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WAEC - Further Mathematics (2011)

  • 1
    A binary operation * is defined on the set of real numbers R, by a* b = -1. Find the identity element under the operation *.
    Jawab
    (A)
    -1
  • 2
    Express 75° in radians, leaving your answer in terms of \(\pi\).
    Jawab
    (A)
    \(\frac{5\pi}{12}\)
  • 3
    If \(\log_{9} 3 + 2x = 1\), find x.
    Jawab
    (C)
    \(\frac{1}{4}\)
  • 4
    Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)
    Jawab
    (B)
    \(\frac{-\sqrt{3}}{2}\)
  • 5
    Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).
    Jawab
    (C)
    29
  • 6
    A function is defined by \(f(x) = \frac{3x + 1}{x^{2} - 1}, x \neq \pm 1\). Find f(-3).
    Jawab
    (B)
    \(-1\)
  • 7
    Simplify \(\sqrt[3]{\frac{8}{27}} - (\frac{4}{9})^{-\frac{1}{2}}\)
    Jawab
    (A)
    \(\frac{-5}{6}\)
  • 8
    Solve \(3x^{2} + 4x + 1 > 0\)
    Jawab
    (B)
    \(x > -1, x > -\frac{1}{3}\)
  • 9
    The equation of a circle is \(3x^{2} + 3y^{2} + 6x - 12y + 6 = 0\). Find its radius
    Jawab
    (B)
    \(\sqrt{3}\)
  • 10
    \(f(x) = p + qx\), where p and q are constants. If f(1) = 7 and f(5) = 19, find f(3).
    Jawab
    (A)
    13
  • 11
    The sum and product of the roots of a quadratic equation are \(\frac{4}{7}\) and \(\frac{5}{7}\) respectively. Find its equation.
    Jawab
    (B)
    \(7x^{2} - 4x + 5 = 0\)
  • 12
    \(f(x) = (x^{2} + 3)^{2}\) is defines on the set of real numbers, R. Find the gradient of f(x) at x = \(\frac{1}{2}\).
    Jawab
    (B)
    6.5
  • 13
    Find \(\lim \limits_{x \to 3} \frac{x + 3}{x^{2} - x - 12}\)
    Jawab
    (A)
    -1
  • 14
    If \(y^{2} + xy - x = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\).
    Jawab
    (C)
    \(\frac{1 - y}{x + 2y}\)
  • 15
    A line is perpendicular to \(3x - y + 11 = 0\) and passes through the point (1, -5). Find its equation.
    Jawab
    (D)
    3y + x + 14 = 0
  • 16
    Solve \(9^{2x + 1} = 81^{3x + 2}\)
    Jawab
    (A)
    \(\frac{-3}{4}\)
  • 17
    The inverse of a function is given by \(f^{-1} : x \to \frac{x + 1}{4}\).
    Jawab
    (A)
    \(f : x \to 4x - 1\)
  • 18
    If \(\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix} \), find x.
    Jawab
    (A)
    5
  • 19
    The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio.
    Jawab
    (B)
    \(\pm 2\)
  • 20
    What percentage increase in the radius of a sphere will cause its volume to increase by 45%?
    Jawab
    (A)
    13%
  • 21
    Evaluate \(\frac{1}{1 - \sin 60°}\), leaving your answer in surd form.
    Jawab
    (D)
    \(4 + 2\sqrt{3}\)
  • 22
    Find the equation of a circle with centre (-3, -8) and radius \(4\sqrt{6}\).
    Jawab
    (B)
    \(x^{2} + y^{2} + 6x + 16y - 23 = 0\)
  • 23
    Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).
    Jawab
    (C)
    \(135a^{4}\)
  • 24
    The mean of 2, 5, (x + 2), 7 and 9 is 6. Find the median.
    Jawab
    (D)
    7.0
  • 25
    The probability that Kofi and Ama hit a target in a shooting competition are \(\frac{1}{6}\) and \(\frac{1}{9}\) respectively. What is the probability that only one of them hit the target?
    Jawab
    (B)
    \(\frac{13}{54}\)
  • 26
    In how many ways can 3 prefects be chosen out of 8 prefects?
    Jawab
    (C)
    56
  • 27
    Find the standard deviation of the numbers 3,6,2,1,7 and 5.
    Jawab
    (B)
    2.16
  • 28
    Marks 5-7 8-10 11-13 14-16 17-19 20-22
    No of students 4 7 26 41 14 8

    The table above shows the distribution of marks of students in a class. Find the upper class boundary of the modal class.

    Jawab
    (C)
    16.5
  • 29
    If \(^{3x}C_{2} = 15\), find the value of x?
    Jawab
    (A)
    2
  • 30
    Four doctors and two nurses are to sit round a circular table. In how many ways can this be done if the nurses are to sit together?
    Jawab
    (A)
    48
  • 31
    A basket contains 3 red and 1 white identical balls. A ball is drawn from the basket at random. Calculate the probability that it is either white or red.
    Jawab
    (D)
    1
  • 32
    A force of 200N acting on a body of mass 20kg initially at rest causes it to move a distance of 320m along a straight line for t secs. Find the value of t.
    Jawab
    (C)
    8s
  • 33
    Two forces 10N and 15N act on an object at an angle of 120° to each other. Find the magnitude of the resultant.
    Jawab
    (B)
    \(5\sqrt{7}N\)
  • 34
    A body of mass 25kg changes its speed from 15m/s to 35m/s in 5 seconds by the action of an applied force F. Find the value of F.
    Jawab
    (A)
    100N
  • 35
    A particle starts from rest and moves in a straight line such that its velocity, v, at time t seconds is given by \(v = (3t^{2} - 2t) ms^{-1}\). Calculate the distance covered in the first 2 seconds.
    Jawab
    (B)
    4m