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INTERNATIONAL ADVANCED LEVELMathematics, Further Mathematics and Pure Mathematics

SAMPLE ASSESSMENT MATERIALSPearson Edexcel International Advanced Subsidiary in Mathematics (XMA01)

Pearson Edexcel International Advanced Level in Mathematics (YMA01)

Pearson Edexcel International Advanced Subsidiary in Further Mathematics (XFM01)

Pearson Edexcel International Advanced Level in Further Mathematics (YFM01)

Pearson Edexcel International Advanced Subsidiary in Pure Mathematics (XPM01)

Pearson Edexcel International Advanced Level in Pure Mathematics (YPM01)

For first teaching in September 2013First examination January 2014

9781446906903_IAL_MATHEMATICS_SAMS_PRINT.indd 1 05/08/2013 15:01

Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

1

Contents

WMA01/01: Core Mathematics C12 Question Paper 3

WMA01/01: Core Mathematics C12 Mark Scheme 47

WMA02/01: Core Mathematics C34 Question Paper 57

WMA02/01: Core Mathematics C34 Mark Scheme 101

WFM01/01: Further Pure Mathematics F1 Question Paper 111

WFM01/01: Further Pure Mathematics F1 Mark Scheme 131

WFM02/01: Further Pure Mathematics F2 Question Paper 135

WFM02/01: Further Pure Mathematics F2 Mark Scheme 159

WFM03/01: Further Pure Mathematics F3 Question Paper 167

WFM03/01: Further Pure Mathematics F3 Mark Scheme 195

WME01/01: Mechanics M1 Question Paper 203

WME01/01: Mechanics M1 Mark Scheme 231

WME02/01: Mechanics M2 Question Paper 235

WME02/01: Mechanics M2 Mark Scheme 267

WME03/01: Mechanics M3 Question Paper 275

WME03/01: Mechanics M3 Mark Scheme 303

WST01/01: Statistics S1 Question Paper 311

WST01/01: Statistics S1 Mark Scheme 339

WST02/01: Statistics S2 Question Paper 347

WST02/01: Statistics S2 Mark Scheme 371

WST03/01: Statistics S3 Question Paper 379

WST03/01: Statistics S3 Mark Scheme 403

WDM01/01: Decision Mathematics D1 Question Paper 411

WDM01/01: Decision Mathematics D1 Answer Booklet 423

WDM01/01: Decision Mathematics D1 Mark Scheme 443

Notes on Marking Principles for all Mark Schemes 454

Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

2

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.

Instructions• Use black ink or ball-point pen.• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Coloured pencils and highlighter pens must not be used.• Fill in the boxes at the top of this page with your name,

centre number and candidate number.• Answer all questions and ensure that your answers to parts of questions are clearly labelled.• Answer the questions in the spaces provided – there may be more space than you need.• You should show sufficient working to make your methods clear. Answers without working may not gain full credit.• When a calculator is used, the answer should be given to an appropriate degree of accuracy.

Information• The total mark for this paper is 125.• The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

Advice• Read each question carefully before you start to answer it.• Try to answer every question.• Check your answers if you have time at the end.

Core Mathematics C12Advanced Subsidiary

You must have:Mathematical Formulae and Statistical Tables (Blue)

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper ReferenceSample Assessment MaterialTime: 2 hours 30 minutes

S44999A©2013 Pearson Education Ltd.

1/2/2/2/

*S44999A0144*Turn over

Pearson Edexcel InternationalAdvanced Level

WMA01/01

Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

3

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.

Instructions• Use black ink or ball-point pen.• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Coloured pencils and highlighter pens must not be used.• Fill in the boxes at the top of this page with your name,

centre number and candidate number.• Answer all questions and ensure that your answers to parts of questions are clearly labelled.• Answer the questions in the spaces provided – there may be more space than you need.• You should show sufficient working to make your methods clear. Answers without working may not gain full credit.• When a calculator is used, the answer should be given to an appropriate degree of accuracy.

Information• The total mark for this paper is 125.• The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

Advice• Read each question carefully before you start to answer it.• Try to answer every question.• Check your answers if you have time at the end.

Core Mathematics C12Advanced Subsidiary

You must have:Mathematical Formulae and Statistical Tables (Blue)

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper ReferenceSample Assessment MaterialTime: 2 hours 30 minutes

S44999A©2013 Pearson Education Ltd.

1/2/2/2/

*S44999A0144*Turn over

Pearson Edexcel InternationalAdvanced Level

WMA01/01

Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

4

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2. Find the first 3 terms, in ascending powers of x, of the binomial expansion of

(3 – x)6

and simplify each term.(4)

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___________________________________________________________________________ Q2

(Total 4 marks)

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1. Simplify fully

(a) ( )25 412x ,

(1)

(b) ( )25 432x

−.

(2)

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(Total 3 marks)

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2. Find the first 3 terms, in ascending powers of x, of the binomial expansion of

(3 – x)6

and simplify each term.(4)

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(Total 4 marks)

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*S44999A0244*

1. Simplify fully

(a) ( )25 412x ,

(1)

(b) ( )25 432x

−.

(2)

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(Total 3 marks)

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Question 3 continued

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(Total 6 marks)

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3. Answer this question without the use of a calculator and show all your working.

(i) Show that

( )( )5 8 1 2 2− + +≡ a b

giving the values of the integers a and b.(3)

(ii) Show that

80 305

5+ ≡ c , where c is an integer.(3)

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(Total 6 marks)

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3. Answer this question without the use of a calculator and show all your working.

(i) Show that

( )( )5 8 1 2 2− + +≡ a b

giving the values of the integers a and b.(3)

(ii) Show that

80 305

5+ ≡ c , where c is an integer.(3)

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(Total 7 marks)

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4. Given that y = 2x5 + 7 + 1x3

, x ≠ 0, find, in their simplest form,

(a) dd

yx

,(3)

(b) ∫ y dx.(4)

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(Total 7 marks)

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4. Given that y = 2x5 + 7 + 1x3

, x ≠ 0, find, in their simplest form,

(a) dd

yx

,(3)

(b) ∫ y dx.(4)

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Question 5 continued

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(Total 4 marks)

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5.

yx

=−

53 22

The table below gives values of y rounded to 3 decimal places where necessary.

x 2 2.25 2.5 2.75 3

y 0.5 0.379 0.299 0.242 0.2

Use the trapezium rule, with all the values of y from the table above, to find an approximate value for

∫23 5

3 22x − dx

(4)

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(Total 4 marks)

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5.

yx

=−

53 22

The table below gives values of y rounded to 3 decimal places where necessary.

x 2 2.25 2.5 2.75 3

y 0.5 0.379 0.299 0.242 0.2

Use the trapezium rule, with all the values of y from the table above, to find an approximate value for

∫23 5

3 22x − dx

(4)

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Question 6 continued

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(Total 7 marks)

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6. f (x) = x4 + x3 + 2x2 + ax + b,

where a and b are constants.

When f(x) is divided by (x – 1), the remainder is 7

(a) Show that a + b = 3(2)

When f(x) is divided by (x + 2), the remainder is –8

(b) Find the value of a and the value of b.(5)

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Question 6 continued

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(Total 7 marks)

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6. f (x) = x4 + x3 + 2x2 + ax + b,

where a and b are constants.

When f(x) is divided by (x – 1), the remainder is 7

(a) Show that a + b = 3(2)

When f(x) is divided by (x + 2), the remainder is –8

(b) Find the value of a and the value of b.(5)

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Question 7 continued

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(Total 5 marks)

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*S44999A01244*

7. A sequence a1, a2, a3, ... is defined by

a1 = 2

an+1 = 3an – c

where c is a constant.

(a) Find an expression for a2 in terms of c.(1)

Given that aii

==∑ 0

1

3

(b) find the value of c.(4)

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Question 7 continued

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(Total 5 marks)

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*S44999A01244*

7. A sequence a1, a2, a3, ... is defined by

a1 = 2

an+1 = 3an – c

where c is a constant.

(a) Find an expression for a2 in terms of c.(1)

Given that aii

==∑ 0

1

3

(b) find the value of c.(4)

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Question 8 continued

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___________________________________________________________________________ Q8

(Total 7 marks)

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*S44999A01444*

8. The equation

(k + 3)x2 + 6x + k = 5, where k is a constant,

has two distinct real solutions for x.

(a) Show that k satisfies

k2 – 2k – 24 < 0(4)

(b) Hence find the set of possible values of k.(3)

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Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

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(Total 7 marks)

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8. The equation

(k + 3)x2 + 6x + k = 5, where k is a constant,

has two distinct real solutions for x.

(a) Show that k satisfies

k2 – 2k – 24 < 0(4)

(b) Hence find the set of possible values of k.(3)

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Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

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(Total 6 marks)

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9. Given that y = 3x2,

(a) show that log3 y = 1 + 2 log3 x(3)

(b) Hence, or otherwise, solve the equation

1 + 2 log3 x = log3 (28x – 9)(3)

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Pearson Edexcel International © Pearson Education Limited 2013 Sample Assessment Materials Advanced Level in Mathematics

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Question 9 continued

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