The document outlines mark schemes and guidance notes for various mathematics questions, detailing the required answers, methodologies, and points allocation. It covers a wide range of topics and question types, providing specific marking criteria for responses. Each section includes information on correct answers, methods for simplification, and graphical representations.

1. Guidance
Notes
AO Element
Marks
Answer
Question
B1 for 14x or 13y as
answers
2
final answer
1
If 0 scored, SC1 for
correct answer seen then
spoilt
1
Diagram 4 correctly drawn
2(a)
1
28
2(b)
M1 for
or
2
8n − 4 oe final answer
2(c)
M1 for
their (a)(iii) = 300
provided their (a)(iii) is
linear
2
38
2(d)
M1 for 7 × 7 × 14
or 0.07 × 0.07 × 0.14
or 70 × 70 × 140 oe
3
B2 for 686
2(e)
Units must be consistent
with working or
numerical answer
B1 for cm3
M1 for
oe
2
18a final answer
3(a)
M1 for
2
14a 2
final answer
3(b)
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2. Guidance
Notes
AO Element
Marks
Answer
Question
B1 for 2 correct
or 5 6 9
2
6 9 14
4
B2 for 4 or 5 correct
3
−4 −6 −12 6 4 3
5(a)
or B1 for 2 or 3 correct
B3FT for 9 or 10 points
correctly plotted
4
Correct curve
5(b)
or B2FT for 7 or 8 points
correctly plotted
or B1FT for 5 or 6 points
correctly plotted
1
Correct ruled line drawn
5(c)
FT their curve and their
line
1
1.3 to 1.7
5(d)
M1 for oe
or
2
or final answer
6
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3. Guidance
Notes
AO Element
Marks
Answer
Question
oe
3
M1 for correct method seen to
eliminate one variable
7
A1 for x = 4
If M0 scored, SC1 for 2
values that substitute to
give
y – 3x rounding to 13.0,
or
y – 7x rounding to
−3.0
A1 for y = 25
or
SC1 if no working
shown, but 2 correct
answers given
M1 for 90 ÷ their time
for A to B [× 60]
2
120
8(a)(i)
or B1 for 2[km/min]
1
10
8(a)(ii)
1
Ruled line from (1440, 90) to
(1520, 155)
8(a)(iii)
1
A [and] B
8(a)(iv)
M1 for 155 ÷ 62
2
2 [hours] 30 [minutes]
8(b)(i)
FT their (b)(i) + 1245
1
1515
8(b)(ii)
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4. Guidance
Notes
AO Element
Marks
Answer
Question
1
Ruled line from (1245, 155) to
(their (b)(ii), 0)
8(b)(iii)
FT their crossing
point
1
58 to 63
8(b)(iv)
B1 for 2 correct
2
−3 5 2
9(a)
B3FT for 6 or 7 points
correct
4
Correct curve
9(b)
or B2FT for 4 or 5 points
correct
or B1FT for 2 or 3 points
correct
1
Ruled line x = 1 drawn
9(c)(i)
1
x = 1
9(c)(ii)
B1 for each
2
−0.5 to −0.3 and 2.3 to 2.5
9(d)
If 0 scored, B1 for y = 4
drawn
1
Correct ruled continuous line
9(e)(i)
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5. Guidance
Notes
AO Element
Marks
Answer
Question
B2 for [y =] 2x + k
3
[y =] 2x + 4
9(e)(ii)
or M1 for
B1 for kx + 4 , k ≠ 0,
or c = 4
1
80
10(a)
M1 for or
or better
2
7
10(b)
M1 for
or
3
2.2 oe
10(c)
M1 for second correct
step
B1 for
or
2
final answer
11
M1 for 4 × 32
+ 3 × −2
or better
2
30
12
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6. Guidance
Notes
AO Element
Marks
Answer
Question
B3 for 14x = 315
4
22.5
13
or M2 for
45 + 3x + 5x + 6x = 360
oe
or M1 for
45 + 3x + 5x + 6x oe
or 14x
If 0 scored and
45 + bx = 360 or better
seen then
SC1 for
oe
OR
B3 for
or B1 for 14
and B1 for 360 − 45 oe
1
3
14(a)
B1 for 3 or 4 correct
2
_ _ _ 10
14(b)
_ 1 _ 6
_ _ 9 16
1
[t =] n 2
oe
14(c)
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7. Guidance
Notes
AO Element
Marks
Answer
Question
2
M1 for
or
14(d)
A1 for [=] 6
3
B1 for [w =] 120
14(e)
B1 for [g =] 105
If final two B marks not
scored, award B1 if
their w + their g = their t
or FT(c) for their t if
their (c) is quadratic
B1 for [t =] 225
1
y = −2 drawn, ruled
15(a)
1
y = −2x drawn, ruled
15(b)
M1 for a correct equation
in terms of x or y.
2
[x =] 3.5, [y =] 3
with supporting working
16
If 0 scored SC1 for both
answers correct.
1
cao
17(a)
1
cao
17(b)
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8. Guidance
Notes
AO Element
Marks
Answer
Question
M1 for ,
or or
or
2
18
as final
answers
1
4 tables and 14 chairs correctly
drawn
19(a)
B1 for 2 correct
or k, k + 2, k + 4
2
14, 16, 18
19(b)
B1 for 2t + j
or kt + 6 , k ≠ 0
2
2t + 6 oe final answer
19(c)
M1 for 18 correctly
substituted into their (c),
2
42 cao
19(d)
provided a linear
expression
M1 for their (c) = 80
2
37 cao
19(e)
1
55
20(a)
M1 for oe
2
108
20(b)
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9. Guidance
Notes
AO Element
Marks
Answer
Question
4
Correct graph
Ruled lines
20(c)
B1 for ruled lines
(0955, 31.5) to
(1030, 31.5)
and (1030, 31.5) to
(1050, 30)
(0955, 31.5) to (1030, 31.5)
(1030, 31.5) to (1050, 30)
B1 for ruled line from
(their 1050, 30) to
(their 1050+20, 12)
(1050, 30) to (1110, 12)
B1 for ruled line from
(their 1110, 12) to
(their 1110+10, 12)
(1110, 12) to (1120, 12)
B1 for ruled line
(their 1120, 12) to
(their 1120+15, 0)
or for 15 mins soi
(1120, 12) to (1135, 0)
B1 for each
3
–28, –4, 2
21(a)
B3FT for 6 or 7 correct
plots
4
correct smooth curve
21(b)
or B2FT for 4 or 5
correct plots
or B1FT for 2 or 3
correct plots
accept (x, y) where
1 < x < 2 and 2 < y < 4
1
(1.5 , 2.25)
21(c)
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10. Guidance
Notes
AO Element
Marks
Answer
Question
B1 for or
2
final answer
22
B1 for 25 or 12
2
37
23
1
cao
24
1
1025
25(a)
B1 for line from
(1055, 9) to (1120, 9)
2
Graph completed correctly
25(b)
B1 FT for line from
(their 1120, 9) to
(their 1120 + 30 min,
0)
B1 for 5x – 15 or 6x + 2
or for answer of 11x + j
or kx – 13
2
11x – 13 final answer
26
1
23
27(a)
B1 for 3n + j or kn + 5,
k ≠ 0
2
3n + 5 oe
27(b)
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- Mark Scheme

11. Guidance
Notes
AO Element
Marks
Answer
Question
4
M1 for multiplying both equations
to get a common coefficient
28
M1 for correctly adding or
subtracting their equations
A1 for [x = ] 10
If zero scored then SC1
for two answers which
A1 for [y = ] 8
satisfy one of the original
equations or for 2 correct
answers with no
working
If zero scored, SC1 for 2
values satisfying one of
3
M1 for correctly eliminating one
variable
29
the original equations or
A1 for [x = ] 3
for 2 correct answers
with no working
A1 for [y = ] −2
1
45
30
B1 for 6n + c or kn – 10
(k ≠ 0)
2
6n – 10 oe
31
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12. Guidance
Notes
AO Element
Marks
Answer
Question
Examples
3
M1 for any example of equivalence
from the conversion graph
32
Pounds (£)
Dollars ($)
3.5
5
7
10
14
20
21
30
28
40
5
7
10
14 to 14.5
15
21
20
28 to 29
A1 for [£]81 to [£]87 or
[$]126 to [$]138
A2 for shop and [£]81 to [£]87
or [$]126 to [$]138 nfww
If M0 allow SC1 for
[$]120 = [£]81 to [£]87
or [£]90 = [$]126 to
[$]138 with ‘shop’ as the
answer
B1 for −3p or −4q
2
−3p – 4q final answer
33
M1 for or
or better
2
13
34
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13. Guidance
Notes
AO Element
Marks
Answer
Question
M1 for first correct
step
3
0.7 or
35
M1 for second correct
step, FT their first step
1
y(1 – 2y) final answer
36
M1 for 3x + x + x + 15 or
better
4
3x + x + x + 15 = 180 or better
leading to
[x = ] 33
37
M1 for their expression
= 180
M1 for rearranging their
equation to ax = b
If 0 scored, SC2 for 33
nfww
M1 for x – 3 = 8
or 7x – 21 = 56 or
better
2
11
38
M1 for or
2
oe
39
M1 for or
better
2
32
40
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14. Guidance
Notes
AO Element
Marks
Answer
Question
[Total: 154]
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