- Mark Scheme /

Question Answer Marks AO Element Notes Guidance

1 5 2 M1 for correct trial to at

least two balls one of
which is not green

2(a) 3, 5, 28, 14 correctly placed 2 B1 for 28 in the

intersection

2(b) 1 FT their 28 where their

oe
28 < 50

2(c) 2
oe M1 for

2(d) 2 FT their 28
oe
M1 for

3(a)(i) 2 B1 for one correct pair

3(a)(ii) 2 FT their tree diagram

oe
M1 for
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

3(a)(iii) 3
oe M2 for

or M1 for or

3(b) 3
oe M2 for
oe

or M1 for

3(c) 2
oe M1 for

4 3 M2 for
oe

or M1 for

or

5(a) 2
oe B1 for or provided
fraction is less than 1
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

5(b) 46 1

6(a) 14 1

6(b) 16 1

6(c) 3
oe M2 for

or M1 for seen

6(d) Correct shading 1

 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

7 4 M3 for
oe

oe
or M2 for

oe or

oe

or M1 for or

or or

oe

If 0 scored, SC1 for

oe

8(a) 1

8(b) 22 1
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

8(c) 2 M1 for
oe
or

or or

or for 8 and 23
identified

9(a) 1

9(b) 3
oe M2 for
oe

or M1 for
oe

If 0 scored SC1 for

 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

10 4 0.712[1…]
oe
M3 for

oe
or

oe
or M2 for sum of 3 or
more correct product
pairs and no incorrect
pairs
or for

and no other pairs

or M1 for
seen
If 0 scored SC1 for
answer oe

11(a) 2
cao M1 for
oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

11(b) 3 M2 for
oe
or

oe

or M1 for either or

or or

If 0 scored, SC1 for

answer oe

12(a) oe 1

12(b) 28 1

12(c) 1
oe

12(d) 3
oe M2 for

or M1 for or

for and seen

If 0 scored SC1 for

answer oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

13 3 M2 for
oe

or M1 for or

If 0 scored, SC1 for

oe

14 0.845 oe 3 M2 for 0.7 × 0.95 + (1

– 0.7) × 0.6 oe
or M1 for one of these
products

15(a) 1
oe

15(b) 3 M2 for addition of two of

or M1 for one of the

products seen
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

15(c) 4 M3 for
oe

oe
or

or M2 for the sum of at

least two of
,

seen

or for

or

seen
or M1 for
or

or
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

seen

If 0 scored SC1 for

oe

16(a)(i) 1

16(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

16(b)(i) 1
oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

16(b)(ii) 4 M3 for
oe

or M2 for
isw

or M1 for

After 0 scored, SC1 for

answer
or
oe

16(c)(i) 55, 79, 106, 120 2 B1 for 2 or 3 correct

16(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 Guidance

16(d)(i) 1.62 to 1.63 1

16(d)(ii) 1.57 to 1.58 2 B1 for 48 soi

17 2
oe M1 for oe

18 4 M3 for
oe

or M2 for

or

or M1 for
seen

or seen

If 0 scored, SC1 for

oe

19(a) 2 B1 for either numerator

or denominator correct
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

19(b)(i) 4
B1 for 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

19(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 AO Element Notes Guidance

19(b)(iii) 7 1 FT their positive

solution

20 3 M2 for
oe
oe

or M1 for oe

If 0 scored, SC1 for

oe

21 4 M3 for
oe

oe
or M2 for
oe

or oe

or M1 for

or

If 0 scored, SC1 for

oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

22(a) 2
oe M1 for oe

22(b) 14.1 or 14.07… 3 M2 for

oe

or M1 for
oe

23(a) 1
oe

or and
or 0.6 and 0.25
or 60% and 25%

23(b) 3
oe M2 for
oe
or
oe

or M1 for or

oe
(but not as part of a larger
product)
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

24 3
oe M2 for
oe
or
oe

or M1 for or

or for a correct tree

showing all 25 outcomes
with the 11 correct
outcomes identified

25(a) 2
oe M1 for oe

If 0 scored, SC1 for

answer oe

25(b) 0 1
Accept

26(a)(i) M2
oe B1 for oe seen
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

26(a)(ii) 4 M3 for
oe

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
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

26(b) 3 M2 for
oe

oe
or for
oe
or

oe

or M1 for
oe seen

27 3
oe M2 for oe

or oe

or M1 for or

or
oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

28(a) 2
oe M1 for or
better

28(b) 3
oe 3FT
correctly evaluated
M2 for

oe

or M1 for or

29(a) 3 B1 for each pair

29(b) 2 M1FT for

oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

29(c) 3 M2 for
oe
+

oe

or M1 for
or

oe

30(a) 3
oe 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 with

replacement
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

30(b) 3
oe 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

30(c) 1 1FT their (a) and (b) dep

Jojo and e.g.
on being in range 0 to
1
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

31 3 M2 for
oe

oe
or M1 for any one correct
product
OR
M1 for 4, 5, 4 and 5, 4, 4
and 5, 5, 4 clearly
identified on a tree or in
a list

32(a) 1
oe

32(b)(i) 2
M1 for

A1 for oe
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

32(b)(ii) 4 M3 for
oe

oe
or M2 for

or

oe
or M1 for for one correct
product other than

33(a) 0.16 oe 2 M1 for 0.4 × 0.4

If zero scored SC1 for
fully correct evaluated
method involving a
without replacement
method
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

33(b) 0.58 oe 4 M3 for

e o
or
M2 for

ALT method
M3 for
0.4× (0.5 + 0.1) + 0.5 ×
(0.4 + 0.1) + 0.1× (0.4 +
0.5) oe
or
M2 for addition of any
three of:
0.4 × 0.5, 0.4 × 0.1, 0.5
× 0.4, 0.5 × 0.1, 0.1 × 0.4
and 0.1× 0.5
or
M1 for addition of any
two of:
0.4× 0.5, 0.4× 0.1, 0.5×
0.4, 0.5× 0.1, 0.1× 0.4
and 0.1× 0.5
If zero scored SC2 for
fully correct evaluated
method involving a
without replacement
method
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

34 0.96 oe 3 M2 for 1 − 0.2 × 0.2 or

0.8 + 0.2 × 0.8
or 0.8 × 0.8 + 0.8 × 0.2
+ 0.2 × 0.8
or B1 for one of
0.2 × 0.2 , 0.8 × 0.8, 0.8
× 0.2, 0.2 × 0.8 seen

35(a) 2 B1 for one correct

oe on all late branches
vertical pair oe and
oe on all not late branches oe

35(b) 2 FT their tree

oe
M1 for

36(a) 2
5 probabilities oe B1 for on first branch

correctly on the branches towards Blue or one

correct pair on the second
branch

36(b) 2 FT their tree diagram for

oe
2 marks
M1 for
 - Mark Scheme /

Question Answer Marks AO Element Notes Guidance

37(a) 1
oe

37(b) 2
oe M1 for or

37(c) 0 1

[Total: 193]