PreambleGeneral Marking Guidance:

This mark scheme is designed to reward candidates for their achievements and Examiners should ensure that they use it with the same intention. Examiners should be prepared to use all of the marks available on this mark scheme judiciously; where full marks are deserved, this should always be awarded to candidates; likewise, Examiners should beprepared to award no marks to responses that are not worthy of credit. At all times, Examiners should ensure that they only use this mark scheme when assessing a response and not any other private schemes.

It should be remembered that a mark scheme is a working document that may be further developed or refined in thefuture.

General Marking Instructions:

This question paper has 80 marks.

In this mark scheme, marks are awarded in one of these forms: M marks - these are method marks and are awarded when candidates know a correct method and apply it correctly. P marks - these are process marks and are awarded for a correct process as part of a problem solving. A marks - these are accuracy marks and are awarded for the correct answer. They can only be awarded in conjunction with the relevant method mark(s). B marks - these are accuracy marks and are independent of method marks. C marks - these are communication marks. Common abbreviations used in this mark scheme include:

bod - benefit of doubt ft - follow through cao - correct answer onlycso - correct solution onlyisw - ignore subsequent workingsc - special caseoe - or equivalentd... - dependentowtte - or words to that effect * - answer given in question

Crossed out working should be marked unless it is replaced by alternative workings.

Examiners should always ignore any subsequent working once a correct answer has been reached provided it does not change the answer in a way that is inappropriate for the question. This includes when candidates incorrectly cancel down a fraction in a question not testing fractions or when candidates make transcription errors (provided that it is clear that thecorrect answer is the one intended).

Probability answers should be given as fractions, decimals or percentages. Decimals should be given to two decimal places(unless tenths). Incorrect or ambiguous notation should always lose accuracy marks, but may gain method or process marks.

In the context of solving linear equations, full marks should always be awarded for the answer alone. If there is a contradiction seen anywhere in that (part of the) question, retract the marks. Unless specifically asked by the question to use verification, if a correct answer is seen substituted, but not identified as the final answer, do not award the accuracy marks, but you should award the method marks.

Unless instructed, marks from one part of the question cannot be awarded in another.

Unless stated otherwise, where a range of answers is given in the mark scheme, this is inclusive of the end points of the interval.

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 1 sketch

2

C1 for interpreting the diagram e.g. draws a solid shape with at least two correct dimensions C1 for the correct prism with all necessary dimensions

2 (a)

1.990369453

1.9904

2 1

B1 for the first three digits correct B1 for all ten digits B1ft for rounding their (a) correctly to five significant figures

3 nm2 = 6 − n

m2 = 6 − nn

m = 6 − nn

m = 6 − nn

3

M1 for multiplying both sides by m to obtain an m2 term M1 for attempting to square root both sides of the equation A1 for correctly expressing m in terms of n. Accept

equivalent forms, i.e. m = 6n−1

4 (a)

(b)

(c)

enlargement

suggestion

O , B

2 1 1

B1 for increasing the sides by a scale factor of 2 B1 for using the centre O C1 for an apt suggestion, i.e. ‘a point that is unchanged by a transformation’, ‘a point whose coordinates are unchanged by a transformation’. Do not credit points only about enlarging, i.e. ‘a point not enlarged by T’ C1 for ticks in the boxes O and B. Ignore hybrid ticks.

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 5 (a)

(b)

46 × 0.45 or 200.45

Charlie is wrong + reason

no + reason

3

1

P1 for attempting convert either James’ or Charlie’s speed A1 for 20.7 or 44.4 C1 for concluding that Charlie is wrong / James is travelling faster and a reason, i.e. ‘20.7 is greater than 20’ or ‘44.4 is smaller than 46’ oe C1 for the idea that the values will still be correct two significant figures which in no case will mean Charlie is travelling faster OR for the values re-worked out again

6 (a)

(b)

16× π × 0.042

16

8.4 ×10−4 m2

1

4

B1 for the correct proportion oe. Accept 0.16 or 0.1666... but not 0.17 or 0.1666 (i.e. finitely many 6s without indication of recursion). 0.17 can be accepted if it is stated that this is to 2 dp M1 for attempting to convert the units (at any stage) M1 for using the area of a sector formula with their (a) A1 for the correct area of {awrt} 8.4 ×10−4 or 0.00084 B1 for the units of m2 on the answer line

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 7 (a)

(b) (i)

(ii)

36× 84

84800

× 12

42 21400

reason

3 3 1

P1 for attempting to find the correct proportion factor, i.e. adding up 1+3+2

M1 for 36× 84

A1 for the correct answer of 42

M1 for 84800

M1 for multiplying their 84800

with their (a)84

A1 for the correct answer oe C1 for a valid reason, i.e. ‘all students are equally likely to be chosen for the trip’, ‘all students are eligible for the trip’, ‘all students want to go on the trip’, etc.

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 8 (a)

(b)

(c)

(d)

12 0

89

89

1 1 1 1

B1 for 12 B1 for 0 B1 for 89 B1ft for their 89

9 A = kB3

k = 6

4 = 6B3⇒ B = 6

4⎛⎝⎜

⎞⎠⎟3

278

3 M1 for the correct inverse relation between A and B oe (i.e.

accept if k is under the square root too or in other forms) M1 for attempting to find their k and using this to find B when A = 4 A1 for the correct value of B when A = 4 oe

10

explanation

2

B1 for stating that the time period is not specified on the horizontal axis OR the frequency for 30 < t < 40 is wrong B1 for stating that Andrew has plotted the end points of his intervals rather than the mid points

11 (a) geometric 1 B1 for correctly identifying that it is a geometric progression

(b)

0 < r <1

1

C1 for ticking the third box, 0 < r <1

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance

(c)

2000 = 5400r4

r = 20005400

4 = 0.78011...

After 5 years, his old car is worth 5400 0.78011...( )5 = £1560.23 Yes, he has made profit (£60.23)

Yes + working

4

P1 for attempting to find the value of r P1 for attempting to use their value of r to find the value of the car after 5 years A1 for the correct value of the car after 5 years C1 for concluding ‘Yes {Michael has made profit}’ and giving a reason, i.e. ‘he has made £60 profit’, ‘£1560.23 > £1500’, etc.

12 f x +1( )− f x( ) = x +12 x +1( ) +1 −

x2x +1

= x +12x + 3

− x2x +1

=

x +1( ) 2x +1( )− x 2x + 3( )2x + 3( ) 2x +1( )

= 2x

2 + 3x +1− 2x2 − 3x2x + 3( ) 2x +1( )

= 12x + 3( ) 2x +1( )

12x + 3( ) 2x +1( )

5 M1 for the correct expression for f (x + 1) – f (x) M1 for attempting to form a common denominator A1 for correct workings up until line 3 M1 for attempting to expand the brackets generating 5 terms A1 for a complete and convincing solution with no errors

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 13 Expression 1:

Area of the square ABCD = c2 Expression 2: Area of the outer square = a + b( )2

Area of the triangle = 12ab

Area of ABCD =

a + b( )2 − 4 12ab⎛

⎝⎜⎞⎠⎟ = a

2 + b2

⇒ a2 + b2 = c2 , i.e. Pythagoras’ theorem

solution 5 B1 for the area of ABCD as c2 P1 for attempting to find out the area of outer square and one inner triangle M1 for a correct expression for the area of ABCD involving the outer square and four triangles A1 for obtaining the area of ABCD as a2 + b2 C1 for stating that this implies Pythagoras’ Theorem or is a proof for it

14 10n× 9n −1

= p

pn2 − pn − 90 = 0

Comparing coefficients gives

p = 37

p = 37

3 P1 for forming a correct probability based equation OR for

attempting to solve the quadratic equation (obtaining n = 15) M1 for attempting to compare coefficients or implied use of

trial and error / inspection OR computing 1015

× 914

A1 for the correct value of p

15

See appendix for a sketch

sketch

2

B1 for the correct shape of the upper half of the container B1 for the correct shape of the lower half of the container (these are qualified in the appendix)

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 16

(a)

(b)

(c)

(d)

AC 2 = 52 + 7.22 − 2 5( ) 7.2( )cos34 AC = 4.141... Perimeter = 5 + 5 + 4.141...+ 4.141...= 18.28... 18.28...1.5

= 12.18...

⇒ Need 13 lots of 1.5m of gate Cost = 13× 32.50 = £422.50

True False False True False

sketch

reason

£422.50

5

2 2 6

B5 for the correct options ticked (B1 for each correct option). Ignore ambiguous markings, such as hybrid ticks or unclear selections B1 for a graph in phase with the given graph B1 for maximum and minimum values of 0.5 and – 0.5 respectively C1 for ‘no’ C1 for the reason that cosx = 0 at x = 90 and division by 0 is undefined or 1 divided by 0 is undefined. Condone 1 divided by 0 = infinity P1 for attempting to find the angle ABC and using this with the cosine rule to find AC A1 for a correct expression involving AC or AC2 A1 for the correct value of AC P1 for attempting to find their perimeter and hence the number of 1.5 m of gate the school should order A1 for 13 lots of 1.5m of gate A1 for £422.50

CM GCSE Practice Papers / Set A / Paper 3H Question Working Answer Marks Guidance 17

Height of cone = 4 cm

Volume of cone =

13π 3( )2 4( )

= 12π Total volume of cylinder = 18π

Volume of sphere =

43π 2( )3 = 32

3π

Volume of shaded region =

18π − 323π =

223π

223π

5

M1 for attempting to find the volume of the cone using the correct height M1 for using the ratio and their volume of the cone to find the total volume of the sphere A1 for the correct total volume of the cylinder M1 for attempting to find the volume of sphere and using this to find the volume of the shaded region A1 for the correct volume of the shaded region as an exact value. Candidates that resort to decimals should award A0. However, if a candidate finds the exact value but THEN gives a decimal equivalent, award A1 for the exact value and ISW

Appendix

First B1 for a container that curves outwards initially Second B1 for a container that curves inwards from about the half way point Note: only the cross section is required. The 3D version is shown for illustrative purposes only but is not required. You should IGNORE any attempts to draw a 3D shape by candidates and mark the cross section only.

Breakdown of Marks by AOsThe table below provides a breakdown of the distribution of marks for each AO in the questions.

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

Q12

Q13

Q14

Q15

Total

AO1 AO2 AO3 Total

0 2 0 2

3 0 0 3

3 0 0 3

0 2 2 4

1 2 2 5

0 4 0 4

3 0 0 3

0 2 0 2

1 0 6 7

5 0 0 5

1 1 3 5

2 0 1 3

4 1 0 5

2 2 3 7

0 2 0 2

8036 22 22

Weighting (%) 45.0 27.5 27.5

This table is for reference purposes only. Examiners should not use this to assist their judgements of the responses they assess. It should be remembered that this mark scheme and table are part of a collection of working documents that may be refined for future practice sets or mock examinations.

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Q13

Total

2 1 2 5

8032 24 24

Weighting (%) 40.0 30.0 30.0

Q16 5 5 5 15