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Ma KEY STAGE 3 LOWER TIER & HIGHER TIERS Mark schemes for Mental arithmetic Tests A, B and C 2002 KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk First published in 2002 © Qualifications and Curriculum Authority 2002 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 arithmetic tests. In addition, please apply the following principles unless specific instructions to the contrary are given in the mark scheme: I accept responses in words and/or figures, eg 7 point 3, 4 hundred; I accept any unambiguous indication of the correct response from a given list, eg circling, ticking, underlining; I accept unambiguous misspellings; I 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; I 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 What number do you need to add to eighty-seven to make one hundred? Multiply nine by five. How many sides has a pentagon? What number multiplied by seven equals forty-two? A book gives the height of Mount Everest, in feet, as twenty-nine thousand and twenty-eight. Write this height in figures. What is one third of twelve? Write down the number that is five greater than minus two. 2 3 4 5 6 7 8 How many seconds are there in two minutes? What number is the arrow pointing to on the number line? The time is now one p.m. My train is due at sixteen hundred hours. How many hours is it before my train is due? What is the next number in this halving sequence? Twenty, ten, five, … Look at the straight line. Estimate the length of this line, in centimetres. A teacher asked some pupils if they had a part-time job. The pie chart shows the results. The teacher asked twenty pupils. How many of them said yes? Four packets of biscuits cost one pound. How much would six packets of biscuits cost? 10 11 12 13 14 15 16 ‘Now turn over your answer sheet.’ The tally chart shows the number of questions a teacher asked in a lesson. How many questions did the teacher ask? 9 ‘For the next group of questions, you will have 10 seconds to work out each answer and write it down.’ Look at the numbers on your answer sheet. Add them. 1 ‘Now we are ready to start the test. For this first group of questions, you will have 5 seconds to work out each answer and write it down.’ Lower tier Test C questions Test C 8 7 6 5 4 3 2 1 Time: 5 seconds Practice question Pupil number School Last name First name Mental arithmetic 36 –2 feet 35 17 Total marks Key stage 3 mathematics 2002 Pupil answer sheet 8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9 £ 20 10 hours 5 cm 1pm 1600 pupils seconds Time: 10 seconds 16 15 14 13 12 11 10 9 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 5 Look at the expression in the square. Which answer below is the same as the expression in the square? Ring the correct one. Look at the equation. When x equals five, what is the value of y? The diagram shows a line inside a square. What is the size of the angle labelled t? In my family, the range of heights is thirty-five centimetres. The height of the shortest person is one hundred and twenty-five centimetres. What is the height of the tallest person? Multiply four point seven by one hundred. Look at the triangle. Work out the size of angle What is the next prime number after nineteen? What is twenty per cent of three hundred pounds? 18 19 20 21 22 23 24 25 Which of the nets on your sheet will fold to make a triangular-based pyramid? Put a tick inside the correct net. A jar of coffee costs one pound twenty pence. I buy three jars of coffee. How much change should I get from twenty pounds? What fraction of one kilogram is two hundred and fifty grams? I am thinking of two numbers that add to twelve. One of the numbers is double the other. What are my two numbers? 27 28 29 30 ‘Put your pens down. The test is finished.’ I asked some pupils how many hours they spent on their homework last night. The bar chart shows the results. Altogether, how many pupils did I ask? 26 ‘For the next group of questions, you will have 15 seconds to work out each answer and write it down.’ a Look at the rectangle. What is its perimeter? 17 23 22 21 20 19 18 7 7a cm y = 3x + 6 52 a degrees 4.7 125 cm degrees 52 cm 23 22 21 20 19 18 30 29 28 27 26 £ and Time: 15 seconds 250g £ 1.20 pupils 20% 25 £ 19 24 17 17 Time: 10 seconds continued Time: 10 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2002 Mental arithmetic lower tier Test C Time: 10 seconds 9 10 120 seconds 11 330 12 Test C 22 3 hours Mark scheme Time: 5 seconds 1 Accept equivalent fractions or decimals 1 71 13 22 2 13 14 5 cm ≤ answer ≤ 6 cm 3 45 4 5 5 6 Accept embedded value, eg 7 t 6 6 29 028 feet Do not accept responses given in words 7 4 8 3 15 5 pupils Do not accept incorrect units, eg 5% or 5° 16 £ 1.50 Accept 1 2 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 1 Time: 10 seconds continued 30 cm Time: 10 seconds continued 24 23 25 17 £ 60 Do not accept 60% Time: 15 seconds 18 7 7a 52 52 a 26 19 21 20 60 degrees 21 160 cm 22 470 16 pupils 27 23 28 £ 16.40 29 1 4 30 Accept equivalent values, eg 470.0 4 and 8 75 degrees Accept equivalent fractions or decimal fractions, but not 25% Accept in either order. Do not accept incomplete processing, eg 1 t 4, 2 t 4 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 How many faces has a cube? 2 Look at the numbers on your answer sheet. Add them. What is the sum of the angles in a triangle? Write the ratio twelve to six in its simplest form. Multiply nought point two by nought point three. 4 5 6 7 What number is the arrow pointing to on the number line? There are red, blue and yellow balls in a bag. I am going to take out one ball at random. The table shows the probabilities of getting a red ball and of getting a blue ball. What is the probability of getting a yellow ball? 10 11 Look at the expression. Simplify it. The pictogram shows the number of boys and girls in a year group that had part-time jobs. How many more boys than girls had part-time jobs? 9 A teacher asked pupils in a class ‘Do you eat meat?’ The percentage bar chart shows the results. Estimate the percentage of pupils that said no. 13 14 ‘Now turn over your answer sheet.’ x AB is a straight line. Work out the size of angle 12 Double seventy-eight. 8 ‘For the next group of questions, you will have 10 seconds to work out each answer and write it down.’ When 3 m equals three, what is the value of five m? I start at one point seven and count up in equal steps. One point seven, one point eight, one point nine, … What is the next number? 1 ‘Now we are ready to start the test. For this first group of questions, you will have 5 seconds to work out each answer and write it down.’ Higher tiers Test A questions 7 6 5 4 3 2 1 1.7 degrees 1.8 Time: 5 seconds 1.9 5m 9 80 0.3 12 : 6 –7 70 Total marks 0.2 Test A Practice question Pupil number School Last name First name Mental arithmetic Key stage 3 mathematics 2002 Pupil answer sheet 7 6 5 4 3 2 1 14 13 12 11 10 9 8 78 % degrees 7a + 2b + 3a + 5b Time: 10 seconds 14 13 12 11 10 9 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 9 Which scatter diagram shows strong negative correlation? Ring the correct answer. Forty per cent of a number is twelve. What is the number? Look at the expression. Multiply out the brackets. Look at the numbers. One of them is the decimal equivalent of one eighth. Ring the correct number. Look at the expression. What is the value of this expression when A drink uses apple juice and carrot juice in the ratio two to three. I want to make a litre of this drink. How many millilitres of apple juice should I use? The volume of a cube is sixty-four centimetres cubed. What is the length of an edge of the cube? 16 17 18 19 20 21 22 Look at the diagram. Mark on the diagram another angle that is the same size as angle Label it y A computer game cost forty-two pounds. Its price increased by ten per cent. What is the new price of the computer game? The table shows the number of goals scored in fourteen matches. How many goals were scored altogether? Work out the answer to the calculation on your answer sheet. x squared equals nine. What are the possible values of ten minus x? Look at the right-angled triangle. Work out the height of the triangle. 25 26 27 28 29 30 ‘Put your pens down. The test is finished.’ How many hours are there in one week? 24 y The diagram shows a rectangle. Its perimeter is twelve centimetres. What is the height of the rectangle? 23 ‘For the next group of questions, you will have 15 seconds to work out each answer and write it down.’ k equals three? What is the total cost of three books at nine pounds ninety-nine pence each? 15 0.125 £ 0.8 cm ml 0.18 23 Time: 15 seconds 22 21 20 19 18 17 16 15 1.8 cm 2:3 10 k 2 0.215 a ( a + 2) 40% 12 £ 9.99 Time: 10 seconds continued 23 22 21 20 19 18 17 16 15 30 29 28 27 26 25 24 £ and hours x2 = 9 10 – x 2 4 t 32 £ 42 Time: 15 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2002 Mental arithmetic higher tiers Test A Time: 10 seconds 8 156 9 12 10 –2 Do not accept 2– 11 0.3 Accept equivalent probabilities 12 10 a + 7b Do not accept partially simplified expressions, eg 10a + 2b + 5b 13 105 degrees Test A Mark scheme Time: 5 seconds 1 2(.0) 2 6 3 15 4 2 5 180 degrees 6 7 2:1 Accept 2 to 1 Do not accept 2 fraction notation, eg 1 or incorrect ordering, eg 1 : 2 or ratio not in its simplest form 0.06 14 32 % ≤ answer ≤ 36 % Accept equivalent fractions or decimals 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 10 seconds continued 15 £ 29.97 Time: 15 seconds continued 24 16 168 hours 25 Accept angle not labelled provided there is no ambiguity 26 27 17 18 30 a 2 + 2a £ 46.20 18 28 144 Do not accept 30% Accept a t a for a2 19 20 90 21 400 ml 22 4 cm 29 7 and 13 Accept in either order Time: 15 seconds 30 23 2 cm 12 Do not accept incomplete processing, eg √144 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 Look at the equation on your answer sheet. When x equals seven, what is the value of y? What number is nought point one less than two? How many pairs of parallel sides does a parallelogram have? Look at the fraction. Write it in its simplest form. In a quiz, I got eighteen out of twenty questions correct. What percentage of questions did I get correct? Nine to the power six divided by nine to the power two is equal to nine to the power what? 2 3 4 5 6 7 I start at six and count back in equal steps. Six, one, minus four, … What is the next number in my sequence? Look at the spinner. It has five equal sections. What is the probability that I spin a three? What is half of one hundred and seventy-six? The diagram shows three equal angles. What is the size of one of the angles? 11 12 13 14 ‘Now turn over your answer sheet.’ m equals two, what is the value of h? In a survey, people were asked which they liked best – milk chocolate or dark chocolate. The bar chart shows the results. Sixty people said milk. About how many said dark? 10 Look at the equation. When Look at the number. How much must you add to it to make four thousand? 9 15 Write down a number that is both a multiple of four and a multiple of six. 8 ‘For the next group of questions, you will have 10 seconds to work out each answer and write it down.’ How many seconds are there in one and a half minutes? 1 ‘Now we are ready to start the test. For this first group of questions, you will have 5 seconds to work out each answer and write it down.’ Higher tiers Test B questions 7 6 5 4 3 2 1 % seconds Time: 5 seconds 70 80 Total marks 96 ÷ 92 18 5 20 0.1 y = 10 – x Test B Practice question Pupil number School Last name First name Mental arithmetic Key stage 3 mathematics 2002 Pupil answer sheet 7 6 5 4 3 2 1 15 14 13 12 11 10 9 8 6 1 –4 Time: 10 seconds h = 3m – 10 degrees 176 people 3096 15 14 13 12 11 10 9 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 13 There are one hundred balls in a bag. I am going to take a ball out at random. The probability that it will be red is one fifth. How many red balls are in the bag? The exterior angle of a regular pentagon is seventy-two degrees. What size is the interior angle of the pentagon? I am thinking of a solid shape. It has a circular base and one vertex. What is the mathematical name of this solid shape? What is half of one third? Your answer sheet shows the nth term of a sequence. What is the eighth term of the sequence? Look at the expression. When k equals seven, what is its value? 18 19 20 21 22 The table shows the number of goals per match scored by a team. How many matches did the team play altogether? When I drive on the motorway, my car uses petrol at the rate of eleven miles per litre. How many litres should I expect to use on a motorway journey of one hundred and seventy-six miles? Multiply together the first four odd numbers. The diagram shows a triangle. Which value underneath the triangle shows the length of the hypotenuse? Ring the correct answer. The angles of a triangle are in the ratio one to two to three. What are the sizes of the three angles? I have one hundred pounds in five pence coins. How many five pence coins is that? Some people were asked if they voted in an election. The pie chart shows the results. Work out the angle for the sector that represents ‘No’. 24 25 26 27 28 29 30 ‘Put your pens down. The test is finished.’ The diagram shows a shaded square drawn on a centimetre square grid. What is the area of the shaded square? 23 ‘For the next group of questions, you will have 15 seconds to work out each answer and write it down.’ Multiply three y by five y Write your answer in its simplest form. 17 16 3y 1 5 5y 23 Time: 15 seconds cm2 k3 k 23 22 21 2 1 (n – 3) 2 21 22 20 19 20 19 18 18 17 1 3 17 degrees 30 29 28 27 26 25 ° ° litres 1:2:3 degrees ° 11 miles/litre 176 miles 24 16 16 Time: 15 seconds continued Time: 10 seconds continued 30 29 28 27 26 25 24 Key stage 3 mathematics 2002 Mental arithmetic higher tiers Test B Time: 10 seconds 8 9 Test B Mark scheme 10 12 or any other multiple of 12 904 35 people ≤ answer ≤ 45 people 11 –9 Do not accept 9– 12 2 5 Accept equivalent probabilities 13 88 14 120 degrees 15 –4 Time: 5 seconds 1 90 seconds 2 3 3 1.9 4 2 5 1 4 6 90 % 7 4 or 94 Accept equivalent fractions or decimals Do not accept equivalent fractions or decimals Do not accept 4– 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 10 seconds continued Time: 15 seconds continued 16 108 degrees 17 20 18 15 y2 Accept 15 t y 2 but not 15 t y t 19 Cone Accept ‘circular pyramid’ 20 1 6 21 12 1 24 25 16 litres 26 105 Do not accept 20% y Accept equivalent fractions or 0.17 or 0.167 or 0.166(…) 2 20 27 Accept equivalent decimals or fractions, including 25 2 Do not accept incomplete processing, eg 25 ÷ 2 49 Accept 72 but not incomplete processing, eg 7 t 7 Time: 15 seconds 23 28 30°, 60°, 90° 29 22 2000 30 54 degrees Accept in any order 8 cm2 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) Order ref: QCA/02/831 Sourced from SATs-Papers.co.uk 01-8666 http://www.SATs-Papers.co.uk