ANSWERS & MARK SCHEMES
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1 Key Stage Mathematics TESTS ANSWERS & MARK SCHEMES Page 48 of 34
2 Answers & Mark Schemes About the KS Maths Practice Papers There are three full sets of KS Maths Practice Papers within this book. Each set of KS Maths Practice Papers consists of three separate papers: Paper (Arithmetic), Paper (Reasoning) and Paper 3 (Reasoning). Calculators are strictly not allowed for any of these tests. This pencil sign means that an answer needs to be written either where indicated by the pencil or in the position instructed in the question. Some questions will have an answer box that says Show your working. Children should use this space to write out their working and their final answer in the smaller box within it. This way, even if a child ultimately gets the answer wrong, they could still be awarded marks for approaching it in the right way. Paper (Arithmetic) Paper lasts for 30 minutes and is out of a total of 40 marks. Paper (Reasoning) and Paper 3 (Reasoning) Paper and Paper 3 each last for 40 minutes and have a total of 3 marks each. Marking and Assessing Once your child has completed a test, mark it using the Answers and Mark Schemes within this book, add up the marks and enter them in the table below. After completing a full set of papers, add up the scores for Paper, Paper and the Paper 3 to get a total out of 0. Maths Marks Table Paper (30 mins, out of 40) Paper (40 mins, out of 3) Paper 3 (40 mins, out of 3) Total (out of 0) SET A SET B SET C Page 49 of 34
3 Remember! No Calculators. Mathematics - Paper : Set A Answers Marks., , , Accept an equivalent fraction or decimal such as 4. 9,400.,000, or 0.0. Page 0 of
4 Mathematics Paper : Set A Answers 9. Accept an equivalent fraction or decimal such as 4 0 or , Up to,440 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Do not award a mark if the error is in the place value. Do not award a mark if the final answer is missing Up to 3 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Award mark for a correct short-division method only if there is evidence of carrying figures. Do not award a mark if the final answer is missing. 6. Accept an equivalent fraction or decimal such as 4 0 or ,04 9. Up to,363 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Do not award a mark if the error is in the place value. Do not award a mark if the final answer is missing. Page of 34
5 Remember! No Calculators. Marks or 0.7 Do not award a mark if the decimal is rounded or truncated. There must be evidence that the digits and 7 is a recurring pattern Up to 4 Accept an equivalent fraction or decimal such as 4 or 48 or.046. Do not award a mark if the decimal is rounded or truncated. There must be evidence that the digit 6 is a recurring digit. 3 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Award mark for a correct short-division method only if there is evidence of carrying figures. Do not award a mark if the final answer is missing Accept an equivalent fraction or decimal such as 8 or 6 6 or Page of
6 Mathematics Paper : Set B Answers Mathematics - Paper : Set B Answers , Accept an equivalent fraction or decimal such as ,940. 0, or 0.8. Do not award a mark if the decimal is rounded or truncated. There must be evidence that the digits and 8 are a recurring pattern. Page 3 of 34
7 Remember! No Calculators. Marks Accept an equivalent fraction or decimal such as 9 or or 6.. Do not award a mark if the decimal is rounded or truncated. There must be evidence that the is a recurring digit. 0., Up to 79.9 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Do not award a mark if the error is in the place value. Do not award a mark if the final answer is missing Up to 37 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Award mark for a correct short-division method only if there is evidence of carrying figures. Do not award a mark if the final answer is missing Accept an equivalent fraction or decimal such as 3 or Accept an equivalent fraction or decimal such as 8. or ,06 Page 4 of
8 Mathematics Paper : Set B Answers 9. Up to 36,408 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Do not award a mark if the error is in the place value. Do not award a mark if the final answer is missing Accept an equivalent fraction or decimal such as or Do not award a mark if the decimal is rounded or truncated. There must be evidence that the 6 is a recurring digit. 34. Up to 4 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Award mark for a correct short-division method only if there is evidence of carrying figures. Do not award a mark if the final answer is missing Accept an equivalent fraction or decimal such as or 0.9. Page of 34
9 Remember! No Calculators. Mathematics - Paper : Set C Answers Marks Accept an equivalent fraction or decimal such as ,040., , , , or 0.3. Page 6 of
10 Mathematics Paper : Set C Answers 9. 4 Accept an equivalent fraction or decimal such as 0. 0, or Up to,330 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Do not award a mark if the error is in the place value. Do not award a mark if the final answer is missing ,04 7. Up to Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Award mark for a correct short-division method only if there is evidence of carrying figures. Do not award a mark if the final answer is missing. Accept an equivalent fraction or decimal such as 0 4 or Do not award a mark if the decimal is rounded or truncated. There must be evidence that the 6 is a recurring digit. Page 7 of 34
11 Remember! No Calculators. Marks 9. Up to 39,93 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Do not award a mark if the error is in the place value. Do not award a mark if the final answer is missing Accept an equivalent fraction or decimal such as or Up to or 0 4 Award marks for the correct answer. Incorrect answer? Award mark for a correct method which contains no more than one arithmetic error. Award mark for a correct short-division method only if there is evidence of carrying figures. Do not award a mark if the final answer is missing. 7 0 Accept an equivalent fraction or decimal such as or 4 or.46. Do not award a mark if the decimal is rounded or truncated. There must be evidence that the 6 is a recurring digit Accept an equivalent fraction or decimal such as.8 or 3. Page 8 of
12 Mathematics Paper : Set A Answers Mathematics - Paper : Set A Answers Up to Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a correct method e.g. 8 7 = 6 or = 44. Rome C Do not accept - C. 4. Up to Award marks if all four shapes have been correctly matched. Incorrect answer? Award mark if two shapes have been correctly matched. Do not award a mark for any shape that s been matched to more than one fraction hours 7 minutes 6. minutes to ten. 9: 9: am 9: pm : Accept any other equivalent answer. 7. Up to 8. Up to 8, or or 00 Award marks for three correct answers. Incorrect answer? Award mark if there are two correct answers. 3.6 apples Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method e.g. 4. p = 4.0 or p =. Page 9 of 34
13 Remember! No Calculators. Marks 9. Up to Award marks for the correct answer. Incorrect answer? Award mark if there s one correct digit. 0. Within the range of 7.9cm to 8.3cm. Within the range of 8 to.. The number in the second box should be equal to the number in the first box, plus and then multiplied by. E.g. 3, 0 or 8, A A The four hexagons must be a similar shape to the example below to have a perimeter of 8cm. 4. cm. Up to 0 Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 39 = 78 or = 0. Page 60 of
14 Mathematics Paper : Set A Answers Up to 9 minutes Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. the sum of the minutes is 637 or that the sum of the minutes is divided by Up to,780 Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g =.78 or = Elsie is correct because ¼ (or %) of 00 is greater than ½ (or 0%) of Up to 7 pages Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 7 page total = 00 so page total = 00 4 = of. Up to 87,40 87,400 87,000 90,000 Award marks for stating all the correct answers. Incorrect answer? Award mark if there are two correct answers. Page 6 of 34
15 Remember! No Calculators. Mathematics - Paper : Set B Answers Marks.. Up to 3. Up to (accept 90p) Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a correct method e.g. 0 0p = 9.90, 9.90 = 90p. 700cm Award 3 marks for the correct answer. Incorrect answer? Award marks for the correct calculation 4 36 =,84cm or if there s evidence of a suitable method with one arithmetic error. Award mark if there s evidence of a correct method that has more than one arithmetic error. Do not award any marks if the error is in the place value of the multiplication. 4. Up to Type of book Tally Total Science Fiction & Fantasy 9 Detective Stories 6 Comedy/Humour 0 Animal Tales 9 Adventure Non-Fiction 4 Award marks for a correctly filled in table. Incorrect answer? Award mark if three cells are correctly filled in.. Page 6 of
16 Mathematics Paper : Set B Answers Up to 6 (accept 6.0) CXXX A, B and D. Award marks for the correct answer. Incorrect answer? Award mark if there are two correct letters Up to ,0 36,00 37,000 40,000 Award marks for stating all the correct answers. Incorrect answer? Award mark if there are two correct answers. 4 Trapezium Kite people Wales.4m 3.4m Up to 70 Award marks for the correct answer. Incorrect answer? Award mark if there is evidence of a suitable method. E.g. 00 = 48, 48 = 70. Page 63 of 34
17 Remember! No Calculators. Marks 8. 8 (accept answers between 7 and 7 (accept answers between 73 and 77) 9 ) 9. Up to 40 pupils Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 9 of pupil total = 0, page total = 0 9 = Aisha is not correct because 3 (or another suitable value such as 3 or 43) is not a multiple of 3. Do not award the mark if a suitable example such as 3, 3 or 43 is missing. Page 64 of
18 Mathematics Paper : Set C Answers Mathematics - Paper : Set C Answers.. 70 minutes 0 p.m. 8 sides Pentagon Octagon 3. hour 3 minutes 9 seconds m 93.7m C 9 C Accept answers between 9:30am and 9:4am 6. Up to Award marks if all four shapes have been correctly matched. Incorrect answer? Award mark if two shapes have been correctly matched. Do not award a mark for any shape that s been matched to more than one fraction Up to Award marks for the correct answer. Incorrect answer? Award mark if there s one correct digit. 8. Page 6 of 34
19 Remember! No Calculators. Marks 9. Up to 3.04 Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g..99 = 3.98, =., =.0,.0 = cars. 6 9, 3. Up to girls Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 3/8 /3 number of girls in class = 9, 3/8 /3 = ¼, number of girls in class = 9 ¼ = ml 900ml 600ml 300ml 4. c = 4b -., balloons 3km Page 66 of
20 Mathematics Paper : Set C Answers 8. Up to 3., 7 Award marks for the correct answer. Incorrect answer? Award mark if there s one correct number. 9. +, 3, -4, 4 0. Up to Incorrect answer? Award mark if there s one correctly drawn shape element. Page 67 of 34
21 Remember! No Calculators. Mathematics - Paper 3 : Set A Answers Marks. Up to Multiple of 4 Not a multiple of 4 Multiple of 6 4 6, 8, Not a multiple of 6 4, 8, 6...,, 3,... Award marks if the sorting table has been completed correctly. Incorrect answer? Award mark if two cells have been correctly completed.. Up to 3 or an equivalent fraction such as 3 4 or an equivalent fraction such as Award marks for two correct answers. Incorrect answer? Award mark if there s one correct answer. 3..4, 3 4. October 600. Up to The total will be more than. The total will be an even number. The number on B will be greater than the score on A. Certain Possible Impossible Award marks for completing the table correctly. Incorrect answer? Award mark if there are two correctly ticked statements. The total will be less than Up to 00, 000 Award marks for two correct answers. Incorrect answer? Award mark if there is one correct answer. 7. Thirty thousand, five hundred and eight. 8. A B 9. Up to 8.g Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g = 40., 40. = 8.. Page 68 of
22 Mathematics Paper 3 : Set A Answers 0. Up to 0.7 (accept 7p) Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g = p, 8 6 = 38p, 38p p = 7p.. Up to Award marks for the correct answer. Incorrect answer? Award mark if there are two correct values Up to 4 9 < 3 < < 3 < < 3 4 < 6 3 < 3 4 < 6 Award marks for any two of the above expressions. Incorrect answer? Award mark if there is one complete expression. 4. Up to Award marks for the correct answer. Incorrect answer? Award mark if there are two correct values. Accept any of the above. 6. Up to. Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. (number 3) + = 6., 6. = 4., 4. =.,. + 3 =.. Page 69 of 34
23 Remember! No Calculators. Marks 7. 40% 8. 60p, 6p, 7p 9. 4, Swimming Netball, basketball A = (6, -7) B = (0, -7) Page 70 of
24 Mathematics Paper 3 : Set B Answers Mathematics - Paper 3 : Set B Answers. Up to Factors of Factors of Award marks if the Venn diagram has been completed correctly. Incorrect answer? Award mark if three numbers have been correctly placed.. -7, - Do not accept 7-, 7, - or. 3. Up to 4. Up to 0.9 Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g = = , 46 Award marks for the correct answer. Incorrect answer? Award mark if there s one correct answer.. Fifty-nine thousand and two kg 7cm 8. A B Page 7 of 34
25 Remember! No Calculators. Marks 9. Up to 7g Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 60g 00g = 40g, 40 6 = 7g. 0. There are 90 sweets in a bag. friends share them equally. Each friend gets 7 sweets. There are 6 sweets left over. Or There are 90 sweets in a bag. 7 friends share them equally. Each friend gets sweets. There are 6 sweets left over.. Up to Award marks for the correct answer. Incorrect answer? Award mark there are two correct values Up to 8 eggs Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 3 (number of eggs) + 6 = 30, 3 (number of eggs) = 4, number of eggs = 4/3 = Up to Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. ((number + 0) ) 0 = 8, (number + 0) ) = 48, number = 96 0 = Page 7 of
26 Mathematics Paper 3 : Set B Answers 8. Up to 9. Up to 3 0. ml Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 300ml = ml.,606.cm Award 3 marks for the correct answer. Incorrect answer? Award marks if there s evidence of the total area being 3 7. =,64.cm. Award mark for a suitable method that includes no more than one arithmetic error. Do not award any marks if the error is in the place value of the multiplication. B = (, 7) C = (0, -6) Centre = (7., 0.) Page 73 of 34
27 Remember! No Calculators. Mathematics - Paper 3 : Set C Answers Marks Up to. Up to 0g 4% ,048, Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g =.00,.00 8 = (accept 40p) 7km Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g. 4 unit distance = 36, unit distance = 9km, distance = 3 unit distance = 7km. 6. C g, 0.3kg, 3 kg, 40g, 00g 8. Page 74 of
28 Mathematics Paper 3 : Set C Answers 9. A B cm.4cm. Up to Award marks for the correct answer. Incorrect answer? Award mark if there are two correct values Up to % Award marks if all the fractions, decimals and percentages have been correctly linked % Incorrect answer? Award mark if there are three correct links % % Award mark for either of the two example right angled triangles shown or any other right angled triangle. Page 7 of 34
29 Remember! No Calculators. 7. Up to Marks Award mark for each correctly drawn shape. Do not award a mark if the shape(s) are not labelled. trapezium parallelogram 8. Up to Month Sunny Days Wet Days May 6 June 4 8 July 8 6 August 6 8 September 4 0 October 0 8 Award marks for a correctly completed table and chart. Incorrect answer? Award mark if either the table or the chart is correctly completed. Days May June July August Sept Oct Month Sunny Days Key Wet Days 9. Up to.96m Award marks for the correct answer. Incorrect answer? Award mark if there s evidence of a suitable method. E.g..m - 9cm = 8cm,.m + 9cm + 8cm =.4m, 40cm + ( 8.cm = 96.cm =.96m. 0. Up to Number of flat surfaces Number of curved surfaces Sphere 0 Cone Cylinder Cube 6 0 Award marks for a correctly completed table. Incorrect answer? Award mark for three correct answers. Page 76 of
30 Mathematics Paper 3 : Set C Answers BLANK PAGE Page 77 of 34
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