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    End of Term One Examinations Senior Five Pure Mathematics: 3 Hours

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    Peter Kan
    The document is an exam paper for a senior five pure mathematics exam. It contains two sections, with section A containing 8 compulsory questions and section B containing 5 questions to attempt from 10 options. The questions cover a range of mathematics topics including simultaneous equations, inequalities, differentiation, trigonometry and algebra.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    End of Term One Examinations Senior Five Pure Mathematics: 3 Hours

    Uploaded by

    Peter Kan
    18 views4 pages
    The document is an exam paper for a senior five pure mathematics exam. It contains two sections, with section A containing 8 compulsory questions and section B containing 5 questions to attempt from 10 options. The questions cover a range of mathematics topics including simultaneous equations, inequalities, differentiation, trigonometry and algebra.

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    s5 material

    Original Title

    S5_143_1503683185

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    The document is an exam paper for a senior five pure mathematics exam. It contains two sections, with section A containing 8 compulsory questions and section B containing 5 questions to attempt from 10 options. The questions cover a range of mathematics topics including simultaneous equations, inequalities, differentiation, trigonometry and algebra.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    18 views4 pages

    End of Term One Examinations Senior Five Pure Mathematics: 3 Hours

    Uploaded by

    Peter Kan
    The document is an exam paper for a senior five pure mathematics exam. It contains two sections, with section A containing 8 compulsory questions and section B containing 5 questions to attempt from 10 options. The questions cover a range of mathematics topics including simultaneous equations, inequalities, differentiation, trigonometry and algebra.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 4

    P425/1

    PURE MATHEMATICS

    PAPER 1

    Nov. / Dec. 2016

    3 hours

    END OF TERM ONE EXAMINATIONS

    SENIOR FIVE

    PURE MATHEMATICS

    Paper 1

    3hours

    INSTRUCTIONS:

    Answer all the eight questions in section A and any five questions from section B

    Any additional question(s) will not be marked.

    All working must be shown clearly

    ©2016 end of term one examinations


    SECTION A ( 40 marks)
    Attempt all questions from this section.
    1. Solve the simultaneous equations:
    x + 2y – z = 2
    3x – y + z = 4
    2x + 3y – 5z = -7
    2. Find the equation of a line through the point (2,3) and perpendicular to the

    line x+2 y+5=0 .


    2 1
    ≤
    3. Solve the inequality x−2 x +1 .

    4 ( 3− x )
    log 27 = x 16
    log =
    4. Given that 12 , show that 6 3+ x
    t 2 +5 dy
    x=
    5. If y=t−2 and t −1 , find dx .
    2
    cos x−3 cosx +2 o o
    6. Find the values of x for 2 ¿ 1 , for θ ¿ x ≤360
    sin x

    7. Given that
    y =2 ln {√ ( 1 -x2 )
    ( 2 -x ) } , show that
    dy
    dx
    =
    x 2 -4x +1
    ( 1-x )( 2-x )( 1+ x )
    .

    2 2
    8. Find the equation of a normal at ( 2 , 1 ) to the curve y + 3 xy = 2 x − 1 .

    SECTION B (60marks)
    Attempt any five (5) questions from this section

    9. (a) Differentiate the following with respect to x


    e 2 x ( 5 x −1 ) 2
    (i) (3 marks)
    2
    1+ x
    √ 3−x
    (ii) (3 marks)

    2 End of term one examinations


    d 2 y dy
    −5 x +5 +25 y+5=0
    (b) Given that y=3 x e , show that dx 2
    dx (6 marks)

    +¿ sin 240o
    2+ tan 60 o ¿
    10. (a) Simplify ,without using tables or calculators 3−tan 135o , giving

    your answer in the form a+b √ 3


    (4marks)
    1 =
    1−sin θ
    (b) Show that sec θ+ tan θ cos θ . Hence solve the equation
    1 =cos θ o o
    sec θ+ tan θ , for 0 ¿ θ ¿ 180 . (8marks)

    dy
    11. (a) Find the dx at x = 1 , if y = x2 x (4marks)
    ax +b dy
    y= =0
    2
    (b) Given that at the point (2,1) on the curve x +1 , dx , find the values
    of a and b . (8marks)
    3 x−7
    2
    12. (a) Express ( x+1) ( x−3) as partial fractions. Hence or otherwise , find the
    3 x−7
    y=
    gradient of the curve ( x+1)2 ( x−3) at the point where x=1 . (9marks)

    (b) The expression f ( x ) =mx + nx+2 where m and n are constants leaves a
    2

    remainder of R when divided by ( x −2 ) and a remainder of ( 2 R−8 ) when


    divided by ( x +3 ) . Show that m−7 n+6=0 .
    (3 marks)

    (a) Solve the equation √ ( ) √ x )


    (
    20 + x 20 −x
    + =√ 6
    13. x (6 marks)

    (b) If the roots of the equation 2 x 2+ ( x +3 )2=5 k +2 are ∝∧β .


    2 ( 5 k −1 )
    (i) Show that ∝2+ β2 =¿
    3
    (ii) Hence find k if k +(∝+ β)2=8
    (6 marks)

    3 End of term one examinations


    14. The triangle below is isosceles such that AB=BC =25 cm , and AC =30 cm

    25cm 25cm
    E F

    G C
    A H
    (4x)cm
    30cm

    A rectangle EFGH is drawn inside the triangle with GH on AC , and E and F on

    AB and BC respectively. Given that HG =( 4 x ) cm ,


    8x
    A= ( 15−2 x ) cm2
    (a) Show that the area of the rectangle is given by 3

    (b) Find the stationary value of the volume and determine whether it is a
    minimum or maximum.
    (12marks)

    END

    4 End of term one examinations

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