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    STPM 2014 - MATHEMATICS T 954/2 (U2) : X X X X X y X X X

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    加卡内-张进哲
    1. This document contains 8 mathematics questions covering calculus topics like functions, derivatives, integrals, differential equations, and curve sketching. 2. Question 1 asks to determine if a piecewise defined function is continuous at a point. Question 2 involves solving a differential equation. 3. Question 3 requires finding the derivative of a trigonometric function. The remaining questions involve additional calculus techniques like substitution, solving differential equations, finding Maclaurin series, curve sketching using calculus concepts, and applying numerical methods like the trapezium rule.

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    STPM 2014 - MATHEMATICS T 954/2 (U2) : X X X X X y X X X

    Uploaded by

    加卡内-张进哲
    93 views1 page
    1. This document contains 8 mathematics questions covering calculus topics like functions, derivatives, integrals, differential equations, and curve sketching. 2. Question 1 asks to determine if a piecewise defined function is continuous at a point. Question 2 involves solving a differential equation. 3. Question 3 requires finding the derivative of a trigonometric function. The remaining questions involve additional calculus techniques like substitution, solving differential equations, finding Maclaurin series, curve sketching using calculus concepts, and applying numerical methods like the trapezium rule.

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    2014_U2_QS

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    1. This document contains 8 mathematics questions covering calculus topics like functions, derivatives, integrals, differential equations, and curve sketching. 2. Question 1 asks to determine if a piecewise defined function is continuous at a point. Question 2 involves solving a differential equation. 3. Question 3 requires finding the derivative of a trigonometric function. The remaining questions involve additional calculus techniques like substitution, solving differential equations, finding Maclaurin series, curve sketching using calculus concepts, and applying numerical methods like the trapezium rule.

    Copyright:

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

    STPM 2014 - MATHEMATICS T 954/2 (U2) : X X X X X y X X X

    Uploaded by

    加卡内-张进哲
    1. This document contains 8 mathematics questions covering calculus topics like functions, derivatives, integrals, differential equations, and curve sketching. 2. Question 1 asks to determine if a piecewise defined function is continuous at a point. Question 2 involves solving a differential equation. 3. Question 3 requires finding the derivative of a trigonometric function. The remaining questions involve additional calculus techniques like substitution, solving differential equations, finding Maclaurin series, curve sketching using calculus concepts, and applying numerical methods like the trapezium rule.

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    © All Rights Reserved
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    STPM 2014 – MATHEMATICS T 954/2 (U2)

    SECTION B (15 Marks) : Answer one question only in this section.


    SECTION A (45 Marks) : Answer all questions in this section.

     x2  4 7. For the graph of y = 3x4 + 16x3 + 24x2 – 6,


     ,x  2
    1. Function f is defined by f(x) =  x  2 . (a) determine the intervals on which the graph is concave upward and
     4 ,x  2 concave downward, [6]

    (b) find the points of inflexion, [3]
    Determine whether f is continuous at x = 2. [5]
    (c) determine the extremum point and its nature. [3]
    –1 dy 4 3 2
    2. If y sin 2
    2x = 1 4 x , show that (1 – 4x )2
    + 4xy + 2y2 = 0. [5] Hence, sketch the graph of y = 3x + 16x + 24x – 6. [3]
    dx
    1
    8. Sketch the graphs of y = – 1 and y = –x3 – 2 on the same coordinate axes.
    3. Show that d (cosec x) = – cosec x cot x. [2] 2 x
    dx
    Hence, show that the equation x4 – 2x3 + x – 3 = 0 has two real roots.
    x
    dx [7]
    Using the substitution x = 2 tan θ, find . [6]
    2
    4  x2 Using the Newton-Raphson method with the initial approximation xo = 2,
    find the positive real root of the equation x4 – 2x3 + x – 3 = 0, correct to
    four decimal places. [6]
    4. Show that the substitution u = 1 transforms the non-linear differential equation
    y State, with a reason, a situation in which the Newton-Raphson method fails. [2]
    dy y
    + = y2 ln x into the linear differential equation du – u = – ln x. [4]
    dx x dx x

    Solve this linear differential equation, and hence, obtain y in terms of x,


    given that y = 1 when x = 1. [8]
    2

    2
     dy 
    5. If y = (cos –1 x)2 , show that (1 – x2 )   = 4 y. [3]
     dx 
    Show that the Maclaurin's series for (cos –1 x)2 is  – x + x2 –  x3 + . . . .
    2
    [7]
    4 6

    6. The curve y = x x 2  5 and the straight y


    line y = 3x in the first quadrant is shown
    in the diagram.
    Using the trapezium rule with four intervals, y = 3x
    determine the area of the region bounded
    by the curve and the straight line. y = x x2  5 [5]

    0 x

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