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GCSE (9-1) Mathematics Component 2 Grades 1-4 Practice Materials (Set 1)

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GCSE (9-1) Mathematics Component 2 Grades 1-4 Practice Materials (Set 1) Qualification Accredited GCSE (9-1) MATHEMATICS Practice Materials Grades 1-4 Practice Materials Set 1, Component 2 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 2 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 2Grades 1-4 Practice Materials 3 GCSE (9-1) Mathematics © OCR 2020 3Grades 1-4 Practice Materials 4 GCSE (9-1) Mathematics © OCR 2020 4 (b) (ii) 7 (b)(i) 19 [1] [1] (c) (c)Grades 1-4 Practice Materials 5 GCSE (9-1) Mathematics © OCR 2020 5 (b) (b) (a) (a) 6Grades 1-4 Practice Materials 6 GCSE (9-1) Mathematics © OCR 2020 7 8 (b) 9 (b) (b) (a)Grades 1-4 Practice Materials 7 GCSE (9-1) Mathematics © OCR 2020 10 (a) (a) (b) (b) (c) (c) ? (c)Grades 1-4 Practice Materials 8 GCSE (9-1) Mathematics © OCR 2020 11 12Grades 1-4 Practice Materials 9 GCSE (9-1) Mathematics © OCR 2020 13 14 (a) (c) (b)Grades 1-4 Practice Materials 10 GCSE (9-1) Mathematics © OCR 2020 15GCSE (9-1) Mathematics Grades 1-4 Practice Materials 11 © OCR 2020 Component 2 – 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 12 © OCR 2020 Question Answer Marks Part marks and guidance 1 (a) 1 1 Condone 3 (b) 4 1 (c) Isosceles 1 Ignore spelling providing intention is clear 2 100 gram packet with a correct comparison isw 3 M1 for correctly finding the cost of 1 gram, 25 grams, 100 grams or other amount suitable for comparison M1 for attempting to find the cost of the same amount of tea for each packet weight (e.g. 25 grams or 100 grams) evaluation does not need to be correct e.g. 100g of 25g pkt costs [£]4.2[0] e.g. 25g of 100g pkt costs [£]1.04 other comparisons must be correct to 3sf or better Or for attempt to fnd two values of grams per pound or grams per pence 3 0 and 5 3 B1 for one correct M1 for putting times in order isw Given values or their 9 or their 10 values e.g. 0, 0, 2, 2, 6, 7, 7, 9 4 (a) (i) 13 1 Ignore subsequent terms (ii) 128 1 Ignore subsequent terms (b) (i) 15 11 1 (ii) 38 193 1 (c) 18 – 3n oe 2 M1 for –3n + k oe or for mn + 18 oe (m ≠ 0) For 2 or M1, condone e.g. n = 18 – 3n For 2 or M1, condone use of other variable instead of n 5 (a) 4p 1 (b) 5j – 2k 2 B1 for 5j or – 2k in final answer 6 (a) Tangent 1 Ignore spelling providing intention is clear (b) Segment 1 Ignore spelling providing intention is clear 7 12 3 M2 for 420 ÷ 7 ÷ 5 or 420 ÷ 35 Or M1 for 420 ÷ 7 soi or 420 ÷ 5 soi Condone 12.0, 12.00 8 (a) 3x2 + 6xy final answer 2 B1 for 3x2 or 6xy seen Condone 6yx Do not accept e.g. 6 × x × y (b) 4 1 9 (a) 7 ¼ oe 1 Accept e.g. isw Do not accept e.g. 6 (b) 36 2 M1 for 63 ÷ 7 soi Implied by [ of 63] = 9 not enough for M1 without 9 or division sign or bus stop e.g. 7)63 17 58 8 54 63 7GCSE (9-1) Mathematics Grades 1-4 Practice Materials 13 © OCR 2020 Question Answer Marks Part marks and guidance 10 (a) 6 1 (b) oe 1 Condone correct probability and unlikely for 1 mark Accept [0].3818 to [0].382 or 38.18% to 38.2% but not ratio or in words (c) oe 1 Condone correct probability and likely for 1 mark Accept [0].509 to [0].51 or 50.9% to 51% but not ratio or in words 11 2 × 5 × 72 oe 2 B1 for only 2, 5 and 7 identified Or M1 for any correct factor pair of 490 Condone inclusion of 1 for B1 Not 1 and 490 12 Correct enlargement (6, 3) (12, 3) (12, 9) (9, 12) (6, 9) 3 B2 for correct enlargement incorrect centre or enlargement scale factor 2 from correct centre Or M1 for 3 points correctly plotted Condone good freehand 13 (a) Point (0.8, 120) indicated 1 (b) No oe and Correct supporting value(s) and justification 2 B1 for 200 to 260 visitors expected or about 0 to 1mm and 320 or line of best fit or negative trend/correlation or markings in relevant region above 2mm Justifcation includes reference to line of best ft (drawn or not) or trend or negative correlation or markings in relevant region above 2mm or surrounding values See below (c) Outside range of data [collected] 1 Accept “The data (or diagram) only goes to 5.5 (or 6)” oe Do not accept “By 6 to 7 it would give no visitors” oe There is no data around 9mm oe The line of best ft does not reach 9mm oe Condone “[Because] there would be a negative number of people” See below 14 1.25 3 B2 for 125 [cm] oe seen or ans figs 125 OR M1 for 4 ft 2 in = 50 [inches] soi M1 for their 50 × 2.5 soi Condone e.g. 48 for their 50 21 55 28 55GCSE (9-1) Mathematics Grades 1-4 Practice Materials 14 © OCR 2020 Question Answer Marks Part marks and guidance 15 (a) When multiplying [12.4] by 10, Nathan has not moved the figures to the left [he has just added a 0] 285.2 1 2 Accept 12.4 × 10 = 124 not 12.40 M1 for 12.4 × 20 = 248 or 124 × 2 = 248 Condone he has not moved the decimal point to the right soi Accept reference to either frst or second line of working See below Accept 248 seen If 12.4 × 23 is worked out using grid method, allow M1 if no more than one error If other long multiplication method used, allow M1 if not more than one arithmetic slip but M0 if error in place value (b) 8.60 3 M2 for 6.45 × 4 ÷ 3 oe Or M1 for 6.45 × 4 oe or 25.8[0] seenGCSE (9-1) Mathematics Grades 1-4 Practice Materials 15 © OCR 2020 Exemplar responses for Q13(b) Response Mark (Line drawn on graph) No, following the scatter diagram points there would be an estimate of around 240 visitors Take “following the scatter diagram points” refers to the line and a supporting value 2 No, we expect 250 (reference to line or markings drawn) 2 No, a line of best fit would show 250 (no line) 2 No, 0-1mm shows 320 but we would expect less as it is decreases/negative trend 2 No, (point below 2mm and point above 2mm stated) so there is a negative trend 2 No as with 1mm rain it's 280 visitors so with 2mm you should get around 245 B1 for 245 expected at 2mm but no reference to trend 1 Having drawn a line of best fit the scatter diagram wouldn’t support this as it’s too big a number No explicit supporting value used 1 No, by looking at the diagram you would expect about 240 Supporting value in range but no justification 1 No because with 1mm there’s less than 320 visitors 1mm and 320 are the supporting values but no reference to trend 1 No because there were 320 visitors on a day with 0mm rainfall 0mm and 320 are the supporting values but no reference to trend 1 No we expect 250 (nothing else) 1 No, 0-1mm shows 320 1 No, 320 is for 1mm 1 No, negative trend 1 No, (point below 2mm and point above 2mm stated) 1 The scatter diagram doesn’t support his statement as there isn’t any rainfall that is 2mm No supporting value 0 No it doesn’t because when the rainfall was 2mm he didn’t have any visitors Wrong 0 The closest amount of visitors to 2mm of rainfall is 290 An estimate that is out of range and is probably referring to the nearest point plotted. No reference to trend 0 No, as on a day with 1mm there are fewer customers 0 Yes … 0GCSE (9-1) Mathematics Grades 1-4 Practice Materials 16 © OCR 2020 Exemplar responses for Q13(c) Response Mark Outside range of data collected Perfect!! 1 Because there is no data to show above 6mm of rainfall Equivalent answer 1 Because the values of 7 and 8mm are not plotted, therefore it would be hard to estimate 9mm Similar to “no data around 9mm” 0 No record of any visitors are shown at 9mm of rainfall. Visitors stop coming when it hits 6mm of rainfall Equivalent to “no data for 9mm” 0 Because there is not enough data to estimate the amount of visitors for 9mm of rainfall Does not say “no data beyond 5.5 (or 6) mm” 0 We don’t have the data to do a line of best fit Wrong 0 There is nothing recorded Wrong 0 You can’t plot this data the graph isn’t big enough Wrong 0 Because that would create an outlier or anomalous piece of data Maybe but wrong 0 It wouldn’t be on the line Wrong 0 There would be under 50 visitors so it would be hard to get an accurate number Wrong 0 Because the experiment was only tested for 10 days, you would need to have more evidence to estimate how many visitors would come on 9mm rainfall Probably correct but has missed the point that THESE data do not extend beyond 5.5mm 0 Because the rain might be too heavy for visitors to come True but not answering the question 0GCSE (9-1) Mathematics Grades 1-4 Practice Materials 17 © OCR 2020 Exemplar responses for Q15(a) Response Mark For 10 × 12.4 Nathan has only times by 1. For 20 × 12.4 he has only times by 2. 10 × 12.4 = 124 Accept identifying that he has timesed by 1 instead of 10, or by 2 instead of 20 1 10 × 12.4 is not 12.40 it is 124. He didn’t add the 0s onto the numbers 10 × 124 is not 12.40 it is 124 scores 1, ignore the rest of the explanation because it is unclear rather than being incorrect 1 He added 0 to 12.4 Explains what he has done wrong 1 He does not move the decimal place when he × by 10 so it should have been 124.0 Doesn’t need to say where 1 Nathan has got the place value wrong on frst answer They have correctly identifed that the error is in the place value 1 10 × 12.4 = 124 so 20 × 12.4 is wrong Allow identifcation of error in second line 1 Instead of moving the decimal place to the right he just added a zero to the end of the number and instead of multiplying he added Ignore fnal part of statement 1 He hasn’t multiplied it he just added a zero that makes no diﬀerence Error identifed and ‘makes no diﬀerence’ explains error 1 He said that 20 × 12.4 is 24.80 when it is 248 which means the answer is 285.2 Accept reference to second line of working 1 When Nathan done 10 × 12.4 it should equal 124 10 × 12.4 = 124 is not enough. ‘It should equal 124’ is just about enough to identify the error 1BOD When he multiplied by 10 he didn’t remove the decimal place and same when he multiplied by 20 Multiplying by 10 isn’t the same as removing the decimal place 0 Nathan kept the decimal in. When calculating a sum with a decimal you take it out as you do the sum then put it back at the end Too vague 0 Nathan has divided the 12.4 rather than moving the decimal point to the right (positive/ multiplying) Moving the decimal point to the right would score 1, but we can’t ignore the rest of the explanation because it is incorrect rather than unclear 0 12.40 is wrong Identifes error but doesn’t explain 0OCR 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. 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