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Mathematics tests Ma KEY STAGE 3 LOWER TIER & HIGHER TIERS 2004 2004 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 2004 © Qualifications and Curriculum Authority 2004 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 http://www.SATs-Papers.co.uk Introduction This booklet contains the mark schemes for the higher tiers tests (Tests A and B) and the lower tier test (Test C). 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 http://www.SATs-Papers.co.uk 4 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Multiply four by four. Subtract forty-eight from seventy. What is fifty per cent of ten? Look at the equation. Find the value of k. What is half of two-thirds? 2 3 4 5 6 I bought three tickets for a concert. The total cost was forty-five pounds. How much was one ticket? Your answer sheet shows part of a train timetable. How long does the journey take from Twyford to Maidenhead? What is one quarter of sixty? What is the perimeter of this square? Look at the numbers. Put a ring round the median. Look at the scale. About what value is the arrow pointing to? My birthday is twenty-two days after my friend’s birthday. This year my friend’s birthday is on a Monday. On what day will my birthday be this year? The longest flight of stairs in the world is in Switzerland. Your answer sheet shows how many stairs there are. Write this number to the nearest thousand. Look at the numbers. What is the largest number that will divide exactly into both of these numbers? 8 9 10 11 12 13 14 15 16 ‘Now turn over your answer sheet.’ In a local swimming pool, thirty-two lengths is half a mile. How many lengths is one mile? 7 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ Your answer sheet shows the price of a book. How much is the book, to the nearest pound? 1 ‘Now we are ready to start the test. For the first group of questions you will have 5 seconds to work out each answer and write it down.’ Lower tier Test C questions £ 16.55 70 £ 20 Total marks k – 20 = 40 4 2 3 5 50% 3 2 1 Time: 5 seconds Practice question School Last name First name Mental mathematics Test C Key stage 3 mathematics 2004 Pupil answer sheet 6 6 5 4 3 2 1 16 15 14 13 12 11 10 9 8 7 £ 4 9 cm 10 £ 45 32 20 12 20 11 674 22 days 13 60 minutes lengths Time: 10 seconds 16 15 14 13 12 11 10 9 8 7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 5 What is the next number in the sequence of square numbers? One, four, nine, sixteen … On the grid is a point marked A. Write the coordinates of this point. There are fourteen girls and thirteen boys in a class. What is the probability that a pupil chosen at random will be a girl? Estimate the size of the angle, in degrees. Look at the equation. When a is ten, what is the value of b ? 19 20 21 22 The diagram shows three circles. Shade the part of the diagram where all three circles overlap. Look at the price list. I buy one sandwich, one yoghurt and two apples. How much money is that altogether? In a survey, pupils were asked if they liked playing sport. Twenty pupils said yes. How many pupils said no? Write three even numbers that add to twenty. Work out the size of angle a. What is the remainder when you divide three hundred by twenty-nine? Look at the types of quadrilaterals on your answer sheet. Which of them must have sides that are all the same length? Ring the correct ones. 24 25 26 27 28 29 30 ‘Put your pens down. The test is finished.’ Look at the cube. I am going to hang it from the corner marked with an arrow. When it is hanging, which corner will be lowest? Mark the correct corner with a cross. 23 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ The chart shows the number of males and females who are members of a sports club. There are thirty males in the club. About how many females are there? 18 17 1, ° 4, ( 23 , females 16, ) x b = 3a + 5 14 girls 13 boys 9, y Time: 15 seconds 22 21 20 19 18 17 Time: 10 seconds continued 23 22 21 20 19 18 17 30 29 28 27 26 25 24 a rhombus 29 kite rectangle 300 ° 20 pupils 30p 75p £1.50 parallelogram square £ Apple Yoghurt Sandwich Time: 15 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2004 Mental mathematics lower tier Test C Time: 1 0 seconds 7 8 £ 15 ( .00 ) 9 8 minutes 10 15 11 Test C 64 lengths 40 cm Mark scheme 12 Time: 5 seconds 1 £ 17 ( .00 ) 2 22 9 10 13 20 16 3 4 4 5 5 13 14 1.7 ≤ answer ≤ 1.8 Accept unambiguous abbreviation, eg Tues, Tu, but do not accept if ambiguous, eg T Tuesday 60 Do not accept 5% 15 16 6 1 Accept equivalent fractions or 0.33(…) 12 000 4 Do not accept 12 Accept value repeated, eg 4 and 4, but do not accept if ambiguous, eg 4 + 4 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 1 0 seconds continued 17 Time: 15 seconds continued 24 ( –2, 1 ) 25 26 18 19 20 21 £ 2.85 8 pupils Do not accept 52 or 5 x 5 25 18 ≤ answer ≤ 22 females 14 Accept equivalent probabilities, including 0.51(…) or 0.52 or equivalent percentages 27 Any three even numbers that add to 20 55 ° ≤ answer ≤ 75 ° 28 22 Accept repeated numbers, eg 2, 2, 16 0, 0, 20 110 ° 29 10 30 square 35 Time: 15 seconds 23 Accept embedded response, eg 10 r10 rectangle parallelogram 7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Divide forty-two by seven. What number is the arrow pointing to on the number line? Centimetres are a measure of length. What are square centimetres a measure of? Look at the expression. Write it as simply as possible. 2 3 4 5 In a survey people were asked if they had a mobile phone. The percentage bar chart shows the results. What percentage of people said yes? I have a bag that contains twenty-pence coins. Altogether, I have twelve pounds. How many twenty-pence coins is that? Add together the fractions on your answer sheet. 7 8 9 Increase one pound fifty by fifty per cent. There are seven red and three 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 blue? 11 Subtract eleven from four. What is the sum of the angles in a rhombus? 13 14 15 ‘Now turn over your answer sheet.’ Look at the triangle. What is the size of the angle marked a? 12 Look at the equation. When 10 y equals forty-six, what is the value of x? How many minutes are there in five hours? 6 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ How many sides does an octagon have? 1 ‘Now we are ready to start the test. For the first group of questions you will have 5 seconds to work out each answer and write it down.’ Higher tiers Test A questions 5 4 3 2 1 Time: 5 seconds Practice question School Last name First name 60 Total marks 7n2 – n2 Mental mathematics Test A Key stage 3 mathematics 2004 Pupil answer sheet 5 4 3 2 1 15 14 13 12 11 10 9 8 7 6 £ £12 % 1 7 ° ° £1.50 50% 7 red 3 blue y = 2x + 6 2 7 minutes Time: 10 seconds 15 14 13 12 11 10 9 8 7 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 9 To the nearest whole number, what is the square root of eighty-three point nine? It takes me one and a half minutes to swim one length of the pool. How many lengths can I swim in fifteen minutes? 18 n squared by to get five n cubed? A club played twenty-four games in a season. They won the same number of games as they lost. Use the pie chart to work out how many games they won. 25 Write three numbers that have a mean of ten and a range of two. The diagram shows a quadrilateral. Work out its area. The first odd number is one. What is the hundredth odd number? 28 29 30 ‘Put your pens down. The test is finished.’ A solid pyramid has seven faces. What shape is its base? 27 k plus ten and k plus twenty. Look at the fractions. Which of them are less than a half? Ring your answers. 24 The angles in a triangle are k, What is the value of k? The most popular months to get married are July, August and September. The table shows the percentages of marriages that are in those months. What percentage of marriages are not in those months? 23 26 The hands of a clock are at right angles. The minute hand is pointing to twelve. What could the hour hand be pointing to? There are two answers. Write them both. 22 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ What must I multiply One hundred pet owners had a dog or a cat, or both. Fifty-five of the hundred had a dog. Sixty-five had a cat. How many had both a dog and a cat? 20 21 Write an equation that shows that 19 k is one more than twice m. A circle has radius r. What is the formula for the area of the circle? 17 16 65 23 22 13% August September % 14% July or 12% n2 21 Time: 15 seconds 5n3 55 k is one more than twice m 83.9 20 19 18 17 15 23 22 21 20 19 18 17 30 29 28 27 26 25 k 1 50 3 4 ( k + 10 ) 2 3 3 7 cm 2 mean 10 range 2 ( k + 20) 1 10 24 lengths 16 16 Time: 15 seconds continued Time: 10 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2004 Mental mathematics higher tiers Test A Time: 1 0 seconds 6 300 minutes 7 40 % 8 60 9 3 Do not accept equivalent fractions or decimals Test A Mark scheme 10 20 11 Accept equivalent fractions or 0.42(…) 3 Time: 5 seconds 1 8 2 6 3 2.43 4 Area 5 6n2 Accept equivalent probabilities 12 Do not accept unsimplified expressions, eg 6 x n2 13 30 ° 14 Accept equivalent fractions or decimals £ 2.25 –7 15 360 ° Do not accept 7– 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 15 seconds continued Time: 1 0 seconds continued 16 10 lengths 17 9 24 πr 2 26 50 Accept 50° Hexagon Do not accept a description of a hexagon, eg 6-sided Accept equivalent formulae, eg π x r x r, A = πr 2 19 k = 2m + 1 20 Accept equivalent equations, eg 2 x m + 1 = k 20 21 9 27 18 25 5n Accept 5 x n 28 Time: 15 seconds 22 3 and 9 Accept in either order 23 61 % Any three numbers that total 30 and have a range of 2 eg 9, 10, 11 Do not accept equivalent fractions or decimals 29 30 cm2 30 199 11 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk I asked people whether they used the internet last week. The pie chart shows the results. What percentage of people said no? How many lines of symmetry does a rectangle have? Ten per cent of a number is seven. What is the number? Multiply minus six by minus two. 2 3 4 5 How many days are there in seven weeks and one day? What is the smallest whole number that is divisible by five and by three? I face south-west, then I turn through one hundred and eighty degrees. What direction am I facing now? Multiply eight point seven by two. Look at the polygon. What is its mathematical name? Tariq won one hundred pounds in a maths competition. He gave two-fifths of his prize money to charity. How much of his prize money, in pounds, did he have left? I am thinking of a number. I call it n. I double my number then I subtract three. Write an expression to show the result. An event is certain to happen. Which number on your answer sheet represents its probability? Ring it. Look at the grid. It is made from two sets of parallel lines. The angle marked is one hundred and forty degrees. On the grid, mark two different angles that are forty degrees. Look at the equation. What is the value of x? What percentage of fifty pounds is thirty-five pounds? 7 8 9 10 11 12 13 14 15 16 17 ‘Now turn over your answer sheet.’ A magazine costs one pound forty pence. I buy two of them and pay with a five pound note. How much change should I get? 6 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ How many hundreds are there in one thousand? 1 ‘Now we are ready to start the test. For the first group of questions you will have 5 seconds to work out each answer and write it down.’ Higher tiers Test B questions 5 4 3 2 1 Time: 5 seconds Practice question School Last name First name 60 Total marks % Mental mathematics Test B Key stage 3 mathematics 2004 Pupil answer sheet 5 4 3 2 1 17 16 15 14 13 12 11 10 9 8 7 6 £ £ 0 1 2 % 1 days Time: 10 seconds 100 £ 50 34 – 2x = 14 50 n 2 5 8.7 SW £ 1.40 17 16 15 14 13 12 11 10 9 8 7 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 13 The instructions for a fruit drink say to mix one part blackcurrant juice with four parts water. I want to make one litre of this fruit drink. How much blackcurrant juice should I use? Give your answer in millilitres. A rectangular picture measures six centimetres by four centimetres. I enlarge the picture so that the longer side measures nine centimetres. What does the shorter side measure? Look at the sequence of numbers. What could an expression for the nth term be? 19 20 21 The answer sheet shows the cost of theatre tickets. Mrs Jones wants to go with some children to the theatre. In total, she does not want to spend more than twenty-five pounds. What is the greatest number of children she can take? The net of a triangular prism is made from triangles and rectangles. How many of each shape are needed? I am going to throw a fair eight-sided dice, numbered twelve to nineteen. What is the probability that I will throw a prime number? Four people went running. The graph shows the time taken and the distance travelled by each of the four. Write the letter of the person who had the greatest average speed. Twenty different families were asked how many children they had. The table shows the results. Altogether, how many children are there in the twenty families? Look at the calculation. Write down an approximate answer. Look at the diagram. What is the equation of the line marked A? I pay five pounds for a book and a magazine. The book costs four pounds more than the magazine. How much does the book cost? 23 24 25 26 27 28 29 30 ‘Put your pens down. The test is finished.’ The scale drawing shows a lake. I walk around the perimeter of this lake. Use the scale to estimate how many kilometres I walk. 22 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ Multiply out the brackets. 18 25 24 23 22 cm 1 litre 4(7 – y) £ 6.99 £ 3.99 12 to 19 rectangles triangles Each adult Each child km 1, 4, 9, 16, … ml Time: 15 seconds 21 20 19 18 Time: 10 seconds continued 25 24 23 22 21 20 19 18 30 29 28 27 26 £ 40.04 t 29.8 9.83 Time: 15 seconds continued 30 29 28 27 26 Key stage 3 mathematics 2004 Mental mathematics higher tiers Test B Time: 1 0 seconds 6 7 Test B Mark scheme £ 2.20 50 days 8 15 9 North-east Accept unambiguous abbreviation, eg NE, and unconventional ordering, eg East-north 10 17.4 Accept equivalent fractions or decimals 11 Hexagon Do not accept a description of a hexagon, eg 6-sided 12 £ 60 13 2n – 3 Time: 5 seconds 1 2 10 25 % Do not accept equivalent fractions or decimals Accept unsimplified expressions, eg 2 x n – 3 1 14 0 15 Indicates any two 40° angles, with none incorrect 1 3 2 4 70 Do not accept 70% 16 10 5 12 Accept +12 17 50 70 % 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 100 Time: 15 seconds continued Time: 1 0 seconds continued Accept use of multiplication sign within 4y, eg 28 – 4 x y 28 – 4y 19 A 33 200 ml 20 26 27 18 6 cm 21 n2 Accept nxn Time: 15 seconds 22 11 km ≤ answer ≤ 17 km 28 29 23 y=3 30 £ 4.50 Accept equivalent equations 4 24 115 ≤ answer ≤ 125 2 triangles 3 rectangles 25 3 Accept equivalent probabilities 15 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 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 Publications, PO Box 99, Sudbury, Suffolk CO10 2SN (tel: 01787 884444; fax: 01787 312950) SourcedOrderSATs-Papers.co.uk from ref: QCA/04/1205 259921 http://www.SATs-Papers.co.uk