• Common Questions Ask in Post UTME Mathematics Exam Day3

    Mathematics

    Chima Sunday (Tutor)
    24-06-2016 12:14:00 +0000

    Try your best to solve these questions. Show working on paper when necessary and include a picture of your hand written Solution in your response. Wish you the best!

    1. The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 43cm
    A. 60cm
    B. 50cm
    C. 42,8cm
    D. 30cm
    (uniben)

    Updated Solution
    If a line is drawn from the vertex down to the centre of square and perpendicular to its surface. This line is the height of the pyramid
    The new geometry formed is the a right angled triangle, so applying Pythagoras
    43^2 = (8/2)^2 + h^2
    43^2 - 4^2 = h^2
    (43 - 4)(43 + 3) = h^2
    (39)(47) = h^2
    thus h = 42.8cm
    Answer is Option C

    2. SinA = 4/5 and cosB = 12/13. Find the value of sin(A + B)
    A. 63/65
    B. 23/11
    C. 56/65
    D. 5/13
    E. 12/13
    (futo)

    Updated Solution
    sinA = 4/5, then opp = 4, hyp = 5 and then adj = 3; thus cos A = 3/5
    cosB = 12/13, here adj = 12, hyp = 13 and then opp = 5; sinB = 5/13
    Then sin(A + B) = sinAcosB + cosAsinB = 4/5*12/13 + 3/5*5/13 = 63/65
    Answer is Option A

    3. Find the radius of circle 2x2 + 2y2 = 18
    A. 3
    B. 2
    C. 4
    D. 1
    E. 5
    (abu)

    recall that equation of a circle is given as x^2 +y^2 = r^2
    were r is the radius, so
    2x^2 + 2y^2 = 18
    dividing through by 2 x^2 + y^2 = 9 = 3^2
    comparing with equation of circle, it is seen that r = 3
    Answer is Option A



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