• Selected Questions From Some Federal Universities Post UTME

    Mathematics

    Chima Sunday (Tutor)
    15-06-2016 12:34:00 +0000

    Try and do justice on these questions, as rightly said that practice makes one better. Please Show working on paper and include a picture of your hand written Solution in your response. Wish you the best!

    1. Solve the following simultaneous equations for x
    x2 + y - 5 = 0
    y = 7x + 3
    A. 2,4
    B. -2,4
    C. -1,0
    D. 1,-8

    Updated Solution
    x2 + y - 5 = 0 ---------(1)
    y = 7x + 3 -------------------(2)
    putting (2) into (1)
    x2 + 7x + 3 - 5 = 0
    x2 + 7x - 2 = 0
    using completing the sqaure
    x2 + 7x = 2
    x2 + 7x + (7/2)2 = 2 + 49/4
    (x + 7/2)2 = (8 + 49)/4 = 57/2
    x = 7/2 + √57/2 or 7/2 - √57/2
    x = (7 + √57)/2 or (7 - √57)/2
    so from the Optional given, it is wise to conclude that its option not there

    2. If y = 3x2 (x3 + 1)1/2, find dy/dx
    A. [6x(x3 + 1) + 3x2]/2(x3 + 1)1/2
    B. [12x(x3 + 1)3x2]/2(x3 + 1)1/2
    C. [15x4 + 6x]/6x2(x3 + 1)1/2
    D. [12x(x3 + 1) + 9x4]/2(x3 + 1)1/2

    Updated Solution
    y = 3x2(x3 + 1)1/2
    we use the product rule
    dy/dx = vdu/dx + udv/dx
    where u = 3x2, du/dx = 6x
    v = (x3 + 1)1/2
    we apply function of function to obtain
    z = x3 + 1, dz/dx = 3x2
    so v = z1/2, dv/dz = 1/2(z)1/2 = 1/2(x3 + 1)1/2
    thus dv/dx = dv/dz * dz/dx = 3x2 * 1/2(x3 + 1)1/2 = 3x2/2(x3 + 1)
    dy/dx = vdu/dx + udv/dx
    = (x3 + 1)1/26x + 3x2*3x2/2(x3 + 1)1/2
    so dy/dx = 6x(x3 + 1)1/2 + 9x4/2(x3 + 1)1/2
    to simplify further by finding LCM
    [12x(x3 + 1) + 9x4]/2(x3 + 1)1/2
    So correct Option is D



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