Mathematics Practice Tests: Paper 2H-3H Mark Scheme & Performance Data, High school final essays of Mathematics

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

2019/2020

Uploaded on 02/13/2025

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Practice Tests Set 20 – Paper 2H-3H mark scheme, performance data and suggested grade boundaries 1.0
Q
Working
Answer
Mark
Notes
1
7200 × 0.025 (= 180)
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)
7200 + ‘180’ + ‘184.5’ + ‘189.1…’ (= 7753.6125)
7753.6125
7754
A1 answer in range 7753 – 7754
Total 3 marks
2
(a)
1 – (0.24 + 0.16 + 0.38) oe
M1
0.22
A1 oe
(b)
0.24 + 0.16 (= 0.4) oe
M1
0.4
A1 oe
Total 4 marks
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff

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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

M

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

P

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

  • 24

2

(=^768 )

( AC =) (= = 27.712…) or

M1 for a correct

trig ratio for AC

( AC =) (= = 27.712…)

( AC =)

´ 2 ´ p ´ 3 (= 3 π = 9.424…)

M

for using p ´ 2 ´3or 2 p ´ 3

‘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

´ p´

2

cos

( AC )

sin'60'

( AC )

sin'60' sin 90

24 ( AC )

2 2

cos 30

sin'60 '

24 sin 90

sin'60 '

Q Working Answer Mark Notes

8 22 × 260 (= 5720) or

50 × 218 (= 10 900)

3 M

M

185 A

Total 3 marks

  • (^) æ ö

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 ÷

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

12 × 2.5 (= 30)

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

M

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

IBC

Angle may be seen on diagram.

M

76.5 A

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

16 740 A

Total 4 marks

[ ]

[ ]

[ ]

Q Working Answer Mark Notes

p x

2

  • 2 p x ´ 3 x +

´ 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

p = 81 p

(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