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    Harkness Test 10B

    Uploaded by

    Lia C
    This document contains 9 math problems involving trigonometric functions, differential equations, curve sketching, parametric equations, integration techniques like substitution and integration by parts. The problems cover a range of calculus and trigonometry topics and ask the reader to find specific values, expressions, equations or integrals.

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

    Harkness Test 10B

    Uploaded by

    Lia C
    73 views1 page
    This document contains 9 math problems involving trigonometric functions, differential equations, curve sketching, parametric equations, integration techniques like substitution and integration by parts. The problems cover a range of calculus and trigonometry topics and ask the reader to find specific values, expressions, equations or integrals.

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    © © All Rights Reserved

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    DOCX, PDF, TXT or read online from Scribd

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    This document contains 9 math problems involving trigonometric functions, differential equations, curve sketching, parametric equations, integration techniques like substitution and integration by parts. The problems cover a range of calculus and trigonometry topics and ask the reader to find specific values, expressions, equations or integrals.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    73 views1 page

    Harkness Test 10B

    Uploaded by

    Lia C
    This document contains 9 math problems involving trigonometric functions, differential equations, curve sketching, parametric equations, integration techniques like substitution and integration by parts. The problems cover a range of calculus and trigonometry topics and ask the reader to find specific values, expressions, equations or integrals.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
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    Harkness Test 10B

    12
    1. Given that 5 sin x cos y+ 3 cos x sin y =0 and that cot y= find the value of cot x .
    5
    [3]
    1
    2. Use the general binomial expansion to find the expansion of ( 3+2 x ) up to and including the
    2

    term in x 3, simplifying your answer.


    [5]
    2
    ⅆy y +3 π
    3. Find the particular solution of the differential equation 2 y = for x= , y=1
    ⅆx cosec x 2
    giving your answer in the form y=f ( x )
    [7]
    2x
    4. The curve C has equation y= ⅇ cos x
    a. Show that the stationary points of C occur when tan x=2
    [4]
    b. Find the equation of the tangent to C at the point when x = 0.
    [3]

    {
    t
    x =ⅇ
    5. Find the equation of the normal to the curve with parametric equations t −t at
    y=ⅇ + ⅇ
    the point P when t=0.
    [6]
    6. Use the substitution u=ln x to find the integral
    sec 2 ( ln x 2 )
    ∫ 2 x dx
    [3]

    7. Express
    4 3 2
    x −4 x + 9 x −17 x +12
    3 2 in partial fractions.
    x −4 x +4 x
    [7]
    8. a. Show that 2 cos 2 θ−5 tan θ ≡ 4 cos θ+3 cos θ−5
    2 4 2

    [3]
    2
    b. Hence solve 2 cos 2 θ=5 tan θ−2 π ≤ θ ≤ 0giving answers to 1 dp.
    [4]
    9. Integrate by parts giving exact answers
    4

    ∫ 8 x √ 4−x dx
    0
    [5]

    Total: 50

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