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
Fo
...
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/
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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
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GCSE (9-1) Mathematics
© OCR 2020
5 6Grades 1-4 Practice Materials
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GCSE (9-1) Mathematics
© OCR 2020
7Grades 1-4 Practice Materials
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GCSE (9-1) Mathematics
© OCR 2020
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GCSE (9-1) Mathematics
© OCR 2020
10Grades 1-4 Practice Materials
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GCSE (9-1) Mathematics
© OCR 2020
11Grades 1-4 Practice Materials
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GCSE (9-1) Mathematics
© OCR 2020
12Grades 1-4 Practice Materials
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GCSE (9-1) Mathematics
© OCR 2020
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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
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