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Ma Mathematics tests KEY STAGE 3 for Mental mathematics Tests A, B and C 2007 LOWER TIER & HIGHER TIERS Mark schemes National curriculum assessments Sourced from SATs-Papers.co.uk 275684_mmMs.indd 1 http://www.SATs-Papers.co.uk 19/12/06 2:09:09 pm QCA wishes to make its publications widely accessible. Please contact us if you have any specific accessibility requirements. First published 2007 © Qualifications and Curriculum Authority 2007 ISBN 1-85838-875-9 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 275684_mmMs.indd 2 http://www.SATs-Papers.co.uk 19/12/06 2:09:11 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 Sourced from SATs-Papers.co.uk 275684_mmMs.indd 3 http://www.SATs-Papers.co.uk 3 19/12/06 2:09:11 pm 4 275684_mmMs.indd 4 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 19/12/06 2:09:11 pm What number multiplied by ﬁve makes forty? Look at the list of numbers on your answer sheet. What number is the mode? Write in ﬁgures the number two thousand and twenty. How many centimetres are seventy millimetres? Write a number that is more than nought point one but less than nought point two. I am thinking of a number. I call it n. I add eight to my number. Write an expression to show the result. Look at the fraction. Write down a different fraction that is equivalent to four-ﬁfths. 2 3 4 5 6 7 8 I start at forty and count down in equal steps. Forty, thirty-seven, thirty-four … What are the next two numbers? ‘Now turn over your answer sheet.’ 15 What is half of twenty-three? 14 Look at your answer sheet. Estimate the length of the line in centimetres. 13 Add the numbers on your answer sheet. 12 I face north. I turn through half a turn. What direction am I facing after the turn? 11 Shade one quarter of the square on your answer sheet. 10 The bar chart shows the eye colours of some pupils. How many of the pupils have blue eyes? 9 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ What is seventeen pounds eighty-ﬁve pence rounded to the nearest pound? 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 6 5 4 3 2 1 £ 7 5 Time: 5 seconds 8 5 40 0.2 70 mm 4 5 £17.85 195 Total marks 0.1 Test C cm Practice question School Last name First name Mental mathematics Key stage 3 mathematics 2007 Pupil answer sheet 6 5 4 3 2 1 15 14 13 12 11 10 9 0 40, Brown Blue 34, , 4 5 n 54 cm 66 North pupils 2 4 6 8 Number of pupils 37, Time: 10 seconds 8 7 Time: 5 seconds continued 15 14 13 12 11 10 9 8 7 Sourced from SATs-Papers.co.uk 275684_mmMs.indd 5 http://www.SATs-Papers.co.uk 5 19/12/06 2:09:12 pm ‘Put your pens down. The test is ﬁnished.’ 30 Look at the graph on your answer sheet. Write down the coordinates of any point on the line marked A. 29 Your answer sheet shows the answer to twenty-eight multiplied by sixteen. Use this information to help you work out the answer to twenty-eight multiplied by thirty-two. 28 Look at the scale. About what value is the arrow pointing to? 27 Your answer sheet shows the percentages of pupils born in different seasons for class A. The percentage for winter is missing. Fill in the percentage of class A that was born in winter. 26 The number one is a factor of both ﬁfteen and twenty-four. What other number is a factor of both ﬁfteen and twenty-four? 25 Look at the price list. I buy one notebook, one ruler and one pencil. Altogether, how much do they cost? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 24 The diagram shows a line inside a square. What is the size of angle k? 23 There are three red balls and two blue balls in a bag. I am going to take a ball out of the bag at random. What is the probability that the ball will be red? 22 Look at the rectangle. What is its area? 21 At sunrise the temperature was minus three degrees Celsius. By midday, the temperature had increased by twelve degrees. What was the temperature at midday? 20 Magazines cost one pound and forty pence each. I buy two of the magazines. How much change do I get from a ten pound note? 19 Look at the shape drawn on the square grid. How many lines of symmetry does it have? 18 Look at the equation. What is the value of y when x is twelve? 17 I have a bag of twenty pence coins. Altogether I have seven pounds. How many twenty pence coins do I have? 16 In a survey, people were asked if they would prefer a cat or a dog for a pet. The pictogram shows the results. Six people said cat. How many people said dog? £ 3 red °C people £7 24 23 22 21 20 3 cm ° k cm2 65° 2 blue 9 cm –3°C £ 1.40 18 19 y=x–7 17 Dog 24 23 22 21 20 19 18 17 30 29 28 27 26 28 28 × × ( –3 A 0 kg –3 0 3 y 32 16 Winter Autumn Summer Spring £ 0 = , = ) kg 1kg % 3 x 448 28% 22% 30% 24 40p Pencil 15 65p £1.05 Ruler Notebook 25 Cat 16 16 Time: 15 seconds Time: 10 seconds continued 30 29 28 27 26 25 2007 Key stage 3 mathematics 2006 lower tiers Test Mental mathematics highertier Test C A Time: 5 seconds continued Do not accept unconventional notation, eg 1 × n + 8 7 n+8 8 4 5 4 that is equivalent to , 5 8 , 40 eg 10 50 Test C Test A Mark scheme Any fraction except Do not accept equivalent decimals Time: 10 seconds 9 31 and 28 10 Accept pair in either order 5 pupils 11 Indicates any two small triangles, eg 12 South Time: 5 seconds 1 £ 18 (.00) 2 8 Accept embedded values, eg 8 × 5 3 5 Accept value indicated in list 4 2020 Do not accept responses given in words 13 120 5 7 cm Do not accept amended units 14 4 cm Accept any unambiguous indication of South, eg S 6 6 275684_mmMs.indd 6 0.1 < answer < 0.2 Sourced from SATs-Papers.co.uk 15 11 1 2 answer 5 cm Accept equivalent fractions or decimals http://www.SATs-Papers.co.uk 19/12/06 2:09:12 pm Time: 10 seconds continued 16 8 people 17 Time: 15 seconds 35 £ 2.10 26 3 27 18 25 20 % 5 19 4 20 £ 7.20 21 9 °C 22 27 cm2 28 Accept equivalent fractions or decimals 29 23 3 5 24 0.2 kg < answer < 0.4 kg Accept equivalent probabilities 896 25 ° Sourced from SATs-Papers.co.uk 275684_mmMs.indd 7 30 Any pair of coordinates such that x + y = –2, eg (1, –3), (–1, –1) http://www.SATs-Papers.co.uk 7 19/12/06 2:09:13 pm 8 275684_mmMs.indd 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 19/12/06 2:09:14 pm Look at the number on your answer sheet. Divide it by one hundred. Look at the numbers on your answer sheet. Add them. Look at the types of triangles on your answer sheet. Put a ring round the one that must have three equal angles. Write the fraction ﬁve-twentieths as simply as possible. Round nought point three four eight to two decimal places. Divide minus one hundred by minus ten. Your answer sheet shows the rule for the nth term of a sequence. What is the ﬁfth term of this sequence? Four to the power nine divided by four to the power three is four to the power what? 2 3 4 5 6 7 8 9 ‘Now turn over your answer sheet.’ 15 A book costs ﬁve pounds and ninety-nine pence. What is the total cost of three of these books? 14 Look at the diagram. Write down the size of angle m. 13 The total of four numbers is eighty. What is their mean? 12 Look at the number on your answer sheet. How much must you add to it to make three thousand? 11 A book has one hundred and twenty pages. I have read a quarter of the pages. How many pages have I read? 10 Look at the triangle drawn on the grid. What are the coordinates of the point marked A? ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ How many days are there in ten weeks and two days? 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 8400 7 Scalene –4 Right-angled Isosceles days 5 Total marks Equilateral 5 20 0.348 5 4 3 2 1 Time: 5 seconds Practice question School Last name First name Mental mathematics Test A Key stage 3 mathematics 2007 Pupil answer sheet 6 6 5 4 3 2 1 15 14 13 12 11 10 £ 0 1 2 3 4 5 0 ( C B 2 , pages ° 1 Time: 10 seconds 9 8 7 3 43 80 2092 £ 5.99 230° m ) 5 120 A 49 4 – 10 ( + 3) – 100 Time: 5 seconds continued 15 14 13 12 11 10 9 8 7 Sourced from SATs-Papers.co.uk 275684_mmMs.indd 9 http://www.SATs-Papers.co.uk 9 19/12/06 2:09:14 pm 20 ‘Put your pens down. The test is ﬁnished.’ 30 A photograph is enlarged using a scale factor of two and a half. After the enlargement, it has a length of twenty-ﬁve centimetres. What was its length before the enlargement? 29 I am going to take a ball at random from a bag. The probability it will be blue is ﬁve-sixths. Twenty of the balls are blue. How many of the balls are not blue? 28 Look at the circle with a radius of ten. One of the values below is its area. Put a ring round the correct area. 24 0 12 1 5 °C 10 15 20 °C 5 90km/h 5< x< 9 2 3 4 Time (pm) Time: 15 seconds 23 5y 3009 599 2x 50 3:2 22 27 One hundred and twenty people chose between three types of orange juice. The pie chart shows the results. Sixty people chose type A. Approximately, how many people chose type B? 2 19 24 Look at the graph. By how much did the temperature fall between two pm and ﬁve pm? 26 Look at the equation. When b is eight, what is the value of a ? km 65° y=x +2 21 25 Look at the rectangle with length six centimetres. Its perimeter is twenty centimetres. What is the width of the rectangle? ° b 700 18 17 16 Time: 10 seconds continued ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 23 A racing pigeon can ﬂy at a speed of ninety kilometres per hour. At this speed, how far would it ﬂy in one minute? 22 Look at the inequality. How many integer solutions are there? 21 Write an approximate answer to the division on your answer sheet. 20 Multiply two x by ﬁve y. Write your answer as simply as possible. 19 The ratio of men to women in a chess club is three to two. There are ﬁfty people in the chess club. How many are women? 18 Look at the equation. When x is three, what is the value of y ? 17 Look at the isosceles triangle. What is the size of angle b? 16 What is twenty per cent of seven hundred? 24 23 22 21 20 19 18 17 16 30 29 28 27 26 25 10 25 cm 30 B C 20 A width 5 6 100 10 cm 20 25 people 60 people b = 2a – 4 cm 6 cm Time: 15 seconds continued 30 29 28 27 26 25 Key stage 3 mathematics 2007 Mental mathematics higher tiers Test A Time: 5 seconds continued 7 8 Test A 10 40 Do not accept incomplete processing, eg 5 × 8 9 6 Accept embedded values, eg 46 Mark scheme Time: 10 seconds 10 ( 4 , 3 ) 11 30 pages 12 908 13 20 14 40 ° 15 £ 17.97 Time: 5 seconds 1 72 days 2 84 3 3 4 Isosceles Scalene Equilateral Right-angled 5 1 4 Do not accept equivalent fractions or decimals 6 10 Accept embedded values, eg 2092 + 908 0.35 Do not accept equivalent fractions or decimals Sourced from SATs-Papers.co.uk 275684_mmMs.indd 10 http://www.SATs-Papers.co.uk 19/12/06 2:09:15 pm Time: 10 seconds continued 16 50 ° 18 Do not accept 140% 140 17 Time: 15 seconds continued 25 4 cm 11 26 6 Accept embedded values, eg 2 × 6 – 4 20 19 27 20 4.9 22 3 answer 22 people 10 xy 21 18 answer 5.1 Accept all integer solutions listed, ie 6, 7, 8 Do not accept a range, eg 6 to 8 1 23 1 km 2 Accept equivalent fractions or decimals 28 10 20 30 25 100 Time: 15 seconds 10 °C 24 275684_mmMs.indd 11 4 30 Sourced from SATs-Papers.co.uk 29 10 cm http://www.SATs-Papers.co.uk 11 19/12/06 2:09:15 pm 12 Sourced from SATs-Papers.co.uk 275684_mmMs.indd 12 http://www.SATs-Papers.co.uk 19/12/06 2:09:15 pm What is ﬁfty-six divided by eight? Look at the expression. Write it as simply as possible. What is seven squared? How many pairs of parallel sides must a trapezium have? What number is nought point eight less than nine? Write the ratio twelve to four as simply as possible. I think of a number. I call it n. I square it and then subtract four. Write an expression to show the result. Multiply minus four by minus ﬁve. 2 3 4 5 6 7 8 9 ‘Now turn over your answer sheet.’ 15 What number is the arrow pointing to on the number line? 14 Look at the triangle. Write down the size of angle c. 13 Look at the rectangle. Write down its perimeter. 12 Four hundred pupils were asked if they wanted to take art GCSE. The pie chart shows the results. How many pupils said no? 11 A television programme lasts for an hour and a quarter. How many minutes is that? ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ 10 A line is twenty centimetres long to the nearest centimetre. What is the minimum length it can be? Write in ﬁgures the number six thousand and ten. 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 Time: 5 seconds Practice question School Last name First name Mental mathematics 12 : 4 7 6 b – 4b 56 5 Total marks 0.8 Test B Key stage 3 mathematics 2007 Pupil answer sheet 9 7 6 5 4 3 2 1 cm 15 14 13 12 11 3.2 c 80° No n –5 30° 5cm 3.3 ° cm pupils 20 cm –4 Yes 6cm Don’t know minutes Time: 10 seconds 10 9 8 Time: 5 seconds continued 15 14 13 12 11 10 9 8 Sourced from SATs-Papers.co.uk 275684_mmMs.indd 13 http://www.SATs-Papers.co.uk 13 19/12/06 2:09:16 pm ‘Put your pens down. The test is ﬁnished.’ 30 Look at your answer sheet. Complete the factorisation. 29 The mean of two numbers is six. One of the numbers is minus three. What is the other number? 28 Look at the graph. The equation of the line marked A is y equals x. Write down the equation of the line marked B. 27 I think of a number. I square my number and get the answer one thousand six hundred. What could my number be? 26 Look at the expression. When a is nought point three and b is nought point four, what is the value of the expression? 25 Look at the quadrilateral. What is the size of angle d ? 24 Eighteen multiplied by twenty-two is three hundred and ninety-six. What is three thousand nine hundred and sixty divided by eighteen? 23 Look at the equation. When y is four, what is the value of x? 22 I have ﬁfty-ﬁve twenty pence coins. How many pounds is this? ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ 21 What is nought point four multiplied by nought point two? 20 A car travels at an average speed of ﬁfty miles per hour. How far does it travel in two and a half hours? 19 Write the fraction three-ﬁfths as a percentage. 18 Look at the scatter graphs. Put a ring round the graph that shows a positive correlation. 17 A cuboid measures three centimetres by four centimetres by ﬁve centimetres. What is its volume? 16 A fair six-sided dice is numbered one to six. I am going to roll the dice. What is the probability that I will roll a four? 21 20 19 18 17 3 50 mph % 2 0.4 miles 1 hours 2 3 5 cm 3 cm by 4 cm by 5cm 0.2 21 20 19 18 17 30 29 28 27 26 25 24 23 10 ( a + b ) 0.3 118° 3960 ÷ 18 = 20p 0.4 + –3 B A 1600 d ° ) y + 11 = 3x 55 18 × 22 = 396 6p2 + 12p = 6p( £ 22 16 16 Time: 15 seconds Time: 10 seconds continued 30 29 28 27 26 25 24 23 22 2007 Key stage 3 mathematics 2006 B Mental mathematics higher tiers Test A Time: 5 seconds continued 8 9 Test B Test A n2 – 4 20 10 19.5 cm Do not accept unconventional notation, eg n × n – 4 Accept equivalent fractions or decimals Mark scheme Time: 10 seconds 11 75 minutes 12 100 pupils 13 22 cm 14 70 ° 15 3.28 Time: 5 seconds 1 6010 2 Do not accept responses given in words 7 3 2b 4 49 5 1 6 Accept equivalent fractions or decimals 7 14 8.2 3:1 Accept equivalent fractions or decimals Do not accept equivalent ratios Sourced from SATs-Papers.co.uk 275684_mmMs.indd 14 http://www.SATs-Papers.co.uk 19/12/06 2:09:16 pm Time: 10 seconds continued Accept equivalent fractions Accept 0.16(…) or 0.17, or percentage equivalents Time: 15 seconds 23 5 24 220 62 ° 7 Do not accept incomplete processing, eg 10 × 0.7 27 40 Accept –40 with 40 or alone 28 y = –x Accept unconventional notation, eg y = –1 × x 29 15 30 60 cm3 17 £ 11 26 1 6 22 25 16 6p ( p + 2 ) or 6p ( 2 + p ) Accept embedded values, eg 3 × 5 18 19 60 % 20 Do not accept equivalent fractions or decimals 125 miles 0.08 21 Accept equivalent fractions or decimals Sourced from SATs-Papers.co.uk 275684_mmMs.indd 15 Accept unconventional notation, eg 6p ( 1p + 2 ) http://www.SATs-Papers.co.uk 15 19/12/06 2:09:17 pm 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 275684_mmMs.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 http://www.SATs-Papers.co.uk 275684 QCA/06/2778 19/12/06 2:09:17 pm