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    C4 - Jun 2008

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    Liam Chong
    This document provides instructions and questions for the GCE AS/A level 976/01 MATHEMATICS C4 Pure Mathematics exam. Candidates are instructed to answer all 10 questions, showing sufficient working. Questions involve skills like partial fractions, differentiation, integration, differential equations, vectors, and proofs. Candidates have 1 1/2 hours to complete the exam.

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    C4 - Jun 2008

    Uploaded by

    Liam Chong
    38 views3 pages
    This document provides instructions and questions for the GCE AS/A level 976/01 MATHEMATICS C4 Pure Mathematics exam. Candidates are instructed to answer all 10 questions, showing sufficient working. Questions involve skills like partial fractions, differentiation, integration, differential equations, vectors, and proofs. Candidates have 1 1/2 hours to complete the exam.

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    This document provides instructions and questions for the GCE AS/A level 976/01 MATHEMATICS C4 Pure Mathematics exam. Candidates are instructed to answer all 10 questions, showing sufficient working. Questions involve skills like partial fractions, differentiation, integration, differential equations, vectors, and proofs. Candidates have 1 1/2 hours to complete the exam.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    38 views3 pages

    C4 - Jun 2008

    Uploaded by

    Liam Chong
    This document provides instructions and questions for the GCE AS/A level 976/01 MATHEMATICS C4 Pure Mathematics exam. Candidates are instructed to answer all 10 questions, showing sufficient working. Questions involve skills like partial fractions, differentiation, integration, differential equations, vectors, and proofs. Candidates have 1 1/2 hours to complete the exam.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
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    GCE AS/A level 976/01 MATHEMATICS C4 Pure Mathematics

    A.M. THURSDAY, 12 June 2008 1 2 hours


    1

    ADDITIONAL MATERIALS In addition to this examination paper, you will need: a 12 page answer book; a Formula Booklet; a calculator.

    INSTRUCTIONS TO CANDIDATES Answer all questions. Sufficient working must be shown to demonstrate the mathematical method employed.

    INFORMATION FOR CANDIDATES The number of marks is given in brackets at the end of each question or part-question. You are reminded of the necessity for good English and orderly presentation in your answers.

    CJ*(S08-976-01)

    1.

    Given that f ( x) = (a) (b) express f ( x ) in partial fractions, find 1 , x ( 2 x 1)


    2

    [4] [3]

    f ( x ) dx

    2.

    Find the equation of the normal to the curve x 2 + xy + 2y 2 = 8 at the point (3, 1). [5]

    3.

    (a) (b)

    Express 3cosx + 2sinx in the form Rcos(x ), where R and are constants with R 1 0 and [3] 0 ! ! 90. Find all values of x between 0 and 360 satisfying 3cosx + 2sinx = 1. [3]

    4.

    3 , the x-axis and the lines x = 1, x = 4. Find the x volume generated when R is rotated through four right-angles about the x-axis. [7] The region R is bounded by the curve y = x +

    5.

    The parametric equations of the curve C are x = 4sint, y = cos2t. (a) (b) Find dy , simplifying your answer as much as possible. dx [6]

    Show that the equation of the tangent to C at the point P with parameter p is xsinp + y = 1 + 2sin2p. [3]

    6.

    (a) (b)

    Find

    ( 3x + 1) e

    2x

    dx.

    [4]

    Use the substitution x = 3sin to show that

    Hence evaluate

    15

    9 x dx =

    k cos d
    2 a

    where the values of the constants a, b and k are to be found.

    15

    9 x 2 dx .

    [8]

    (976-01)

    7.

    A neglected large lawn contains a certain type of weed. The area of the lawn covered by the weed at time t years is W m2. The rate of increase of W is directly proportional to W. (a) (b) Write down a differential equation that is satisfied by W. [1]

    The area of the lawn covered by the weed initially is 010 m2 and one year later the area [6] covered is 201 m2. Find an expression for W in terms of t.

    8.

    The position vectors of the points A and B are given by a = 4i j + k, (a) (i) (ii) Write down the vector AB. Find the vector equation of the line AB. [3] b = 5i + j k.

    The vector equation of the line L is r = i + 3j 3k + (i j + k). (b) (c) Given that the lines AB and L intersect, find the position vector of the point of intersection. [5] Find the angle between the line AB and the line L. [5]

    9.

    Expand

    1 + 3x in ascending powers of x up to and including the term in x 2. State the range of x 1 2x for which the expansion is valid. [5]

    10. Prove by contradiction the following proposition. When x is real and positive,

    x + 49 x14 . x
    The first line of the proof is given below. Assume that there is a positive and real value of x such that

    x + 49 ! 14 . x

    [4]

    (976-01)

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