- Mark Scheme
Question
1
Answer
Marks
5
M2 for
or
/
AO Element
Notes
M1 for
oe
or
seen oe
M1 for
or
or for correct factors for
their 3-term quadratic
equation
B2 for x = −2
x=6 y=3
or for correct substitution
into quadratic formula or
correctly completing the
square for their 3-term
quadratic equation
y=7
B1 for x = −2, x = 6
or for y = 7, y = 3
or for one correct pair of
x and y values
2
oe
3
M1 for
M1 for
Guidance
- Mark Scheme
Question
3
Answer
M2 for
or
Marks
5
AO Element
/
Notes
M1 for correct method to
eliminate one variable
e.g.
or
M1 for
or
or for correct factors for
their quadratic equation
or for correct use of
quadratic formula for
their quadratic equation
or for correctly
completing the square for
their quadratic
equation
B2 for
x = 4, y = − 1
x = −10, y = 41
B1 for x = 4, x = − 10 or
for y = − 1, y = 41
or for a correct pair of x
and y values
If B0 scored and at least
1 method mark scored
SC1 for correct
substitution shown of
both of their x values or
their y values into
or
4(a)
1[.0] 0.9
2
B1 for each
Guidance
- Mark Scheme
Question
4(b)
Answer
correct curve
Marks
4
AO Element
/
Notes
B3 FT for 6 or 7
points
B2 FT for 4 or 5
points
B1 FT for 2 or 3
points
4(c)
B1 for ruled line at y = −1
2
B1 for 0.3 to 0.32
5(a)
169
2
5(b)
1 + 4x 2 final answer
1
5(c)
x
1
M1 for g(13) or (1+ 4x)2
or better
Guidance
- Mark Scheme
Question
6
Answer
a = −12
Marks
6
/
AO Element
Notes
B5 for 2 correct
b=5
OR
k = −11
B2 for 3x 2 + a
or B1 for 3x 2 isw
M1dep on at least B1 for
M1dep on at least B1M1
for x = 2 or x = −2
substituted in
equation
M1 for
and
7
correct shape and passes through
origin
3
B1 for any positive cubic
shape
B1 for sketch with one
max and one min and
with 3 roots including
zero
If 0 scored, SC1 for
soi
Guidance
- Mark Scheme
Question
Answer
8
or
Marks
final
4
answer
/
AO Element
Notes
M1 for clearing g – c
from denominator
e.g.
M1 for correctly isolating
terms in g in numerator
on one side
M1 for correctly
factorising or
simplifying, to single
term in g in an
equation
M1 for correctly dividing
by bracket to final
answer
9
final answer
3
B1 for
B1 for
10
final answer
3
B2 for correct expansion
of three brackets
unsimplified or for
simplified expression of
correct form with 3 out
of 4 terms correct
or B1 for correct
expansion of 2 of the 3
given brackets with at
least 3 terms out of four
correct
Guidance
- Mark Scheme
Question
Answer
11(a)
Marks
3
oe isw
/
AO Element
Notes
B2 for
Guidance
oe
isw
OR
B1 for
seen
B1 for time = 2.8 or
or
11(b)
M2 for
4
or better
oe
FT their time, provided
2 algebraic fractions one
in x and other in ± x ±
10
M1 for
seen or better
M1 for
A1 for
or
better
leading to
oe
or
FT their equation dep on
M2
with no errors or
omissions
- Mark Scheme
Question
11(c)
Answer
B2 for
Marks
4
/
AO Element
Notes
Guidance
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
11(d)
84 to 84.01…
2
FT
to
3 sf or better
M1 for
oe
12
256a 4 b 20 final answer
2
B1 for two correct
elements in final
answer
- Mark Scheme
Question
13
Answer
Marks
5
x = 3, x = –3
nfww
/
AO Element
Notes
Guidance
M2 for
oe or better
or M1 for
or
oe or better
B1 for
seen
M1 dep for
oe
simplified or better
14
15
1
27
final answer
2
M1 for
oe
or better
16(a)
final answer
2
M1 for
better
16(b)
or 0.25
1
oe or
- Mark Scheme
Question
Answer
Marks
/
AO Element
Notes
Guidance
17
–1, 0, 1 final answer
2
B1 for
or two correct answers
and no extras
or three correct answers
and one extra/wrong
18
0 and 4 final answer
4
B3 for
better
or
or B2 for
or B1 for
19
final answer
4
or
M1 for expanding
brackets or ÷ g
M1 for isolating terms in
h
M1 for factorising
M1 for dividing by
bracket to isolate h
Incorrect/unsimplified
final answer scores max
3 marks
20
24
3
M1 for
oe
M1 for
oe
- Mark Scheme
Question
Answer
21
Marks
4
final answer
/
AO Element
Notes
B2 for
or B1 for
where ab = –12 or
or
or
B1 for
22
final
answer
3
B2 for unsimplified
expansion with at most
one error
or
for simplified four-term
expression of correct
form with three terms
correct
or B1 for correct
expansion of two
brackets with at least
three terms out of four
correct
Guidance
- Mark Scheme
Question
23
Answer
[x =] –2.1 oe
Marks
4
/
AO Element
Notes
Guidance
M3 for
or
better
OR
M1 for
or
better
M1 for
better
or
If 0 scored SC1 for
answer
oe
24
6
2
M1 for 3 k ÷ 3 t = 32 or
38 ÷ 3 t = 3 k oe or better
or 3 t = 729 oe
25
Correct sketch
2
B1 for correct shape but
crossing x-axis or for
correct shape but just
drawn in one quadrant
- Mark Scheme
Question
Answer
Marks
26
Correct sketch
2
27(a)
12
1
27(b)
144
2
AO Element
/
Notes
B1 for one correct branch
or attempt at correct
shape
FT 12 × their V
M1 for any relevant area
FT their V
28(a)
2
Correct sketch
y
B1 for one correct branch
or attempt at correct
shape
Guidance
- Mark Scheme
Question
28(b)
Answer
Marks
Correct sketch
AO Element
/
Notes
2
B1 for correct shape but
crossing x-axis or correct
shape but just in one
quadrant
y
x
29
oe
2
M1 for any quadratic or
second differences = 2
30
49x 6 final answer
2
B1 for 49xk or nx 6 as
final answer
Guidance
- Mark Scheme
Question
31
Answer
3 correct ruled lines
and R clearly indicated
Marks
5
/
AO Element
Notes
B1 for each line
y = 1 dashed
y = 2x + 2 dashed
x + y = 3 solid
B2 for correct region
or B1 for region
satisfying 2
inequalities
or SC1 for shading of the
wanted region only
5
32
oe
B2 for
or B1 for
or
M1 for their derivative =
0 oe or
B1 for
and
or for 1 correct
coordinate pair
Guidance
- Mark Scheme
Question
33
Answer
M2 for
or
M1 for
or
B2 for [x =] 12 [y =] 5
and [x =] −13 [y =] −20
Marks
5
AO Element
/
Notes
M1 for
or correct substitution
or for correct factors for
their quadratic equation
or for correct use of
quadratic formula or
completing the square for
their equation
B1 for x = 12, x = −13
or for y = 5, y = −20
or for a correct pair of x
and y values
If B0 scored and at least
2 method marks scored
SC1 for correct
substitution of both of
their x values or
their y values into
or
Guidance
- Mark Scheme
Question
Answer
34
Marks
final
3
answer
AO Element
/
Notes
Guidance
B2 for correct
unsimplified expansion
or simplified expression
with 3 terms correct in a
4-term expression of
required form
or B1 for correct
expansion of two of the
brackets with at least 3
terms correct
35
final answer
2
M1 for answer in form (a
+ b) (a – b)
or B1 for correct answer
seen
36
17
3
M2 for
better isw
or
or M1 for
oe or
seen
37(a)(i)
[a = ] 4
2
B1 for [b = ] –3 nfww
[b = ] –3 nfww
37(a)(ii)
y = 4 oe
B1 for [a = ] 4
1
- Mark Scheme
Question
Answer
Marks
AO Element
/
Notes
37(a)(iii)
y = −6x + 7 oe final answer
2
B1 for answer −6x + 7
or answers y = −6x + c or
y = kx + 7 (k < 0)
37(b)(i)
2.25 2.67 3.5
3
B1 for each
37(b)(ii)
correct curve
4
B3 FT for 7 or 8
points
or B2 FT for 5 or 6
points
or B1 FT for 3 or 4
points
37(c)(i)
–0.78 to –0.72 and 0.55 to 0.59
2
B1 for each
Guidance
- Mark Scheme
Question
Answer
37(c)(ii)
Marks
final
4
answer
/
AO Element
Notes
B3FT for 3 out of 4
correct terms
or for
oe
or B2FT for 2 out of 4
correct terms
or for 3 out of 4 terms
from
or M1 for
oe
38
final
answer
2
M1 for correct partial
factorisation by 5 or
isw
eg
or
or
or
or B1 for correct answer
seen
Guidance
- Mark Scheme
Question
Answer
39
Marks
final answer
2
/
AO Element
Notes
M1 for
or
or B1 for correct answer
seen
40(a)
40(b)
final answer
M1 for
oe
M2 for
oe
A1 for
oe
leading to
1
Accept 48 ÷ x
4
FT their (a) provided
expression in x
FT their 3 term eqn with
algebraic denominators,
x and x + 2, for M2 or
M1
M1 for common
denominator x(x + 2) oe
seen
or any two terms in a 3
term equation from
,
,
oe seen
With brackets expanded
and no errors or
omissions seen
Guidance
- Mark Scheme
Question
40(c)
Answer
B2 for
Marks
3
/
AO Element
Notes
B1 for
or
or
where
B1 for 3 and −8
Guidance
or
[a, b
integers]
40(d)
12
1
[Total: 165]