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Ma Mathematics tests KEY STAGE 3 LOWER TIER & HIGHER TIERS 2005 2005 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 2005 © Qualifications and Curriculum Authority 2005 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 What do you need to add to eighty-three to make one hundred? Look at the equation on your answer sheet. When a equals seven, what is the value of b? What number multiplied by eight equals forty-eight? Look at the number on your answer sheet. Divide it by one hundred. What is the sum of the angles in a triangle? Write the fraction on your answer sheet in its simplest form. Look at the expression on your answer sheet. Write it as simply as possible. 2 3 4 5 6 7 8 Look at the numbers on your answer sheet. Add them. A train leaves at ten thirty am and travels for four hours. At what time does the train stop? Write your answer using am or pm. I am counting back in steps of ten. One hundred and twenty-five, one hundred and fifteen, one hundred and five, … Write down the next number. What is half of seven? Look at the temperatures on your answer sheet. Put a ring round the temperature that is the lowest. Six hundred people went on holiday. The pie chart shows how they travelled. How many people travelled by car? 10 11 12 13 14 15 ‘Now turn over your answer sheet.’ I buy a notebook for fifty pence. How much change should I get from a two pound coin? 9 ‘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 five hundred and eight. 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 5 4 3 2 1 Time: 5 seconds Practice question School Last name First name 90 Total marks 9300 b = 14 + a Mental mathematics Test C Key stage 3 mathematics 2005 Pupil answer sheet 5 4 3 2 1 ° 15 14 13 12 11 10 9 –1°C 125, £ 5°C 3 9 28 Car people 0°C –3°C 10:30am 25 50p 3m + m 105, Plane Train 2°C 115, Time: 10 seconds 8 7 6 Time: 5 seconds continued 15 14 13 12 11 10 9 8 7 6 5 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Two rulers cost eighty pence. How much do three rulers cost? How many seconds are there in one and a half minutes? There were two thousand people at a concert. Nine hundred and ninety-two of them were women. How many of the people were not women? Look at the numbers on your answer sheet. Work out their range. The temperature was minus two degrees Celsius. At night the temperature fell by seven degrees. What was the temperature at night? Look at the shaded triangle drawn on a centimetre square grid. What is the area of this triangle? What is twenty per cent of sixty pounds? Look at the triangle on the grid. Write the coordinates of the point marked A. 17 18 19 20 21 22 23 24 I face west, then I turn through two right angles. What direction am I facing now? Look at the shape made from small equilateral triangles. Shade two more triangles so that the shape has three lines of symmetry. I am thinking of two numbers that add to ten. The two numbers multiply together to make twenty-one. What are my two numbers? Which one of the shapes on your answer sheet is the net of a cube? Put a tick inside the correct shape. I have twenty-five cards. Sixteen of them show even numbers and the rest show odd numbers. I am going to take a card at random. What is the probability that the card will show an odd number? 26 27 28 29 30 ‘Put your pens down. The test is finished.’ People at a shopping centre voted for their favourite fruit drink. The bar chart shows the results. Altogether, how many people voted? 25 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ Write down an even number that is a multiple of seven. 16 24 23 22 21 20 19 18 17 £ £ –4 –2 0 2 4 ( 0 B 992 , 2 °C A C £60 ) 4 2 cm –2°C 3, 8, 3, 1, 4 2000 seconds 80p 24 23 22 21 20 19 18 17 30 29 28 27 26 W people 25 cards 16 even numbers and 25 16 16 Time: 15 seconds Time: 10 seconds continued 30 29 28 27 26 25 Key stage 3 mathematics 2005 Mental mathematics lower tier Test C Time: 5 seconds continued 6 7 Test C Mark scheme 180 ° 1 3 8 4m Do not accept equivalent fractions or decimals Time: 10 seconds 9 £ 1.50 10 53 11 2 : 30 pm 12 95 13 3 1 2 Accept 14:30(pm) Do not accept 2:30 without pm Accept equivalent fractions or decimals Time: 5 seconds 1 508 Do not accept responses given in words 2 17 Accept embedded value, eg 83 + 17 3 21 4 6 5 93 14 15 150 people Accept embedded value, eg 6 t 8 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 10 seconds continued 16 Any number that is a multiple of 14, eg 14 or 700 Time: 15 seconds 25 27 people 26 East Accept any unambiguous indication of East, eg E 3 and 7 Accept pair in either order 9 25 Accept equivalent probabilities Accept zero, and negative multiples of 14 17 £ 1.20 18 90 seconds 19 1008 20 7 21 – 9 °C Do not accept 8–1 27 22 5 cm2 23 £ 12 28 24 ( 3 , –2 ) 29 30 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 Look at your answer sheet. Write the coordinates of the point marked A. The population of France is approximately sixty-one million. Write this number in figures. How many millimetres are there in one metre? Write a different fraction that is equivalent to three-fifths. What is six point two multiplied by one thousand? Look at the diagram. The lines marked with arrows are parallel. What is the size of angle p? Round three point seven nine five to one decimal place. 2 3 4 5 6 7 8 Write down a number that is a multiple of three and is also a multiple of five. Two of the angles in a triangle are sixty degrees and seventy degrees. What is the size of the third angle? I start at seven and count down in equal steps; seven, four, one. Write down the next two numbers. Look at the expression on your answer sheet. Write it as simply as possible. What is eighteen multiplied by nine? The perimeter of a rectangle is twenty centimetres. Its length is seven centimetres. What is the width of the rectangle? Five per cent of a number is sixteen. What is twenty-five per cent of the number? Look at the equation on your answer sheet. What is the value of a? 10 11 12 13 14 15 16 17 ‘Now turn over your answer sheet.’ The scale on a map is one centimetre to five metres. On the map the length of a street is eight centimetres. What is the real length of the street in metres? 9 ‘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 fifty-four? 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 5 4 3 2 1 0 2 4 0 ( C , mm 2 Time: 5 seconds Practice question School Last name First name A B 4 3 5 1m ) 54 12 Total marks 38 Mental mathematics Test A Key stage 3 mathematics 2005 Pupil answer sheet 5 4 3 2 1 p 17 16 15 14 13 12 11 10 9 cm ° , 60° 3 9 16 32 – 2a = 24 5% 20 cm 7cm 18 70° 5 1cm : 5m 3.795 100˚ 6.2 6 g + 4h + 3g – 2 h 7, 4, 1, ° m Time: 10 seconds 8 7 6 Time: 5 seconds continued 17 16 15 14 13 12 11 10 9 8 7 6 9 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk I drive ten kilometres in twelve minutes. What is my average speed in kilometres per hour? Look at the expression on your answer sheet. Multiply out the brackets. 19 20 The pie chart shows the colour of cars in a car park. There were twelve blue cars. Approximately, how many cars were there altogether? When a equals minus three and what is the value of a minus b? The mean of three numbers is six. Two of the numbers are five. What is the third number? A circle has a radius of six centimetres. Give an approximate value for the circumference of the circle. What is two-thirds of three-quarters of eighty? Look at the frequency table showing the number of people travelling in cars. Altogether, how many people were travelling? A rectangle has an area of eight square centimetres. What is the area of a rectangle with sides that are all twice as long? Look at the graphs. Put a ring round the graph that has the equation Look at the numbers on your answer sheet. Write down the number that is halfway between them. 22 23 24 25 26 27 28 29 30 ‘Put your pens down. The test is finished.’ y equals x plus one. b equals minus seven, The pictogram shows the number of girls and boys in a youth club. How many more girls than boys are in the youth club? 21 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ Estimate the value of nine point two multiplied by two point nine. 18 10km 2a ( a + 4) Blue = 4 people Other Boys Girls Black a = –3 b = –7 a–b Red 5 24 5 2.9 km/h 23 22 21 9.2 12 minutes Time: 15 seconds 20 19 18 Time: 10 seconds continued 24 23 22 21 20 19 18 30 29 28 27 26 25 3 4 cm 80 y y x x cm2 Frequency 2 5 y y 8cm2 1 x x people 5 4 0 1 No. of people 1 2 3 4 2 3 6cm Time: 15 seconds continued 30 29 28 27 26 25 Key stage 3 mathematics 2005 Mental mathematics higher tiers Test A Time: 5 seconds continued 6 6200 7 80 ° 8 3.8 Test A Mark scheme Do not accept equivalent fractions or decimals Time: 10 seconds 9 10 40 m Any number that is a multiple of 15, eg 15, 30, 300 Time: 5 seconds Accept zero, and negative multiples of 15 1 9 Accept embedded values, eg 9 t 6 11 12 5 162 15 4 9g + 2h 14 3 –2 and –5 13 2 50 ° 3 cm 16 80 Do not accept incorrect % signs 17 4 Accept embedded values, eg 32 – 2 t 4 ( 3 , 1 ) 61 000 000 Do not accept responses given in words 1000 mm Accept pair in either order Do not accept amended units 3 Any fraction equivalent to 5 (except 3 ), eg 6 , 30 5 10 50 Do not accept equivalent decimals 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 10 seconds continued Time: 15 seconds continued 19 2a2 + 8a 28 answer 40 27 38 cm 17 people 32 cm 2 50 km/h 20 answer 36 cm 28 26 25 26 18 Do not accept equivalent expressions containing brackets, eg 2( a2 + 4a ) Time: 15 seconds 21 6 29 22 32 23 answer 40 4 30 24 8 7 10 Accept equivalent fractions or decimals Do not accept incorrect notation, eg 3.5 5 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 numbers on your answer sheet. Write down the number that is the mode. How many centimetres are there in three-quarters of a metre? Look at the expression on your answer sheet. Write it as simply as possible. What number is eight less than minus four? Write one and a half million in figures. Round two point six nine four to one decimal place. The length of a piece of string is fourteen centimetres to the nearest centimetre. What is the minimum length this piece of string could be? 2 3 4 5 6 7 8 Practice question School Last name First name Put a cross on the grid to show the point with coordinates minus two, one. 14 ‘Now turn over your answer sheet.’ The probability I will be late for school is one-twentieth. What is the probability that I will not be late for school? 13 3 4 8 7 5a + 3a cm 5 5 42 –4 4 3 5 Drinks cost twenty-eight pence each. What is the greatest number of these drinks I can buy with one pound? 6 12 6 A train journey began at ten thirty-five am and ended at eleven fifteen am. How long was the train journey in minutes? 11 2 1 Write down a factor of thirty-six that is greater than ten and less than twenty. y equals two x plus three? 10 What is the gradient of the line with equation ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ 9 12 Total marks 38 Mental mathematics Test B Key stage 3 mathematics 2005 Pupil answer sheet Time: 5 seconds What is forty-two multiplied by 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 5 5 4 3 2 1 cm 14 13 12 11 10 –3 –2 –1 –3 –2 –1 0 1 2 3 10:35am 0 Time: 10 seconds 9 8 7 6 1 28p 1 20 2 minutes 11:15am 36 3 £1 y = 2x + 3 14 cm 2.694 Time: 5 seconds continued 14 13 12 11 10 9 8 7 6 13 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk How many thirds are there in two? 16 Solve the equation, t plus three-fifths equals one. Last month my telephone bill was thirty pounds. This month it is twenty per cent more. How much is this month’s bill? Look at the expression on your answer sheet. Its value is eighty-two. Write an expression using a and b with a value of forty-one. What is three-quarters of a half? Your answer sheet shows the nth term of a sequence. What is the sixth term in this sequence? Work out the value of two to the power six divided by two squared. 18 19 20 21 22 23 Look at the calculation on your answer sheet. Write an approximate answer. Ten out of thirty-six people said they ate toast for breakfast. What angle should represent this on a pie chart? Look at the circle with radius three. One of the values below is its area. Put a ring round the correct value. Look at the numbers on your answer sheet. Put them in order of size starting with the smallest. Write two numbers with a mean of six and a range of four. A cube has a volume of eight cubic centimetres. What is the volume of a cube with edges that are all twice as long? 25 26 27 28 29 30 ‘Put your pens down. The test is finished.’ Look at the two points on the square grid. Put one more cross on the grid so that the three points join to form an isosceles triangle. 24 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ Look at the trapezium. Angle What is the size of angle b? 17 a is one hundred and ten degrees. Look at the diagram on your answer sheet. What is the area of the rectangle? 15 23 22 21 20 19 18 17 16 15 £ 4cm 3 =1 5 ° 2 1 2 6 2 22 1 n ( n + 1) 2 3 4 82 £30 20% t+ 1 3 cm2 6a + 4b 6cm Time: 10 seconds continued 23 22 21 20 19 18 17 16 15 30 29 28 27 26 25 24 3π , and 0.4 12 π cm3 1 5 6π ° Time: 15 seconds , 8 cm3 6 4 9π 25% 15 π 3 10 36 52 1.4 + 3.6 30 29 28 27 26 25 24 Key stage 3 mathematics 2005 Mental mathematics higher tiers Test B Time: 5 seconds continued 6 Mark scheme Do not accept responses given in words 7 Test B 1 500 000 2.7 Do not accept equivalent fractions or decimals 8 13.5 cm Accept equivalent fractions or decimals 9 2 Accept 2 1 Time: 10 seconds 10 12 or 18 11 40 minutes 12 3 Accept reference to the remainder, even if incorrect, eg 3 rem 16 Time: 5 seconds 13 1 3 420 2 2 1 5 –3 –2 –1 0 0 1 2 3 –1 –2 3 4 5 75 cm –3 Do not accept amended units Accept inaccurate indication, provided the pupil’s intention is clear 8a –12 14 19 20 Accept equivalent probabilities 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 15 seconds Time: 10 seconds continued 15 24 cm2 16 6 24 Accept embedded values, eg 17 Indicates a point on the line, excluding the circle, or one of the points marked 6 3 70 ° Accept inaccurate indication, provided the pupil’s intention is clear 18 2 5 Accept equivalent fractions or decimals 25 10 answer Do not accept incomplete processing, Accept embedded values, 2 3 eg + 5 5 19 20 £ 36 eg 26 3a + 2b or equivalent or 6a + 4b – 41 10.5 52 5 100 ° 27 Accept correct expressions equated to 41 21 3 8 Accept equivalent fractions, decimals or percentages 22 21 Do not accept incomplete processing, eg 3(6 + 1) 23 16 Do not accept incomplete processing, eg 24 28 1 , 25%, 0.4 5 Accept any unambiguous indication of the correct order, eg 0.2, 0.25, 0.4 29 4 and 8 Accept pair in either order 30 64 cm3 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 Orderline, PO Box 29, Norwich NR3 1GN tel: 08700 606015; fax: 08700 606017 email: orderline@qca.org.uk SourcedOrder ref: QCA/05/1427 from SATs-Papers.co.uk 266104 http://www.SATs-Papers.co.uk