GCSE (9-1) Mathematics Component 3 Grades 1-4 Practice Materials (Set 1)

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GCSE (9-1) Mathematics Component 3 Grades 1-4 Practice Materials (Set 1) Qualification Accredited GCSE (9-1) MATHEMATICS Practice Materials Grades 1-4 Practice Materials Set 1, Component 3 ... Version 1 J560 For first teaching in 2015 www.ocr.org.uk/mathsGCSE (9-1) Mathematics Grades 1-4 Practice Materials © OCR 2020 Introduction These practice materials can be used to support foundation students who are targeting grades 1-4. They are comprised of questions taken from previous series. Mark schemes are included and can be found towards the back of each set of materials. Please remember to omit the mark schemes when distributing the question pages to your students. To see additional GCSE (9-1) Mathematics resources, please visit: https://www.ocr.org.uk/qualifications/gcse/ mathematics-j560-from-2015/planning-and-teaching/ Would you prefer a Word version? Did you know that you can save this pdf as a Word file using Acrobat Professional? Simply click on File > Export to and select Microsoft Word (If you have opened this PDF in your browser you will need to save it first. Simply right click anywhere on the page and select Save as . . . to save the PDF. Then open the PDF in Acrobat Professional.) If you do not have access to Acrobat Professional there are a number of free applications available that will also convert PDF to Word (search for pdf to word converter).Grades 1-4 Practice Materials 1 GCSE (9-1) Mathematics © OCR 2020 GCSE (9-1) Mathematics Component 3 Grades 1-4 Practice Materials (Set 1) Time allowed: 45 minutes Name 50.Grades 1-4 Practice Materials 2 GCSE (9-1) Mathematics © OCR 2020 1 2 320 people go on a coach trip. Each coach holds 53 people. Gary says 6 coaches are needed. Is Gary correct? You must show your working. = = = = = = = =Grades 1-4 Practice Materials 3 GCSE (9-1) Mathematics © OCR 2020 3 4 (a) Which arrow shows the probability of scoring a 2? (b) Which arrow shows the probability of scoring a number less than 6?Grades 1-4 Practice Materials 4 GCSE (9-1) Mathematics © OCR 2020 5 6Grades 1-4 Practice Materials 5 GCSE (9-1) Mathematics © OCR 2020 7Grades 1-4 Practice Materials 6 GCSE (9-1) Mathematics © OCR 2020 8 9Grades 1-4 Practice Materials 7 GCSE (9-1) Mathematics © OCR 2020 10Grades 1-4 Practice Materials 8 GCSE (9-1) Mathematics © OCR 2020 11Grades 1-4 Practice Materials 9 GCSE (9-1) Mathematics © OCR 2020 12Grades 1-4 Practice Materials 10 GCSE (9-1) Mathematics © OCR 2020 13Grades 1-4 Practice Materials 11 GCSE (9-1) Mathematics © OCR 2020 14 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -2 -1 1 2 3 4 x y [2]GCSE (9-1) Mathematics Grades 1-4 Practice Materials 12 © OCR 2020 Component 3 – Mark scheme Types of marks: • M marks are for using a correct method and are not lost for purely numerical errors. • A marks are for an accurate answer and depend on preceding M (method) marks. Therefore M0 A1 cannot be awarded. • B marks are independent of M (method) marks and are for a correct final answer, a partially correct answer, or a correct intermediate stage. • SC marks are for special cases that are worthy of some credit. The following abbreviations are commonly found in GCSE Mathematics mark schemes. • cao means correct answer only. • figs 237, for example, means any answer with only these digits. You should ignore leading or trailing zeros and any decimal point e.g. 237000, 2.37, 2.370, 0.00237 would be acceptable but 23070 or 2374 would not. • isw means ignore subsequent working (after correct answer obtained). • nfww means not from wrong working. • oe means or equivalent. • rot means rounded or truncated. • seen means that you should award the mark if that number/expression is seen anywhere in the answer space, including the answer line, even if it is not in the method leading to the final answer. • soi means seen or implied.GCSE (9-1) Mathematics Grades 1-4 Practice Materials 13 © OCR 2020 Question Answer Marks Part marks and guidance 1 (a) 27 [0].8[0] 80 [0].03 3 B1 for each row (b) final answer 2 B1 for or equivalent fraction (c) or equivalent fraction 1 Ignore attempts to simplify if, for example, given Must be a vulgar fraction not 0.2 or 20% 2 Identifying there are not enough coaches or too many people with correct justification 2 M1 for 320 ÷ 53 soi by 6.03[..] or 53 × 6 soi by 318 or 2 or 320 ÷ 6 soi by 53.3 No, he needs 7 coaches alone scores 0 See below 3 (a) B 1 (b) E 1 4 8 2 M1 for 2 × 16 [÷ 4] or 16 ÷ 2 (speed) 32 alone scores 0 5 –20 2 5 3 B1 for each If 0 scored SC1 for –4 × their 5 correct Middle right box 6 62 cao 2 B1 for 48 or 14 Or M1 for 3 × 16 + 2 × 7 7 (a) 48 2 M1 for 6 × 2 × 4 May be in stages (b) 8 3 M2 for √ 320 5 Or M1 for 320 soi 64 or 5k2 = 320 8 576 2 M1 for [$1=] 40 ÷ 50 or [0].8 or 720 ÷ 50 soi 14.4[0] or 50 ÷ 40 or 1.25 oe Or M1 for full scaling method with correct processes (may be implied by correct values) at each stage e.g. [$]50 is [£][40] (process) 100 is [80] (× 2) 200 is [160] (× 2) 20 is [16] (÷ 10) And sum 200, 200, 200, 100 and 20 27 100 3 100 9 20 15 45 100 10 50 5GCSE (9-1) Mathematics Grades 1-4 Practice Materials 14 © OCR 2020 Question Answer Marks Part marks and guidance 9 9.64 4 B2 for 231.36 OR M1 for 11 × 15.65 soi 172.15 M1 for 403.51 – their 172.15 AND M1 for their 231.36 ÷ 24 Condone £9.64p for 4 marks 10 (a) 240 1 (b) 10 1 (c) No, with correct supporting values and justification 4 B3 for 1.374 to 1.38[kg] or 1374 to 1380[g] or 74 to 80[g] or 0.074 to 0.08[kg] or 14[..people] OR B1 for 1.3 × 1000 soi by 1300 or their 1375 ÷ 1000 and M1 for 15 ÷ 6 soi by 2.5 or 550 ÷ 6 soi by 91.6[6] or 91.7 and M1 for 550 × 2.5 =1375 or 1300 ÷ their 91.6[6] or their 91.6[6] × 15 Accept equivalent method 11 19 5 B4 for 12 nfww OR M1 for x + 7 or x – 7 M1 for x + 7 + x + 7 + x + x + x + x = 86 M1 for 6x + 14 = 86 FT B1 for 12 FT OR M1 for 86 – 7 – 7 A1 for 72 M1 for their 72 ÷ 6 A1 for 12 OR M1 for a = c + 7 oe M1 for 2a + 4c = 86 oe M1 for correct method to eliminate one variable allow one arithmetic error A1 for 12 Allow use of other letters Accept equivalent methods e.g. M1 for y + 7 or y – 7 M1 for y + y + y – 7 + y – 7 + y – 7 + y – 7 = 86 M1 for 6y – 28 = [86] M1 for 6y = 114GCSE (9-1) Mathematics Grades 1-4 Practice Materials 15 © OCR 2020 Question Answer Marks Part marks and guidance 12 68.8 3 M2 for 2 × (12 + 15 + 7.4) OR M1 for 15 – 5.8 – 6.3 soi 2.9 M1 for 12 + 15 + 12 + 6.3 + 7.4 + their 2.9 + 7.4 + 5.8 oe Accept any other complete and correct methods May be 15 – 12.1 If not 2.9 then their 2.9 must be seen on diagram in correct place or come from 15 ≤ 5.8 < 6.3 13 (a) 0.7 0.8 , 0.2, 0.8, 0.2 11 (b) 0.76 with a complete correct method 2 M1 for one correct product from their probabilities e.g.1 – 0.24 = 0.76 or 0.06 + 0.56 + 0.14 = 0.76 Marks may be awarded for work on the diagram 14 (a) -1 [-4 ] [-5] [-4] -1 4 [11] 2 B1 for 1 correct (b) Correct curve 2 B1 for 4 or more points correctly plotted FT their table Tolerance half small square Exemplar responses for Q2 Response Mark No – 6 coaches only hold 318 people which is 2 short 2 Gary needs an extra coach for the other 2 people 2 320 ÷ 6 = 53.3333.. no you can’t split a person up into 3 parts, you will need 7 coaches 2 320/53 = 6.03 No because it’s a decimal you need to round up not down 2 53 × 6 = 318 Gary is not correct as 6 coaches will mean 2 people will not be allowed on the coaches 2 Gary is incorrect 6 coaches only hold 318 people so he needs 7 2 6 coaches hold 318 so there will be 2 people left 2 BOD 320/53 = 6.03…. No he is wrong he will need more 2 Gary is correct 320/53 = 6.0 1 320/6 = 53.3 Not enough room one person will be left behind (in fact two people are left behind!) 1OCR Resources: the small print OCR’s resources are provided to support the delivery of OCR qualifications, but in no way constitute an endorsed teaching method that is required by OCR. Whilst every effort is made to ensure the accuracy of the content, OCR cannot be held responsible for any errors or omissions within these resources. We update our resources on a regular basis, so please check the OCR website to ensure you have the most up to date version. This resource may be freely copied and distributed, as long as the OCR logo and this small print remain intact and OCR is acknowledged as the originator of this work. Our documents are updated over time. 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