the probability of taking a blue ball. 30 29 28 27 26 25 Key stage 3 mathematics 2008 Mental mathematics higher tiers Test A Time: 5 seconds continued 3 7 Time: 10 seconds Test A 145 9 4 2 cm2 10 48 11 100 ° 12 11 13 30 14 100 miles 15 1200 16 Mark scheme 8 3a – 15 1 Accept equivalent fractions or decimals Time: 5 seconds 7 1 4 2 Accept value(s) indicated in list Do not accept incorrect % signs 9b 3 3.9 4 5 4.9 Accept equivalent fractions or decimals Do not accept equivalent fractions or decimals Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 10 Accept unconventional notation, eg 3 × a – 15 Do not accept incomplete processing, eg 3 × a – 3 × 5 6 6 10 Accept embedded values, eg 7 × 6 17 2.85 Accept equivalent fractions or decimals http://www.SATs-Papers.co.uk 3/12/07 11:35:25 am Time: 10 seconds continued 18 0.3 19 £ 1.08 20 36 Accept equivalent probabilities Time: 15 seconds continued 25 5 cm 26 54 27 4 28 3.05 Accept equivalent fractions or decimals 29 24 Ignore any units given 30 6 Accept embedded values, eg 26 Do not accept incomplete processing, eg 216 6 Time: 15 seconds 21 798 22 23 12 people 24 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 11 http://www.SATs-Papers.co.uk 11 3/12/07 11:35:25 am 12 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 12 http://www.SATs-Papers.co.uk 3/12/07 11:35:26 am I start at four point seven and count on in equal steps: four point seven, four point eight, four point nine. Write down the next two numbers in the sequence. Double the expression on your answer sheet. Write seven-hundredths as a decimal. Look at the scatter graph. It shows a type of correlation. Put a ring round the word that describes the type of correlation it shows. Write ten out of twenty-ﬁve as a percentage. 2 3 4 5 6 Look at the scale. About what value is the arrow pointing to? What is half of three pounds sixty? 8 9 ‘Now turn over your answer sheet.’ 14 What is one quarter of one hundred and forty-eight? 13 How many ﬁfths are there in two? 12 Look at the diagram. Estimate the size of angle a. 11 Double two point nine. 10 How many millimetres are there in ten centimetres? Look at the triangle drawn on the grid. What are the coordinates of the point marked A? 7 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ Multiply six by six. 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 5 4 3 2 1 4.8, High 7 100 4 pq , 99 Total marks Negative Gradient 4.9, Positive None 4.7, Time: 5 seconds Practice question School Last name First name Mental mathematics Test B Key stage 3 mathematics 2008 Pupil answer sheet 5 4 3 2 1 % 14 13 12 11 10 9 8 7 £ 0 0 1 2 3 4 0 ( A ° 1 1 , 2 3 a B 2 1 5 148 2.9 2 10 cm £ 3.60 ) 4 10 out of 25 C mm Time: 10 seconds 6 Time: 5 seconds continued 14 13 12 11 10 9 8 7 6 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 13 http://www.SATs-Papers.co.uk 13 3/12/07 11:35:26 am ‘Put your pens down. The test is ﬁnished.’ 30 Look at the graph. Write down the equation of the line labelled A. 29 Four numbers have a mean of twenty-ﬁve. Three of the numbers are shown on your answer sheet. Write down the missing number. 28 Look at the calculation on your answer sheet. Write an approximate answer. 27 A million pound lottery prize is divided in the ratio one to four to ﬁve. How much is the smallest share of the prize? 26 A circle has a radius of ﬁve. One of the values on your answer sheet shows its circumference. Put a ring round the correct value. 25 Look at the fractions. Put rings round all those that are greater than three-quarters. 24 Car parking costs forty pence for every ﬁve minutes. How much will it cost to park for one hour? 23 Think about a pyramid that has a triangular base. How many triangular faces does it have altogether? 22 The line graph shows the number of ice creams sold at a cinema in one week. On how many days were the sales more than one hundred? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 21 A cylinder has a base area of ten square centimetres and a volume of ninety cubic centimetres. What is the height of the cylinder? 20 Look at the expression. When x is three, what is the value of the expression? 19 A square of side two centimetres is enlarged by scale factor two. What is the area of the enlarged square? 18 Look at the equation. What is the value of x? 17 What is the next square number after thirty-six? 16 There are seventeen red and thirteen green apples in a bag. I am going to take out an apple without looking. What is the probability that the apple will be green? 15 Look at the polygon. Write down its mathematical name. 2 cm 2 36 17 red 13 green 10cm 22 0 200 150 100 50 cm 90cm 3 ( x + 2 )( x – 1 ) days M T W T F S S day Time: 15 seconds 21 20 cm2 Scale factor 2 18 19 21 – 3 x = 9 17 16 15 Time: 10 seconds continued 22 21 20 19 18 17 16 15 30 29 28 27 26 25 24 23 £ 3 5 – 20 5 £ –2 5 6 0 2 y 0 10 –2 80 25 4 5 15 7 10 40 2 x A 39.92 × 41.06 1.98 1:4: 5 100 5 6 9 40p for 5 minutes Time: 15 seconds continued 30 29 28 27 26 25 24 23 2008 Key stage 3 mathematics 2006 B Mental mathematics higher tiers Test A Time: 5 seconds continued 6 Do not accept equivalent fractions or decimals 40 % Time: 10 seconds Test B Test A 7 ( 0, 1 ) Mark scheme 8 1.6 answer 1.8 Accept equivalent fractions or decimals Time: 5 seconds 36 1 9 10 8 pq 3 Do not accept unconventional notation, eg 8 × pq Accept equivalent decimals 0.07 4 100 mm Do not accept amended units 11 5.8 Accept equivalent fractions or decimals 12 110 ° 13 10 14 5(.0) and 5.1 2 £ 1.80 37 Accept pair in either order answer 130 ° Do not accept equivalent fractions 5 None Gradient Positive 14 Accept embedded values, eg 10 5 Negative Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 14 High http://www.SATs-Papers.co.uk 3/12/07 11:35:27 am Time: 10 seconds continued Octagon Time: 15 seconds continued 13 30 16 Ignore additional description, eg regular Accept equivalent fractions 23 4 24 15 £ 4.80 25 Accept decimals as 0.43 or better or percentage equivalents 17 4 5 5 6 6 9 7 10 26 49 18 3 5 4 5 10 25 19 10 100 16 cm2 20 15 Do not accept incomplete processing, eg 5 × 2 27 £ 100 000 28 800 29 0 30 y=x+1 9 cm 21 Time: 15 seconds 3 days 22 Sourced from SATs-Papers.co.uk 282686_mmMs04.indd 15 answer 840 Accept equivalent equations Accept unconventional notation, eg y = 1x + 1 http://www.SATs-Papers.co.uk 15 3/12/07 11:35:27 am 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 282686_mmMs04.indd 16 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/08/3286 http://www.SATs-Papers.co.uk282686 3/12/07 11:35:28 am