- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
1(a) Tangent 1
1(b)(i) final answer 2 M1 for
1(b)(ii) 40 2 B1 for angle OBC = 40°
or angle BOG = 140°
1(b)(iii) 7.68 or 7.679 to 7.680.... 2 FT their (b)(ii) and (b)(i)
M1 for
1(c)(i) Angle [between] tangent [and] 1
radius
1(c)(ii) B1 for 180 – 140 or 90 – their 3
(b)(ii)
M1 for
oe
A1 for [BC =] 13.109[...]
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
1(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
2(a) Pentagon 1
2(b) 12 2 B1 for 10 to 14
2(c)(i) Translation 2 B1 for each
2(c)(ii) Rotation 3 B1 for each
[centre] (0, 0) oe
180°
2(c)(iii) Enlargement 3 B1 for each
[centre] (4, 2)
[scale factor] 0.5 oe
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
2(d) Correct reflection 2 B1 for a correct reflection
(−2, −2), (−1, −4), (−2, −6), (−4, in x = 0 or in y = k k ≠
−6) (−6, −4) 0
or for 4 correct points
3(a) 5.83 or 5.832 to 5.833 5 B2 for sector angle = 210
soi
or M1 for
oe
M2 for
oe
or M1 for
oe isw
3(b) 1.21 or 1.208… 3 M2 for
oe
or M1 for
oe isw
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
3(c)(i) 4[.00...] 3 M2 for
oe
or M1 for
or
or for
oe
3(c)(ii) 2.20704 3 M2 for
77.44 × 1.5 × 19 ÷ 1000
oe
or M1 for figs 2207[04]
or figs 221 seen
or [vol =] 77.44 × 1.5
4(a) 4.79 or 4.788 to 4.789 3
M2 for oe
or M1 for
oe
If 0 scored SC1 for
answer 3.8[0…]
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
4(b)(i) 8.7[0] or 8.702 to 8.704 3 M2 for
(300 − 230) ÷ (1.62 )
or M1 for ×1.62 × h
4(b)(ii) 6.4 3 M2 for
oe
or M1 for sf
or oe
or for
5(a) Similar 1
5(b) 4 2
M1 for oe or
better
If 0 scored SC1 for
answer 3.5
5(c)(i) 6.7265 or 6.73 or 6.726 to 6.727 2 M1 for scale factor 22 or
oe soi
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
5(c)(ii) 13.453 or 13.5 or 13.45 to 13.46 1 FT their (c)(i) × 2
6(a) 750 1
6(b) 4.7 cao 3 B2 for 4.658 to 4.66 or
M2 for
or M1 for 11π r 2 = their
(a)
6(c) 6 2
M1 for 23 or oe seen
or for π × (2× their (b))2
× 22
7(a) 1 Accept
oe
or
7(b)(i) 3
M2 for oe M1 for
oe
or
or
A1 for 11.59...
7(b)(ii)A 72.8 or 72.9 or 72.82 to 72.89… 2 M1 for
7(b)(ii)B 12.1 or 12.06 to 12.08 2 M1 for [6 +] their
(b)(ii)(A) ÷ 12 oe
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
7(c) 806 or 807 or 805.9 to 807.4 3 B2 for 402.9… to
403.7
OR
M2 for
e o
or M1 for
oe
8(a) 7.06 or 7.058… or 7.059 3 M2 for
oe
OR
M1 for
oe
A1 = 49.8...
8(b)(i) 97 1
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
8(b)(ii) 15.3[0…] 3 M2 for
or M1 for
oe
8(c) 72.8 to 72.81… 3 M2 for
oe
or M1 for
oe
or
oe
or M1 for height =
oe
9(a) Angle [in] semi-circle [is 90] 1
9(b)(i) 67.4 or 67.38….. 2
M1 for or
better
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
9(b)(ii) 2 M1 for
9(b)(iii) 480 2 M1 for 0.5 × 20 × 48 or
better
9(b)(iv) 582 or 581.8 to 582.0 3 M1 for
or
better
M1 for their 338 – their
(b)(iii)
10(a)(i) 42.8 or 42.79 … nfww 4 M1 for mid-values soi
M1 for Σ fm where m is
any value in interval
including boundaries
M1 (dep on second M1)
for their Σ fm ÷ 120
10(a)(ii) Blocks of height 1.8 4.4 8 2.1 with 4 B1 for each correct
correct widths block
If B0, SC1 for correct
frequency densities
seen
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
10(b) Valid general comment about 1 e.g. [On average],
distributions shoppers spend less time
shopping on Wednesday
oe
11(a) B1 for range = 7 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…
11(b) 1
oe
12(a) 16 1
12(b) 50 1
12(c) 2 FT their (b) for 1 or 2
oe
marks
B1 for ,k>4
or , k < 50
12(d) 19 1
13(a)(i) –a + 2c 1
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
13(a)(ii) 1
or oe FT in
simplest form
13(a)(iii) 1
or oe
13(a)(iv) 2 M1 for a correct
or oe
unsimplified route
13(b) 4 1
14(a) −3 1
14(b) 2
oe M1 for soi
14(c) final answer 2 M1 for
isw
14(d) 2 M1 for a correct first step
oe final answer
,
or
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
14(e) 3 M1 for
final answer oe
isw
B1 for common
denominator
14(f)(i) M1 for 3
B1 for
A1 for
with no errors and must
oe show
leading to with no omissions after
this
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
14(f)(ii) B2 for 4 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
15(a) 4 1
15(b) 52 2 M1 for f(8) seen or
15(c) 1
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
15(d) 3 M1 for
or
final answer
B1 for denominator
or
15(e) −3 2 M1 for
15(f) [p =] 0 and [p =] 1 2 B1 for each
16(a) 3
oe isw B2 for oe
isw
OR
B1 for seen
B1 for time = 2.8 or
or oe
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
16(b) M2 for 4 FT their time, provided
2 algebraic fractions one
or better in x and other in ± x ±
10
M1 for
seen or better
M1 for
FT their equation dep on
A1 for oe M2
or or
better
leading to with no errors or
omissions
16(c) B2 for 4 B1 for
or better
oe
or for or
B2 for 5 and 8.57 or 8.571…
B1 for each
or SC1 for final answers
5 and –8.57
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
16(d) 84 to 84.01… 2 FT
to
3 sf or better
M1 for
oe
17(a)(i) 1
17(a)(ii) 1
17(b) 4 FT their (a)(i) and (a)(ii)
M1 for oe
if expressions in m
M1 for Dependent on M1 and
correct fractions
oe
A1 for
oe nfww
A1 for correct completion to
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
17(c)(i) 3.6 and −4.5 final answer 3 B2 for
or
or better
or B1 for
where ac = 10 and
either bd = −162
or ad + bc = 9
or for
or better or or
better
17(c)(ii) 20 1
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
18(a) 20.8 or 20.76 to 20.79 4 B3 for [BC =] 10.4 or
10.38 to 10.39… or
oe
or M2 for
oe
or M1 for oe
or oe
or oe or
oe
or SC2 for final answer
of or 26.8 or
26.83…
OR
M3 for
oe
or M2 for
or M1 for oe or
oe
or oe
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
18(b) 14.5 or 14.47 to 14.48 3
M2 for
oe
or M1 for recognising the
correct angle GAC
19(a) 4.455 to 4.456… [= 4.46] 2
M1 for oe
19(b) 1250 or 1247 to 1249.9… 2 M1 for
oe
19(c) 66[.0] or 65.95 to 66.02 3 M2 for
oe
or B1 for identifying
angle ANB on cylinder
not on rectangle
20(a) 3 1
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
20(b) 51.3 or 51.30 to 51.34… 4
M3 for
or
oe
or M2 for or
or M1 for angle ARB
clearly indicated
21(a) Correct sketch 2 B1 for one correct branch
or correct sketch but with
branches joined
21(b) 11.3 or 11.30 to 11.31 2 B1 for each
and If 0 scored SC1 for two
answers with a difference
191.3 or 191.30 to 191.31
of 180°
22(a) Correct sketch 2 B1 for correct shape but
inaccurate
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
22(b) Rotational [symmetry] order 2 2 B1 for rotational
[centre] (180, 0) [symmetry]
23(a) 2 B1 for linear equation
with positive gradient or
intercept 5
23(b) oe 2 B1 for recognition of sin
or cos(x – 90)
24(a) 70 or 70.16[5…] or 70.17 or 70.2 3 M2 for
or
or
or B1 for 29 750 or
29 850 or 29 849 or 375
or 425 or 424 seen
24(b) 2399 2 B1 for 27 450 or 27 550
or 27 549 or 29 850 or
or 2400 nfww
29 849 seen
25 70 nfww 3 M2 for
(600 + 2.5) ÷ (9 – 0.5)
or B1 for one of
600 + 2.5
or 9 – 0.5 seen
- Mark Scheme /
Question Answer Marks AO Element Notes Guidance
26(a) 245 1
26(b) 8 2 M1 for 40 + 26.5x = 252
oe
or B1 for 212 seen
26(c) 6 2 M1 for (224 − 2 × 48 ) ÷
32 oe
or 2 × 48 + 32(x – 2) =
224 soi
26(d) 35 : 36 : 32 final answer 2 B1 for their (a) : 252 :
224 or equivalent ratio
27(a) 2.25 final answer 2
M1 for or
oe
27(b) 37.5 1
FT their
27(c) 5.5[0] or 5.499 to 5.500 2 M1 for 6 ÷ 1.091
[Total: 222]
