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A comprehensive mark scheme for paper 2h-3h of a mathematics practice test set. It includes detailed solutions, performance data, and suggested grade boundaries, offering valuable insights for students preparing for their exams. A wide range of mathematical concepts and problem-solving techniques, making it a valuable resource for students seeking to improve their understanding and exam performance.
Typology: High school final essays
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Q Working Answer Mark Notes
1 7200 × 0.025 (= 180) 3 M1 M2 for
or 7200 × 1.025 (= 7380) oe 7200 × (1.025)
3
or 7200 × 1.075 (= 7740) oe
or 7200 × 0.075 (= 540) oe
(7200 + ‘180’) × 0.025 (= 184.5) M1 NB year end
and values are
(7200 + ‘180’ + ‘184.5’) × 0.025 (= 189.1125) 7380 and
and 7564.5(0)
7754 A1 answer in range 7753 – 7754
Total 3 marks
2 (a) 1 – (0.24 + 0.16 + 0.38) oe 2 M
0.22 A1 oe
(b) 0.24 + 0.16 (= 0.4) oe 2 M
0.4 A1 oe
Total 4 marks
Q Working Answer Mark Notes
3 (a) 720 ÷ 12 (= 60) or 78 × 12 (= 936) 4 M
or ‘936’ – 720 (= 216)
' x ' ´ 720 = 936
or 720(1+ ) = '936 '
or (' x ' =) (= 1.3) oe
or
'1.3'´ 100 - 100 oe
or (1.3 - 1) ´ 100
M1 complete method to find P
30 A1 ignore extra % sign if given by
candidate.
(b) 0.18 × 1600 (= 288) oe 3 M1 if 1600 × 18% M2 for 1.5 ×
or 0.82 × 1600 + 800 (= 2112) seen, must have further 12.5 (= 18.75)
processing of the 18% or
or the value (288) 18 ÷ 1.5 (= 12)
given.
0.125 × (1600 + 800) (= 300) oe M
or (1600 + 800) × 0.875 (= 2100)
Coupon B A1 for Coupon B and
and correct 288 and 300 or
figures seen 18.75(%) and 18(%) or
12(%) and 12.5(%) or
2112 and 2100
Total 7 marks
Q Working Answer Mark Notes
oe or oe
2 M1 for a complete method to find the area
48.4 A1 accept 48.3 – 49.
Total 2 marks
or
or oe
5 M1 for correct
trig ratio
involving AC
M2 for use of tan and Pythagoras to
obtain AC
( AB =) 24 tan 30 (= 13.856...)
and
(=^ 27.712...)
If not M2, then M1 for use of tan and
Pythagoras to obtain AC
2
( AB =) 24 tan 30 (= 13.856...)
and
2
2
(=^768 )
( AC =) (= = 27.712…) or
M1 for a correct
trig ratio for AC
´ 2 ´ p ´ 3 (= 3 π = 9.424…)
‘27.712…’ + ‘9.424…’ – 2 × 3 M1 for a complete method to find the length AFEDC
31 A1 accept answers in range from 31 to 31.
Total 5 marks
2
2
cos
sin'60'
sin'60' sin 90
2 2
cos 30
sin'60 '
24 sin 90
sin'60 '
Q Working Answer Mark Notes
8 22 × 260 (= 5720) or
Total 3 marks
ç ÷
è ø
Q Working Answer Mark Notes
220 ÷ 80 (= 2.75 or ) oe
M1 for a method to find the time from B to C
(= 60) oe
M1 for a method to find the distance from
C to D
Allow 0.83(333…) to 2 dp truncated or
rounded
oe
M1 for a complete method to find the
average speed for entire journey
0.83(333…) to 2 dp truncated or rounded
6.0(8333…) to 2 sf truncated or rounded
86.3 A1 for 86.3 – 86.
Total 4 marks
æ ö
ç ÷
è ø
Q Working Answer Mark Notes
11 3 × 2.5 (= 7.5) oe or 2 × 3 × 2.5 (= 15) oe or
12 × 3 (= 36) oe or 2 × 12 × 3 (= 72) oe or
6 M1 for area of rectangle
(2 × 3 × 2.5) + (2 × 12 × 3) + (12 × 2.5) (= 117) or
(2 × 7.5) + (2 × 36) + (12 × 2.5) (= 117) or
M1 for a complete method to find the
surface area
1 + 0.1 (= 1.1) or
100(%) + 10(%) (= 110(%)) or
(= 0.245) oe
26.95 ÷ “1.1” (= 24.5(0)) or
26.95 ÷ “110” × 100 (= 24.5(0)) or
26.95 × 100 ÷ “110” (= 24.5(0)) oe or
“0.245” × 100 (= 24.5(0)) oe
M1 dep on previous M
“117” ÷ 15 (= 7.8 or 8) and “8” × “24.50” (= 196) or
“117” ÷ 15 (= 7.8 or 8) and 200 ÷ “24.5” (= 8.1...) or
“117” ÷ 15 (= 7.8 or 8) and 200 ÷ “8” (= 25)
M1for working with a whole number of
tins (rounded up) to reach figures where a
decision can be made
Correct figures
to show that
Jonty is correct
A1 e.g. 196
7.8 or 8 and 8.1...
24.5 and 25
Total 6 marks
Q Working Answer Mark Notes
Total 3 marks
14 360 ÷ 8 (= 45) or 360 ÷ 5 (= 72) or
180 – (360 ÷ 8) (= 135) oe or
180 – (360 ÷ 5) (= 108) oe
4 M1 finding interior or exterior angle of
octagon or pentagon
Angles may be seen on diagram – but
must be obtuse if interior and acute if
exterior.
‘72’ – ‘45’ (= 27) or
M1 (dep 1st M1) using a pair of interior
or pair of exterior angles to find angle
Angle may be seen on diagram.
Total 4 marks
15 4 B1 for 80
for oe or 73
M1 for setting up an equation using the
median or for 73
for 80 – 16 (= 64) oe M1 for using the range correctly or for 64
64, 73, 80 A1 answers can be in any order
Total 4 marks
a +
Q Working Answer Mark Notes
oe or
(= 161) oe or
(= 397) oe
4 M1 for method to find the sum of the first
100 terms
or
for finding the 41
st term
or
for finding the 100
th term
oe or
oe or
100 – 41 + 1 (= 60) oe
M1 for method to find the sum of the first
40 terms or 41 terms
or
for finding the number of terms from the
st term to the 100
th term
“19 900” – “3160” or
or
oe
M1 for finding the difference
or
for finding the sum from the 41
st term to
the 100
th term
Total 4 marks
[ ]
[ ]
[ ]
Q Working Answer Mark Notes
p x
2
´ 4 p x
2 = 81 p oe or
9 x
2 = 81oe
or 2 p x ´ 3 x +
´ 4 p x
2
= 81 p oe or 8 x
2
= 81
6 M1 for setting up an equation (in a single variable ie
x or r ) for the total surface area of the shape or for
the curved surface area.
( x^ =)
(=^3 )
M1 solving their equation in the form kx
2
(where k follows correctly from their surface area)
to find x
p ´'3'
2 ´ 3 ´'3'+ ´ p '3'
3 oe
(= 81 π + 18 π = 99 π = 311.(017…) )
M1 (indep) for substituting their value of x to find
the volume of the shape.
99 π or 311.(017… ) A
(= 2.7….) oe
M1 (dep on the 3rd M) for using the formula for
density
aluminium A1 for aluminium and correct working leading to
Total 6 marks
Q Working Answer Mark Notes
or oe or
or oe
4 M1 for finding the ratio or fraction for
lengths for A : B or B : A
or oe or
or oe
M1 for finding the ratio or fraction for
lengths for B : C or C : B
A : B = 10 : 15 and B : C = 15 : 21 oe M1 for mainpulating A : B and B : C so
that both B values are equal
10 : 21 A1 Allow 1 : 2.
SC3 for 21 : 10 with all working shown
Total 4 marks
æ ö
ç ÷
è ø
æ ö
ç ÷
è ø
3 3
3
3
æ ö
= ç ÷
è ø
3 3
3
3
æ ö
= ç ÷
è ø
Q Working Answer Mark Notes
Edexcel averages: scores of candidates who achieved grade:
Qn
Mean
score
Max
score
Mean
% ALL 9 8 7 6 5 4 3 U
1 2.60 3 87 2.60 2.97 2.81 2.69 2.45 1.97 1.21 0.33 0.
2 3.48 4 87 3.48 3.88 3.68 3.54 3.35 2.73 2.43 0.50 0.
3 5.84 7 83 5.84 6.73 6.40 5.98 5.20 3.98 3.15 2.04 0.
4 2.32 3 77 2.32 2.87 2.75 2.35 1.72 1.07 0.82 0.29 0.
5 2.99 4 75 2.99 3.74 3.54 3.06 2.39 1.38 0.50 0.19 0.
6 1.49 2 75 1.49 1.95 1.75 1.53 1.06 0.61 0.16 0.00 0.
7 2.08 3 69 2.08 2.85 2.47 1.99 1.19 0.70 0.16 0.00 0.
8 3.42 5 68 3.42 4.63 4.10 3.35 2.16 0.97 0.24 0.00 0.
9 2.72 4 68 2.72 3.53 2.85 2.64 1.92 1.53 1.00 0.78 0.
10 2.49 4 62 2.49 3.32 2.84 2.33 1.77 1.04 0.44 0.15 0.
11 3.58 6 60 3.58 5.11 4.06 3.14 2.12 0.98 0.71 0.07 0.
12 1.75 3 58 1.75 2.64 2.07 1.41 0.71 0.39 0.16 0.04 0.
13 1.67 3 56 1.67 2.55 1.67 1.28 0.85 0.58 0.15 0.08 0.
14 1.90 4 48 1.90 2.49 2.10 1.70 1.42 1.07 0.41 0.17 0.
15 2.14 4 54 2.14 3.07 2.37 1.58 1.36 0.78 0.60 0.22 0.
16 1.60 4 40 1.60 2.72 1.50 0.96 0.65 0.28 0.10 0.00 0.
17 1.27 4 32 1.27 2.24 1.07 0.75 0.35 0.25 0.06 0.00 0.
18 2.34 6 39 2.34 4.58 1.76 0.83 0.37 0.09 0.00 0.00 0.
19 1.59 4 40 1.59 2.98 1.43 0.66 0.22 0.12 0.12 0.00 0.
20 1.20 3 40 1.20 2.33 1.10 0.38 0.12 0.04 0.00 0.00 0.
48.47 80 61 48.47 67.18 52.32 42.15 31.38 20.56 12.42 4.86 0.
Suggested grade boundaries
Grade 9 8 7 6 5 4 3
Q Working Answer Mark Notes
Mark 60 47 37 26 17 9 4