- Mark Scheme
Question
Answer
Marks
1
oe final answer
2
2
52
1
3
7
3
/
AO Element
Notes
B1 for
Guidance
or
M2 for 166 + 2x = 180 or
better
or M1 for 97 – 3x + 69 +
5x = 180 oe
4
2
B1 for any three of x 2,
–5x, –7x, +35
5
2
B1 for
or
or
6
2
final answer
B1 for partial
factorisation
or
7
M2 for
better
or
M1 for
oe or better
A1 for 28
4
or B1 for
or
If 0 scored, SC1 for the
correct answer with no
algebra
- Mark Scheme
Question
8
Answer
Marks
4
28, −34
/
AO Element
Notes
Guidance
Trial and improvement
OR
B1 for x + y = –6 oe
B1 for x – y = 62 oe
B1 for 28 or −34
9
2
10(a)
1
10(b)
1
10(c)
1
11
12
final answer
[y = ] 5x – 4
2
1
B1 for
0)
M1 for
or
(n, k ≠
or
- Mark Scheme
Question
13
Answer
Marks
3
1.8 or
/
AO Element
Notes
M2 for
or M1 for
OR
M2 for
oe
14
final
3
B2 for
answer
or
or
or B1 for
15
990
3
M2 for correct complete
area statement
e.g.
oe
or M1 for one area
calculation
Guidance
- Mark Scheme
Question
Answer
Marks
3
16
/
AO Element
Notes
M2 for
Guidance
,
or
M1 for
,
or
3
17
B2 for correct expansion
and simplification of two
of the brackets
or B1 for correct
expansion of two
brackets with at least 3
terms correct
18
[p = ] –13
2
M1 for
better
or
- Mark Scheme
Question
Answer
Marks
4
19
/
AO Element
Notes
Guidance
B3 for any two correct
OR
B1 for
B2 for
or
or
and
or with
incorrect inequality
signs
or B1 for
or
or SC3 for > instead of ≥
etc.
20
4
2
M1 for
or
or
21
−2
2
M1 for (–3)(–2) + (–8)
- Mark Scheme
Question
Answer
22
final answer
Marks
5
/
AO Element
Notes
Guidance
B2 for
or B1 for
where
or
B2 for
or B1 for
or
23(a)
2
B1 for
23(b)
2
B1 for
24
3
M1 for correct
rearrangement for y or y
2
term
or
or
M1 for correct square
root
M1 for correct division
by 2 or
25
–14
2
M1 for
better
or
or
or better
- Mark Scheme
Question
Answer
26
27
16
Marks
/
AO Element
Notes
2
B1 for correct
unsimplified answer
3
M1 for
M1 for
OR
M2 for
oe
28(a)
Correct lines and correct region
clear
5
B2 for 2x + y = 8
correctly ruled
or B1 for ruled line with
negative gradient
B1 for y = x correctly
ruled
B1 for x = 2 correctly
ruled
28(b)
6
1
29(a)
0.3 oe
1
Guidance
- Mark Scheme
Question
29(b)
Answer
3060
Marks
3
/
AO Element
Notes
Guidance
M2 for
oe
or M1 for one correct
part area
30
[y =] 1
3
M1 for
M1 for
OR
M2 for
oe
2
31(a)
B1 for
or
or k = −9
31(b)
19.4 or 19.39…
2
M1FT for
− 1.39 or − 1.392…
A1 for
32(a)
4 7 4
2
or
B1 for one correct
- Mark Scheme
Question
32(b)
Answer
Correct curve
Marks
4
/
AO Element
Notes
Guidance
B3FT for 6 or 7 points
correct
or B2FT for 4 or 5 points
correct
or B1FT for 2 or 3 points
correct
32(c)
x = 1 oe
1
32(d)
−1.9 to −1.7 and 3.7 to 3.9
2
B1 for each
33
[x =] 2.5
2
M1 for
34
8
2
M1 for correct attempt
e.g. 12 + 14 + 16 ….
35
[h =] 8.4
3
B2 for
or
or
or
or B1 for
or M1 for
- Mark Scheme
Question
36
Answer
Marks
/
AO Element
Notes
Guidance
1
27 – 9x
37
final answer
2
B1 for 2c or −3d
38(a)
oe
2
B1 for each
3
M1 for correctly
eliminating one
variable
oe
38(b)
[x =] 20
[y =] 12
B1 for one correct
39
final answer
2
40(a)
25, 87, 329 circled
1
40(b)
7
1
40(c)
8
2
B1 for
or
M1 for
or B1 for at least four of
39, 78, 117, 156, 195,
234, 273, 312
40(d)(i)
oe
2
B1 for
or
,
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
40(d)(ii)
79
1
FT their (d)(i) if linear
40(d)(iii)
175
2
M1 for
or
or
40(e)(i)
oe
2
B1 for
or
,
40(e)(ii)
174
gives house numbers that
are zero/negative
2
B1 for each
If 0 scored, SC1 for
175
[Total: 128]
- Mark Scheme
Question
Answer
Marks
3
1
/
AO Element
Notes
M2 for
Guidance
,
or
M1 for
,
or
2(a)
19
2(b)
oe final answer
2
M1 for
or for
2
M1 for correct first step
soi
or
or
3
[p = ] –13
2
M1 for
better
4
5 – 2x final answer
2
M1 for 2(1 – x) + 3 oe
5(a)
82
2
M1 for
or
soi by
or g(9) isw
- Mark Scheme
Question
Answer
5(b)
final answer
Marks
2
/
AO Element
Notes
Guidance
M1 for
or
or
5(c)
[a =] 1, [b =] 2, [c =] 2
3
B2 for
or M1 for
5(d)
3
oe
M2 for
or M1 for
f(x) = 4
or for
better
6(a)
6(b)
6(c)
soi
or
1
−3
2
oe
final answer
2
M1 for
soi
M1 for
isw
6(d)
oe final answer
2
M1 for a correct first step
,
or
- Mark Scheme
Question
Answer
6(e)
final answer
Marks
3
/
AO Element
Notes
Guidance
M1 for
oe
isw
B1 for common
denominator
6(f)(i)
M1 for
3
B1 for
A1 for
oe
leading to
with no errors and must
show
with no omissions after
this
- Mark Scheme
Question
6(f)(ii)
Answer
B2 for
Marks
4
/
AO Element
Notes
B1 for
or better
oe
or B1 for
oe
or
B1 for each
B2 for 0.17 and 1.08 final ans
If 0 scored, SC1 for
answer 0.2 and 1.1
or answer − 0.17 and
−1.08
or 0.174... and 1.075 to
1.076 seen
or 0.17 and 1.08 seen in
working
7(a)
27
2
M1 for 33x seen
7(b)
3
2
M1 for 7 + 3x = 24
2
M1 for
or
or
7(c)
oe final answer
or
Guidance
- Mark Scheme
Question
8
Answer
2
5
9(a)
final answer
9(b)
Marks
final answer
/
AO Element
Notes
M1 for
1
2
M1 for correct first step
,
e.g.
,
10(a)
0
1
10(b)
5
2
M1 for
or better
or
10(c)
oe final answer
2
or
M1 for
or
or
or better
10(d)
2
M1 for
oe
10(e)
2
B1 for three terms from
correct
Guidance
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
10(f)
27
2
M1 for
11(a)
−17
2
M1 for f(11) seen
or 5 − 2(5 − 2x) or
better
11(b)(i)
4x 2 + 8 oe
1
11(b)(ii)
oe final answer
2
M1 for x = 5 − 2y
or 2x = 5 − y
or y – 5 = –2x
or
12(a)
26
12(b)
12(c)
5
12(d)
oe
2
M1 for g(5) or for
2
M1 for
2
M1 for 2x − 3 = 7
2
M1 for
or
or
13(a)
1
2
oe
M1 for h(0) or for
Guidance
- Mark Scheme
Question
13(b)
Answer
2
8
13(c)
Marks
or
final answer
3
/
AO Element
Notes
Guidance
M1 for g(¼) or for
M2 for
or
better
or
or better
or
or M1 for
or
or
or
13(d)
5
1
14(a)
2
2
M1 for f(5)
or 7− (7 − x) or better
14(b)
30 − 4x final answer
2
M1 for 4(7 − x) + 2 or
better
or for correct answer then
spoilt
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
14(c)
15 – 4x 2 final answer
2
M1 for 15 – (2x)2 or
better
or for correct answer then
spoilt
15(a)
[0].70 cao
2
B1 for [0].696 to
[0].697
15(b)
4 cao
1
16(a)
1
16(b)
2
M1 for correct first
algebraic step e.g.
y – 5 = 3x or
or better
or
for interchanging x and y,
e.g. x = 3y + 5, this does
not need to be the first
step
16(c)
9x + 20 cao final answer
2
17(a)
−13
1
17(b)
1
M1 for 3(3x + 5) + 5
Guidance
- Mark Scheme
Question
17(c)
17(d)
Answer
9x − 10 cao
final answer oe
Marks
/
AO Element
Notes
Guidance
2
M1 for
2
M1 for correct first step
e.g.
or
or
or better
or
for interchanging x and y,
e.g.
, this does
not need to be the first
step
[Total: 101]
- Mark Scheme
Question
Answer
Marks
1
Acute
1
2(a)
Chord
1
2(b)
16
1
3
7
3
AO Element
/
Notes
M2 for 166 + 2x = 180 or
better
or M1 for 97 – 3x + 69 +
5x = 180 oe
4
109
3
M1 for (180 – 38) ÷ 2
oe
M1 for 180 – their ACB
5
Three correct lines on first shape
3
AND
B2 for three correct lines
on first shape
or B1 for one or more
correct lines and no
wrong lines
One correct line on second shape
B1 for one correct line on
second shape
6
2
1
Guidance
- Mark Scheme
Question
Answer
Marks
7
M1 for angle ACB = 65° or angle
RPQ = 37°
2
/
AO Element
Notes
A1 for 2 pairs of equal angles oe
2
8(a)
B1 for
or
8(b)
Ruled line perpendicular to L
1
9
140
2
10
Correct shape drawn
1
11
Correct shape drawn
2
12
Kite or isosceles trapezium
1
13
2
1
14
Circle with 3.8 cm radius drawn
2
M1 for 11.4 ÷ 1.5 or 5.7
÷ 1.5
15(a)
72
2
B1 for each
Corresponding angles
M1 for 360 ÷ 9
M1 for 3 sides correctly
reflected or 4 correct
vertices
Guidance
- Mark Scheme
Question
15(b)
Answer
65
Marks
AO Element
/
Notes
2
B1 for each
Angles [at a point] sum [to] 360
oe
16
116
2
M1 for angle ACB = 32
soi
17
Complete explanation with
geometrical reasons
3
B1 for RQP = x° QR
bisects angle PQB
B1 for RPQ = x° alternate
segment theorem
B1 for triangle PQR has
two equal angles both
less than 60 (so can’t be
equilateral) so must be
isosceles
Guidance
- Mark Scheme
Question
18
Answer
16.6 or 16.64…
Marks
5
/
AO Element
Notes
Guidance
M2 for
oe
or M1 for scale factor
or
oe soi
Then Pythagoras
method:
and M2 for
or
or M1 for
or
OR
alternative trigonometry
method e.g.
M1 for
and M1 for
- Mark Scheme
Question
19
Answer
[x =] 55
Marks
2
/
AO Element
Notes
Guidance
B1 for each
[y = ] 24
20(a)
49
1
20(b)
98
1
20(c)
20
1
20(d)
70
1
FT 90 – their (c)
21
25
2
B1 for 130 seen
FT 2 × their (a)
or M1 for 50 ÷ 2
22
5
3
M2 for
oe
or M1 for
or
oe
23(a)
Equilateral
1
23(b)(i)
4.1 to 4.5
1
23(b)(ii)
10.25 to 11.25
2
M1 for 0.5 × 5 × their
(b)(i)
- Mark Scheme
Question
23(b)(iii)
Answer
61.5 to 67.5
Marks
2
/
AO Element
Notes
FT their (b)(ii)
B1 for 6 seen
24(a)
Correct position of town B
2
B1 for correct bearing
B1 for correct distance
24(b)(i)
Correct triangle drawn
3
B2 for correct triangle
with no or wrong arcs
or correct position of C
with arcs (no triangle)
or B1 for one line correct
length drawn
or 7 and 5 seen
24(b)(ii)
38 to 42
1
25(a)
Tangent
1
25(b)(i)
final answer
FT their measured angle
at C
2
M1 for
25(b)(ii)
40
2
B1 for angle OBC = 40°
or angle BOG = 140°
25(b)(iii)
7.68 or 7.679 to 7.680....
2
FT their (b)(ii) and (b)(i)
M1 for
Guidance
- Mark Scheme
Question
Answer
Marks
25(c)(i)
Angle [between] tangent [and]
radius
1
25(c)(ii)
B1 for 180 – 140 or 90 – their
(b)(ii)
3
/
AO Element
Notes
M1 for
oe
A1 for [BC =] 13.109[...]
25(c)(iii)
6.11 or 6.112 to 6.114
3
M1 for [OB 2 =] 13.112 +
112
A1 for 17.1 or 17.11 or
17.112 to 17.114
OR
M1 for
oe
A1 for 17.1 or 17.11... or
17.112 to 17.113
26(a)
Kite
1
26(b)(i)
Translation
2
B1 for each
Guidance
- Mark Scheme
Question
26(b)(ii)
Answer
Reflection
Marks
AO Element
/
Notes
2
B1 for each
3
B1 for each
x = 0.5 oe
26(b)(iii)
Rotation
90° clockwise oe
[centre] (0, 0) oe
26(c)(i)
(−5, −6)
1
26(c)(ii)
Image at (−5, 0), (−2, 3), (7, 0),(−2,
−3)
2
B1 for correct size,
wrong position
or correct shape with
incorrect scale factor
27
55
2
M1 for 180 − 70
28(a)
Cuboid
1
28(b)
10
2
29(a)
(−1, −2)
1
1
29(b)
29(c)
C marked at (3, 3)
1
M1 for 5 × 2 [× 1]
Guidance
- Mark Scheme
Question
Answer
Marks
AO Element
/
Notes
1
29(d)(i)
FT their (b) +
1
29(d)(ii)
29(e)(i)
Correct parallelogram drawn
1
FT their (c) provided
ABCD forms a
parallelogram
29(e)(ii)
30
2
FT the area of their
ABCD provided it is a
parallelogram.
cm
2
B1 for each
30
[a =] 32
3
B1 for each
3
B2 for 3 or 4 further
correct faces drawn in the
correct places
[b =] 98
[c =] 82
31
Correct ruled net of cuboid
or B1 for 1 or 2 further
correct faces drawn in the
correct places
32(a)
Hexagon
1
32(b)
6
1
Guidance
- Mark Scheme
Question
33(a)
Answer
24
Marks
3
/
AO Element
Notes
Guidance
M2 for
where k = 1, 2 or 13
or B1 for
soi
33(b)
15
1
FT if
is an
integer
34
Correct ruled triangle with arcs
2
M1 for correct triangle
without arcs
or for correct arcs and no
lines
35
85
2
B1 for either angle in alt
segment = 58
36
72
2
B1 for either angle at J or
H = 108 or angle at F =
72
37(a)
36
2
M1 for
or
oe
- Mark Scheme
Question
37(b)
Answer
30
Marks
3
/
AO Element
Notes
Guidance
M2 for
oe
or M1 for
38
12
2
M1 for
or
oe
39
B1 for OA = OB = OC = OD
Radii
3
B1 for AB = CD chords
equidistant from centre are equal
B1 for SSS implies congruent
40
45
2
B1 for angles at M or K
= 45 or angle at L = 90
[Total: 132]
- Mark Scheme
Question
Answer
1
2
86
Marks
/
AO Element
Notes
Guidance
2
M1 for
2
M1 for correct method to
find the perimeter
e.g. (8 + 3) × 2 × 5 – 3 ×
8
If 0 scored, SC1 for
answer 98
3
45
2
4
5300
1
5
141 or 141.3 to 141.4
4
M1 for
oe
M1 for
M2 for
or M1 for
6
3.7[0] or 3.689 to 3.699…
3
M2 for
or M1 for
oe
- Mark Scheme
Question
7
Answer
25.6 or 25.59 to 25.60…
Marks
4
/
AO Element
Notes
Guidance
M3 for
or M2 for
oe
or M1 for
oe
8
208
1
9
15.5 or 15.48 to 15.49
3
B2 for 1550 or 1548 to
1549
or M2 for
or M1 for
10(a)
Equilateral
1
10(b)(i)
4.1 to 4.5
1
10(b)(ii)
10.25 to 11.25
2
M1 for 0.5 × 5 × their
(b)(i)
- Mark Scheme
Question
10(b)(iii)
Answer
61.5 to 67.5
Marks
2
/
AO Element
Notes
FT their (b)(ii)
B1 for 6 seen
11(a)
Tangent
11(b)(i)
final answer
1
2
M1 for
11(b)(ii)
40
2
B1 for angle OBC = 40°
or angle BOG = 140°
11(b)(iii)
7.68 or 7.679 to 7.680....
2
FT their (b)(ii) and (b)(i)
M1 for
11(c)(i)
Angle [between] tangent [and]
radius
1
11(c)(ii)
B1 for 180 – 140 or 90 – their
(b)(ii)
3
M1 for
oe
A1 for [BC =] 13.109[...]
Guidance
- Mark Scheme
Question
Answer
11(c)(iii)
6.11 or 6.112 to 6.114
Marks
3
/
AO Element
Notes
M1 for [OB 2 =] 13.112 +
112
A1 for 17.1 or 17.11 or
17.112 to 17.114
OR
M1 for
oe
A1 for 17.1 or 17.11... or
17.112 to 17.113
12
8
3
M1 for 384 ÷ 6
M1dep for
13
168
3
M2 for (7 × 4 ÷ 2) × 12
oe
or M1 for (7 × 4 ÷ 2) or
their area × 12
14(a)
28
1
14(b)
192
2
M1 for
oe
or B1 for 16 and 12 or 4
tiles = 1 m2 soi
15(a)
Cuboid
1
Guidance
- Mark Scheme
Question
Answer
Marks
15(b)
10
2
16(a)
(−1, −2)
1
Notes
M1 for 5 × 2 [× 1]
1
16(b)
16(c)
AO Element
/
C marked at (3, 3)
1
1
16(d)(i)
FT their (b) +
1
16(d)(ii)
16(e)(i)
Correct parallelogram drawn
1
FT their (c) provided
ABCD forms a
parallelogram
16(e)(ii)
30
2
FT the area of their
ABCD provided it is a
parallelogram.
cm
2
B1 for each
Guidance
- Mark Scheme
Question
17
Answer
41.1 or 41.09 to 41.112
Marks
5
/
AO Element
Notes
Guidance
M1 for
M2 for
or M1 for
M1 for
18
25
3
B1 for height is 5 [cm]
M1 for
oe
3
19
M2 for
oe
or M1 for
oe
If 0 scored, SC1 for final
answer kx 2
20(a)
39[.0] or 39.03 to 39.04…
3
M2 for
or M1 for
- Mark Scheme
Question
20(b)
Answer
2.71 or 2.708…
Marks
/
AO Element
Notes
4
M3 for
oe
or M2 for
oe
or M1 for
oe seen
20(c)(i)
3.67 or 3.666 to 3.667
2
M1 for
or better
or for
or better
Guidance
- Mark Scheme
Question
20(c)(ii)
Answer
100 or 100.0 to 100.1… final
answer
Marks
4
/
AO Element
Notes
Guidance
M3 for
or M2 for
or M1 for
21
3.375 cao
3
M2 for
better
or M1 for
22
3.63 or 3.627 to 3.628
3
M2 for
or M1 for
or
- Mark Scheme
Question
Answer
23
or
or
Marks
3
/
AO Element
Notes
B2 for 4R 2 = 9x 2 oe or
better
or M1 for
24
2700
4
M2 for 15 × 2.5 × 20 ×
60 × 60
or M1 for 15 × 2.5 ×
20
M1 for their volume ÷
1000
If 0 scored, SC1 for figs
27 with no working
25
576
3
M2 for
[2 ×] (15 × 4 + 12 × 4 +
12 × 15) oe
or M1 for one correct
area,
15 × 4 or 12 × 4
or 12 × 15
26
452 or 452.3 to 452.4...
2
27
460
1
M1 for
Guidance
- Mark Scheme
Question
28
Answer
3500
Marks
2
/
AO Element
Notes
Guidance
B1 for each
14 000
29
6.28 or 6.283 to 6.284
3
M2 for
oe
and
oe
or M1 for
oe
or
or
30
2592
4
oe
oe
M3 for
oe
or M2 for
1.2 × 60 × 60 × 6 oe
or M1 for
figs 12 × figs 6
or 60 × 60
or correct conversion e.g.
their value in cm3 ÷ 1000
their value in m3 × 1000
1.2 × 100
6 ÷ 10 000
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
31(a)
Two correct lines drawn
2
B1 for one correct, no
extras or two correct and
one extra
31(b)
2.16
2
M1 for 1.2 × 1.8
32(a)
B2 for 40
3
M1 for 5 × 4 × 2
3
B2 for 4 more correct
faces in correct
position
B1 for cm3
32(b)
Correct net
B1 for 2 or 3 more
correct faces in correct
position
33
384
2
M1 for 8 × 8 [ × 6]
34
14.7
2
M1 for
oe
35
436 500
1
36
36.7[0]
1
37
5
2
M1 for 180 ÷ 62 oe
Guidance
- Mark Scheme
Question
Answer
Marks
38
23.1 or 23.137 to 23.139 or 23.14
3
/
AO Element
Notes
M2 for
Guidance
oe
or M1 for
39
40
2
40
160
1
M1 for 5 × 4 × 2
[Total: 138]
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
1
34
2
M1 for 12 + 0.5 or 4 +
0.5 or better seen
2
33 500
2
M1 for
oe
3
25 × 34 × 132
1
4
56
2
B1 for 56k
or lists of multiples of 8
and 14 (at least 3 of
each)
5(a)
Correct Venn diagram
3
B2 for 8 or 9 numbers
correct
or B1 for 6 or 7 numbers
correct
5(b)(i)
41, 43, 47
1
FT their Venn
diagram
- Mark Scheme
Question
Answer
Marks
AO Element
/
Notes
5(b)(ii)
44, 46, 49, 50
1
FT their Venn
diagram
5(c)
0
1
FT their Venn
diagram
1
6
7(a)
8
1
7(b)
26 244
1
7(c)
1
1
8(a)
Jan
1
8(b)
9
1
Guidance
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
8(c)
9.5
2
M1 for correctly ordering
at least 7 months from
one end or
identifying the middle
two, 8 and 11
8(d)
8.8
3
M1 for attempt to add the
temperatures ÷ 12
A1 for 8.83[3.......]
After M1 A0, award SC1
for their mean correct to
2 sf
9
3
cao
B2 for
oe as final
answer
or M1 for
or
oe
or B1 for
10
18.4%
2
M1 for 3 in correct order
or for three of
,
[18.4% =] 0.184,
,
- Mark Scheme
Question
Answer
11
12
oe
6
Marks
/
AO Element
Notes
Guidance
1
3
B2 for
or 5.25 shown
in working isw
or M1 for
soi by
answer 5
13
0.048 cao
1
14(a)
M1 for
3
A1 for 13939…
oe
A2 for 118.06…
14(b)
67.8 or 67.9 or 67.83 to 67.88
3
M2 for
oe
or M1 for
oe
14(c)(i)
255
3
B1 for bearing of B from
A is 75 soi
M1 for 180 + 75 oe
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
14(c)(ii)
[00]7.2
2
M1 for their (c)(i) – their
(b) –180
14(d)
11.8 or 11.82 to 11.83
3
M1 for 115 ÷ 35 oe
M1 for their speed in m/s
× 60 × 60 ÷ 1000
14(e)
76.1 or 76.08 to 76.09
3
M2for
oe
or M1 for distance
required is perpendicular
to AC soi
15(a)
23.27 final answer
2
15(b)
2.75 final answer
3
M1 for 9 × 2.97 soi
M2 for
oe
or M1 for 108[%]
associated with 2.97
oe
16
4[.00...]
3
M2 for
or M1 for
oe or
better
- Mark Scheme
Question
Answer
Marks
17
18
final
/
AO Element
Notes
2
M1 for
3
B2 for
Guidance
answer
or
or
or B1 for
19
3
or
final answer
B1 for common
denominator
or
M1 for
or
better
2
20
21(a)
oe
21(b)
M1 for
A1 for one step shown to
1
oe
2
B1 for
or
- Mark Scheme
Question
21(c)
B1 for
Answer
Marks
ruled
5
B2 for
Notes
Broken line
Solid line
B1 for line passing
through (0, 15) or (10,
0)
ruled
B1 for
AO Element
/
ruled
B1 for correct region indicated
Solid line
21(d)
412
2
M1 for (4, 9) identified
or for evaluation 40x +
28y for an integer point
in the region (x > 0 and y
> 0)
22(a)
40 54
4
B1 for each
2
B1 for a quadratic
expression
or for 2nd common
difference 2 (at least 2
shown)
or for 2 correct equations
seen
or for subtracting n 2
2
M1 for their (b) = 10300
seen
26 34
22(b)
22(c)
or
100
oe
Guidance
- Mark Scheme
Question
Answer
22(d)
Marks
2
oe
/
AO Element
Notes
Guidance
B1 for each
or M1 for one correct
equation
or for 2nd difference = 1
soi (at least 2 shown)
and
oe
3
23
M2 for
,
or
M1 for
,
or
24(a)
oe and
6
B2 for
Or B1 for one correct
M1 for derivative = 0 or
their derivative = 0
M1 for
B1 for
and
and 50
- Mark Scheme
Question
24(b)
Answer
minimum
Marks
3
AO Element
Notes
Guidance
B2 for one correct with
reason
or M1 for correct attempt
e.g. 2nd derivatives,
gradients or sketching
maximum
with correct reasons
2
25(a)
/
M1 for
or
or a = 5
25(b)
Sketch of U-shaped parabola with
a minimum indicated at (–5, –11)
with no part of graph in 4th
quadrant
3
FT their
provided in that form
B1 for U shape curve
B1FT for turning point
at (–5, k) or (k, –11)
[Total: 106]
- Mark Scheme
Question
Answer
Marks
1(a)
20 [< t ] 25
1
1(b)
25 [< t
] 30
1
1(c)
28.3 or 28.33..
4
AO Element
/
Notes
M1 for 22.5, 27.5, 32.5,
37.5, 42.5 soi
M1 for Σ fx where x is in
the correct interval
including boundaries
M1dep for Σ fx ÷ 120 or
Σ fx ÷ (44 + 32 + 28 + 12
+ 4)
1(d)
2(a)
2(b)(i)
1
oe isw
1
oe
2
M1 for
A1 for
oe
Guidance
- Mark Scheme
Question
2(b)(ii)
Answer
oe
Marks
4
/
AO Element
Notes
M3 for
oe
or M2 for
or
oe
or M1 for for one correct
product other than
1
3(a)(i)
3(a)(ii)
1.62 or 1.623… nfww
4
M1 for 1.35, 1.45, 1.55,
1.65, 1.75 1.85 soi
M1 for Σ fx
M1 dep for their Σ fx ÷
120
3(b)(i)
oe
1
Guidance
- Mark Scheme
Question
3(b)(ii)
Answer
oe
Marks
4
/
AO Element
Notes
Guidance
M3 for
or M2 for
isw
or M1 for
After 0 scored, SC1 for
answer
or
oe
3(c)(i)
55, 79, 106, 120
2
B1 for 2 or 3 correct
3(c)(ii)
Correct diagram
3
B1 for correct horizontal
plots
B1FT for correct vertical
plots
B1FT dep on at least B1
for reasonable increasing
curve or polygon through
their 6 points
If 0 scored SC1 for 5 out
of 6 points correctly
plotted
- Mark Scheme
Question
Answer
Marks
3(d)(i)
1.62 to 1.63
1
3(d)(ii)
1.57 to 1.58
2
4(a)
oe
4(b)
oe
Notes
Guidance
B1 for 48 soi
1
0
1
5
0
1
oe
AO Element
1
4(c)
6
/
3
M2 for
or M1 for
or
7
8(a)
oe
oe
2
2
M1 for
B1 for
oe
or
provided
fraction is less than 1
- Mark Scheme
Question
8(b)
Answer
Marks
/
AO Element
Notes
1
46
9(a)
1
9(b)(i)
1
FT their (a) dep on (a)
being an expression in r
3
FT their (b)(i)
9(b)(ii)
M1 for
or better nfww
M1 for
Strict FT their expansion
to a quadratic then
equating to 0.4 and then
collecting to 3 terms on
‘one side’
OR
OR
oe
A1 for
Strict FT their expansion
to a quadratic = 0.4 all
multiplied by 10
no errors or omissions
seen
Guidance
- Mark Scheme
Question
9(b)(iii)
Answer
Marks
3
B2 for
AO Element
/
Notes
or B2 for e.g.
5r(2r – 1) – 9(2r – 1) and
then 5r – 9 = 0
and 2r – 1 = 0
or B1 for
5r(2r – 1) –9(2r – 1)[= 0]
or
2r(5r – 9) –1(5r – 9)[= 0]
or
(5r + a)(2r + b) [= 0]
where a, b are integers
and ab = +9
or 2a + 5b = – 23
If 0 scored, SC1 for
5r – 9 and 2r – 1 seen
but not in factorised
form
B1 for
9(b)(iv)
0.8 or
oe
1
Guidance
- Mark Scheme
Question
10
Answer
oe
Marks
4
/
AO Element
Notes
M3 for
or M2 for
or
or M1 for
seen
or
seen
If 0 scored, SC1 for
oe
11(a)
2
B1 for either numerator
or denominator correct
Guidance
- Mark Scheme
Question
11(b)(i)
Answer
B1 for
Marks
4
/
AO Element
Notes
Guidance
FT their (a)(i) =
M1 for
Removes all algebraic
fractions
FT their equation if in
comparable form
M1 for
Correctly expands all
brackets
FT their equation if in
comparable form
A1 for
With no errors or
omissions seen and one
further stage seen after
final M1
11(b)(ii)
M2 for
3
M1 for
or
or for
where either ab = –21 or
4b + a = –25
If 0 scored, SC1 for
4x + 3 and x – 7 seen but
not in factorised form
B1 for 7 and
- Mark Scheme
Question
11(b)(iii)
12
Answer
7
oe
Marks
/
AO Element
Notes
Guidance
1
FT their positive
solution
3
M2 for
oe
or M1 for
oe
If 0 scored, SC1 for
oe
13
oe
4
M3 for
oe
or M2 for
oe
or
oe
or M1 for
or
If 0 scored, SC1 for
oe
- Mark Scheme
Question
14(a)
Answer
111.25
Marks
4
/
AO Element
Notes
Guidance
M1 for midpoints soi
(25, 75, 112.5, 137.5,
175)
M1 for ∑ fx with x in
correct interval including
both boundaries
M1 (dep on 2nd M1) for
∑ fx ÷ 20
14(b)
2 7 11 17
14(c)
oe
15(a)
15(b)
oe
14.1 or 14.07…
2
B1 for three correct
1
2
3
M1 for
oe
M2 for
oe
or M1 for
oe
16(a)
14
1
16(b)
16
1
- Mark Scheme
Question
Answer
16(c)
Marks
3
oe
/
AO Element
Notes
M2 for
or M1 for
16(d)
Correct shading
17(a)
oe
or
Guidance
seen
1
1
and
or 0.6 and 0.25
or 60% and 25%
17(b)
oe
3
M2 for
oe
or
oe
or M1 for
or
oe
(but not as part of a larger
product)
- Mark Scheme
Question
18
Answer
Marks
3
oe
/
AO Element
Notes
Guidance
M2 for
oe
or
oe
or M1 for
or
or for a correct tree
showing all 25 outcomes
with the 11 correct
outcomes identified
19(a)(i)
oe
M2
B1 for
oe seen
- Mark Scheme
Question
19(a)(ii)
Answer
oe
Marks
4
/
AO Element
Notes
M3 for
oe
or
oe
or M2 for the sum of two
products of different
flavours isw
or M1 for one correct
product of different
flavours isw
Guidance
- Mark Scheme
Question
19(b)
Answer
oe
Marks
3
/
AO Element
Notes
Guidance
M2 for
oe
or for
oe
or
oe
or M1 for
oe seen
- Mark Scheme
Question
20(a)
Answer
oe
Marks
3
/
AO Element
Notes
M2 for
or M1 for one of these
products
OR
M1 for probability tree
identifying all 20
outcomes with the correct
8 identified
OR
M1 for completed
possibility space / 2-way
table identifying the 8
possible outcomes out of
20, oe
SC1 for
replacement
with
Guidance
- Mark Scheme
Question
20(b)
Answer
oe
Marks
3
/
AO Element
Notes
Guidance
M2 for
oe
or M1 for one of these
products
OR
M1 for probability tree
identifying all 25
outcomes with the correct
9 identified
OR
M1 for completed
possibility space / 2-way
table identifying the 9
possible outcomes out of
25, oe
20(c)
Jojo and e.g.
1
1FT their (a) and (b) dep
on being in range 0 to
1
[Total: 115]
- Mark Scheme
Question
Answer
Marks
1(a)
0.22 oe
2
1(b)
40
1
2(a)
AO Element
/
Notes
M1 for 0.15 + 0.2 + ? +
0.43 = 1 or better
2
B1 for 2 or 3 correctly
completed regions
2(b)
One of 5, 7, 9, 11, 13, 15
1
FT their Venn
diagram
2(c)
12
1
FT their Venn
diagram
1
FT their Venn
diagram
2(d)
oe
1
3(a)(i)
3(a)(ii)
1.62 or 1.623… nfww
4
M1 for 1.35, 1.45, 1.55,
1.65, 1.75 1.85 soi
M1 for Σ fx
M1 dep for their Σ fx ÷
120
Guidance
- Mark Scheme
Question
3(b)(i)
3(b)(ii)
Answer
Marks
/
AO Element
Notes
Guidance
1
oe
oe
4
M3 for
or M2 for
isw
or M1 for
After 0 scored, SC1 for
answer
or
oe
3(c)(i)
55, 79, 106, 120
2
B1 for 2 or 3 correct
- Mark Scheme
Question
3(c)(ii)
Answer
Correct diagram
Marks
3
AO Element
/
Notes
B1 for correct horizontal
plots
B1FT for correct vertical
plots
B1FT dep on at least B1
for reasonable increasing
curve or polygon through
their 6 points
If 0 scored SC1 for 5 out
of 6 points correctly
plotted
3(d)(i)
1.62 to 1.63
1
3(d)(ii)
1.57 to 1.58
2
4(a)
E cao
1
4(b)
H cao
1
5(a)
5(b)
Arrow at
Arrow at
1
1
B1 for 48 soi
Guidance
- Mark Scheme
Question
Answer
6
oe
Marks
3
/
AO Element
Notes
Guidance
M2 for
or M1 for
or
7
72
2
8
0.41
2
9(a)
oe
9(b)
oe
1
1
9(c)
0
1
10(a)
[0].62 oe
1
10(b)
0
1
11
0.73 oe
1
12
48
1
M1 for
oe
M1 for
1 – (0.35 + 0.04 + 0.2)
- Mark Scheme
Question
13
Answer
oe
15(a)
oe
2
Notes
Guidance
oe
M1 for
oe
1
2
15(b)
16(a)
AO Element
1
0
14
Marks
/
2
B1 for 2 or 3 correct out
of 4 regions
B1 for
or
provided
fraction is less than 1
16(b)
46
1
17(a)
4
1
- Mark Scheme
Question
Answer
Marks
17(b)
3 correct bars drawn on bar chart
4
/
AO Element
Notes
B1 for Mr Smith bar
drawn height 15
M2 for
their (80 − (18 +14 +15))
÷ 3[× 2]
or
M1 for
80 − (18 + 14 +15) oe
17(c)
Mrs Brown
17(d)(i)
oe
17(d)(ii)
oe
1
FT their bar chart
provided 5 bars drawn
1
2
FT their bar chart
M1 for 80 − (18 + 14)
or
oe
OR
M1FT for adding heights
of bars for (Mr Jones,
Mrs Brown and Mr
Smith)
17(e)
81
2
M1 for
or
Guidance
- Mark Scheme
Question
18(a)
Answer
Correct bar
Marks
3
/
AO Element
Notes
M1 for 5, 12, 17 or 34
M1 for 40 – their 34
18(b)
5
1
18(c)
Adult
1
18(d)
19(a)(i)
oe
Correct frequencies
FT
1
2
8 5 3 5 2 1
B1 for 1 frequency
incorrect
or 2 incorrect but total
still 24
or 8 5 3 5 2 1 in tally
column
If 0 scored, B1 for
completely correct
tallies
19(a)(ii)
1
1
19(a)(iii)
5
1
19(a)(iv)
2
1
Guidance
- Mark Scheme
Question
19(a)(v)
Answer
2.625
Marks
3
AO Element
/
Notes
M1 for Σ fx
1×8+2×5+3×3+4
×5+5×2+6×1
M1 dep for
their Σ fx ÷ 24
19(a)(vi)
oe
1
FT their table
B1 for 2 or 3 correct bars
or for all 4 heights
correct
19(b)
Correct bar chart
2
19(c)
Correct generalised comparison
1
20(a)
1
20(b)(i)
1
FT their (a) dep on (a)
being an expression in r
Guidance
- Mark Scheme
Question
20(b)(ii)
Answer
Marks
3
M1 for
or better nfww
M1 for
AO Element
Notes
FT their (b)(i)
Strict FT their expansion
to a quadratic then
equating to 0.4 and then
collecting to 3 terms on
‘one side’
OR
OR
oe
A1 for
/
Strict FT their expansion
to a quadratic = 0.4 all
multiplied by 10
no errors or omissions
seen
Guidance
- Mark Scheme
Question
20(b)(iii)
Answer
Marks
3
B2 for
AO Element
/
Notes
or B2 for e.g.
5r(2r – 1) – 9(2r – 1) and
then 5r – 9 = 0
and 2r – 1 = 0
or B1 for
5r(2r – 1) –9(2r – 1)[= 0]
or
2r(5r – 9) –1(5r – 9)[= 0]
or
(5r + a)(2r + b) [= 0]
where a, b are integers
and ab = +9
or 2a + 5b = – 23
If 0 scored, SC1 for
5r – 9 and 2r – 1 seen
but not in factorised
form
B1 for
20(b)(iv)
21(a)
0.8 or
oe
B1 for range = 7
1
6
B1 for mode = 21
B2 for median = 22.5
M1 for evidence of
middle value
M1 for use of Σ x ÷ 14
B2 for mean = 22.7 or 22.71…
21(b)
oe
1
Guidance
- Mark Scheme
Question
22
Answer
oe
Marks
4
/
AO Element
Notes
M3 for
or M2 for
or
or M1 for
seen
or
seen
If 0 scored, SC1 for
oe
23(a)
2
B1 for either numerator
or denominator correct
Guidance
- Mark Scheme
Question
23(b)(i)
Answer
B1 for
Marks
4
/
AO Element
Notes
Guidance
FT their (a)(i) =
M1 for
Removes all algebraic
fractions
FT their equation if in
comparable form
M1 for
Correctly expands all
brackets
FT their equation if in
comparable form
A1 for
With no errors or
omissions seen and one
further stage seen after
final M1
23(b)(ii)
M2 for
3
M1 for
or
or for
where either ab = –21 or
4b + a = –25
If 0 scored, SC1 for
4x + 3 and x – 7 seen but
not in factorised form
B1 for 7 and
- Mark Scheme
Question
Answer
Marks
7
1
24
[0].03 oe
1
25
70
2
Swimming
1
23(b)(iii)
26(a)(i)
26(a)(ii)
26(a)(iii)
oe
5 cao
/
AO Element
Notes
FT their positive
solution
M1 for
25 000 × 0.0028 oe
1
2
M1 for
or
or for
26(a)(iv)
oe
1
FT
oe
26(a)(v)
Tennis, Judo
1
soi by 6
Guidance
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
26(b)
2 sectors drawn:
Running 60°
Swimming 132°
2
M1 for use of 12°
implied by 60° or 132°
seen
or for 10 [boys] or 22
[boys] seen
26(c)
A valid correct similarity and
difference
2
B1 for each
3
M2 for
27
oe
oe
or M1 for
If 0 scored, SC1 for
oe
oe
- Mark Scheme
Question
28
Answer
oe
Marks
4
/
AO Element
Notes
Guidance
M3 for
oe
or M2 for
oe
or
oe
or M1 for
or
If 0 scored, SC1 for
oe
29
30(a)
oe
111.25
1
4
M1 for midpoints soi
(25, 75, 112.5, 137.5,
175)
M1 for ∑ fx with x in
correct interval including
both boundaries
M1 (dep on 2nd M1) for
∑ fx ÷ 20
- Mark Scheme
Question
30(b)
30(c)
31(a)
Answer
2 7 11 17
oe
Arrow at
Marks
2
Clear indication
32(a)
Arrow at 0.2
1
32(b)
0.8 oe
1
33
[0].36 oe
1
34
0.27 oe
2
14.1 or 14.07…
Guidance
B1 for three correct
Clear indication
1
35(b)
Notes
1
Arrow at 0
oe
AO Element
1
31(b)
35(a)
/
2
3
M1 for
1 − (0.2 + 0.45 + 0.08)
oe
M1 for
oe
M2 for
oe
or M1 for
oe
- Mark Scheme
Question
36
37(a)
37(b)
Answer
Marks
2
540
96
144
240
129
131
260
225
275
500
1
/
AO Element
Notes
M1 for
or
both correct
1
50
2
37(c)
B1 for
or
0.45
37(d)
12 : 13
2
B1 for 240 : 260 oe
If 0 scored, SC1 for
answer 13 : 12
37(e)
38(a)
38(b)
Guidance
oe
Negative
oe
1
1
1
or
- Mark Scheme
Question
Answer
Marks
38(c)
Correct ruled line of best fit
1
38(d)
5 or 6
1
39(a)
39(b)
oe
Notes
must be an integer
1
oe
1
40(a)
14
1
40(b)
16
1
40(c)
AO Element
1
0
39(c)
/
oe
3
M2 for
or M1 for
40(d)
Correct shading
1
seen
Guidance
- Mark Scheme
Question
Answer
Marks
AO Element
/
Notes
Guidance
[Total: 174]
- Mark Scheme
Question
1
Answer
Marks
3
12.8
4.4
0.8
Notes
B2 for 2 correct heights
or 3 correct frequency
densities
or B1 for 1 correct height
or 2 correct frequency
densities
1
2(a)(i)
2(a)(ii)
AO Element
/
1.62 or 1.623… nfww
4
M1 for 1.35, 1.45, 1.55,
1.65, 1.75 1.85 soi
M1 for Σ fx
M1 dep for their Σ fx ÷
120
2(b)(i)
oe
1
Guidance
- Mark Scheme
Question
2(b)(ii)
Answer
oe
Marks
4
/
AO Element
Notes
Guidance
M3 for
or M2 for
isw
or M1 for
After 0 scored, SC1 for
answer
or
oe
2(c)(i)
55, 79, 106, 120
2
B1 for 2 or 3 correct
2(c)(ii)
Correct diagram
3
B1 for correct horizontal
plots
B1FT for correct vertical
plots
B1FT dep on at least B1
for reasonable increasing
curve or polygon through
their 6 points
If 0 scored SC1 for 5 out
of 6 points correctly
plotted
- Mark Scheme
Question
Answer
Marks
AO Element
/
Notes
2(d)(i)
1.62 to 1.63
1
2(d)(ii)
1.57 to 1.58
2
B1 for 48 soi
Correct histogram
4
B1 for each correct
block
3
Guidance
If 0 scored, SC1 for 5,
20, 24, 1 seen
4
16.6 or 16.60 to 16.61 nfww
4
M1 for 5, 12.5, 17.5,
22.5, 30 soi
M1 for Σ fx where x is in
correct interval, including
boundaries
M1 dep on second M1
for
5
Fully correct histogram
4
B1 for each correct bar
If 0 scored, SC1 for
frequency densities of
5.4, 4.2, 0.8 and 0.45
seen
[Total: 33]
- Mark Scheme
Question
Answer
Marks
AO Element
/
Notes
1(a)
Kite
1
1(b)(i)
Translation
2
B1 for each
1(b)(ii)
Reflection
2
B1 for each
3
B1 for each
x = 0.5 oe
1(b)(iii)
Rotation
90° clockwise oe
[centre] (0, 0) oe
1(c)(i)
(−5, −6)
1
1(c)(ii)
Image at (−5, 0), (−2, 3), (7, 0),(−2,
−3)
2
B1 for correct size,
wrong position
or correct shape with
incorrect scale factor
2(a)
Triangle at (–4, –4) (–1, –3) (–4,
–3)
2
B1 for correct points not
joined
or for reflection in any y
=k
or for reflection in x =
–1
Guidance
- Mark Scheme
Question
2(b)
Answer
Triangle at (1, 1) (1, 4) (2, 4)
2(c)
Marks
AO Element
/
Notes
2
B1 for correct points not
joined
or rotation 90° clockwise
around any point
or rotation 90°
anticlockwise around (0,
0)
2
B1 for translation or
correct vector oe
Translation
3(a)
Translation
2
B1 for each
3(b)
Correct reflection at
(6, 2), (6, 6), (7, 6), (7, 3)
2
B1 for three correct
vertices
4(a)(i)
Rotation
3
B1 for each
3
B1 for each
90° clockwise oe
[centre] (0, 0) oe
4(a)(ii)
Enlargement
[sf] 0.5 oe
[centre] (1, 2)
Guidance
- Mark Scheme
Question
4(b)(i)
Answer
Triangle at (3, 2) (1, 5) (1, 2)
Marks
2
/
AO Element
Notes
B1 for translation of
or
4(b)(ii)
Triangle at (–3, –2) (–5, –2)
(–5, –5)
2
B1 for reflection in y = k
or x = 1
5(a)
Rotation
3
B1 for each
3
B1 for each
90° clockwise oe
(1, 0)
5(b)
Enlargement
−2
(0, 2)
6(a)
Trapezium
1
6(b)(i)
16 or 15.8 to 16.2
1
6(b)(ii)
14
1
6(c)(i)
Translation
2
B1 for each
Guidance
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
6(c)(ii)
Rotation
90° clockwise oe
[about] (0, 0) oe
3
B1 for each
6(d)(i)
Correct shape
Vertices
(−1, 4), (−1, 6), (−5, 6), (−5, 1)
2
B1 for reflection in x = k
or y = 1
6(d)(ii)
Correct shape
Vertices
(3, 0.5), (3, 3), (1, 3), (1, 2)
2
B1 for any enlargement,
SF with different
centre
7(a)
Rotation
3
B1 for each
3
B1 for each
2
B1 for a correct
translation of
[centre] (0, 0) oe
90[°] clockwise oe
7(b)
Enlargement
[centre] (5, −7)
[sf =] 3
7(c)
Correct shape plotted with points
(6, −1) (8, −1) (6, −3) (8, −3)
(6, −5)
or
7(d)
Correct shape plotted with points
(−2, 5) (−6, 5) (−2, 7) (−4, 5)
(−4, 7)
2
B1 for reflection in y = k
or x = 1
Guidance
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
8(a)(i)
16
1
8(a)(ii)
12
1
8(b)(i)
(5, 2)
1
8(b)(ii)A
(−5, 2)
1
8(b)(ii)B
(5, 10)
2
B1 for (5, k) or (7, 2)
2
FT their (b)(i)
8(b)(iii)
B1 for
or
or
or
8(c)(i)
Enlargement
(SF) 0.5 oe
(centre) (−3, 1)
3
B1 for each
Guidance
- Mark Scheme
Question
8(c)(ii)
Answer
Rotation
Marks
AO Element
/
Notes
3
B1 for each
2
B1 for translation by
Guidance
180°
(centre) (4, 8)
9(a)
Image at (1, 7), (4, 7), (4, 9),
(3, 9)
or
9(b)
Image at (5, 3), (6, 3), (8, 5),
(5, 5)
2
B1 for 180° rotation with
wrong centre
9(c)
Rotation
180°
(4.5, 6)
3
B1 for rotation
B1 for 180°
B1FT for centre from
their (a)
OR
Enlargement
[factor] –1
(4.5, 6)
10
Image at (1, 2), (1, 5), (3, 5),
(3, 4)
B1 for enlargement
B1 for –1
B1FT for centre from
their (a)
2
B1 for y = x drawn
or for 3 correct points
[Total: 82]
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
1
1(a)
cao
1(b)
4.47 or 4.472…
2
M1 for
1(c)
(7, 10)
2
B1 for each
1(d)
y = 2x − 4 oe
3
M1 for gradient =
oe
or answer y = mx – 4
M1 for substituting (3, 2)
or (5, 6)
into y = their mx + c or
into y – k = their m(x – h)
or into their y = mx – 4
1(e)
(0, –4)
1
2(a)
(–2, 5)
1
1
2(b)
2(c)
(5, 4) plotted
1
FT their (d)
Guidance
- Mark Scheme
Question
2(d)
Answer
B1 for parallelogram PQRS
correctly drawn
Marks
2
B1 for (1, 7)
AO Element
/
Notes
FT their R
FT their S dep on first B1
3(a)
(5, 3)
1
3(b)
Point plotted at (4, −3)
1
3(c)
1
4(a)
1
4(b)
1
5(a)
1
5(b)
1
FT their (a)
Guidance
- Mark Scheme
Question
6
Answer
Marks
/
AO Element
Notes
2
B1 for
or
7(a)
1
7(b)
1
8(a)
1
8(b)
1
9(a)
2
or
or
B1 for answer
or
or for
seen
or
Guidance
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
9(b)
3.61 or 3.605 to 3.606
2
M1 for
oe
9(c)
B1 for
and
5
Accept equivalents
B4 for
and
with evidence of a correct algebraic
method
M1 for correctly equating
one set of coefficients of
their equations
or rearranges one of their
equations to make m or n
the subject e.g.
oe
M1 for correct method to
eliminate one variable for
their equations
or correctly substitutes
their m or their n into the
other equation e.g.
oe
B1 for one correct
answer
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
10(a)
2
M1 for correct
unsimplified form or
correct route e.g.
10(b)(i)
2
M1 for correct
unsimplified form or
correct route e.g.
10(b)(ii)
3 : 2 oe
2
11(a)(i)
–a + 2c
1
11(a)(ii)
or
oe
1
B1 for
oe or
FT
in
simplest form
11(a)(iii)
or
11(a)(iv)
11(b)
or
4
1
oe
oe
2
1
M1 for a correct
unsimplified route
- Mark Scheme
Question
12(a)
Answer
12.6 or 12.64 to 12.65
Marks
3
/
AO Element
Notes
Guidance
M2 for 122 + (−4)2
OR
B1 for
M1 for
2
12(b)
B1 for
or
or for
13(a)
13(b)
14(a)
oe
oe
oe simplified
2
M1 for correct
unsimplified answer or
correct route
2
M1 for correct
unsimplified answer or
correct route
2
M1 for a correct
unsimplified answer or a
correct route
- Mark Scheme
Question
14(b)
Answer
oe simplified
2
AO Element
Notes
M1 for a correct
unsimplified answer or a
correct route
1
15(a)
15(b)
Marks
/
oe simplified
3
M2 for correct
unsimplified e.g.
or
or M1 for a correct route
e.g.
or
or
16(a)
oe simplified
2
M1 for correct
unsimplified answer
or
or
or for a correct route
Guidance
- Mark Scheme
Question
Answer
Marks
2
16(b)
/
AO Element
Notes
Guidance
B2FT for
(a) is
if their
oe
M1 for
(a)
or
or
(a)
or
or
oe
17(a)
6a – 2b or 2(3a – b)
2
M1 for
4a + b – (–2a + 3b) or
better
17(b)
5a – b
2
M1 for a correct route
e.g.
,
,
18(a)
oe
2
M1 for any correct route
eg
or B1 for
oe
- Mark Scheme
Question
Answer
18(b)
oe simplified
Marks
2
/
AO Element
Notes
Guidance
FT their (a) + a
simplified only if in
terms of a and b.
M1 for for identifying
as position vector or
correct route in any form
or for correct
unsimplified answer
2
19
M1 for a correct route or
for
20
21
26
2
M1 for
better
2
M1 for a correct route
or
[Total: 83]