Stepwise
Start practisingPractise

Theory paper · 1 questions · partial

WAEC · 2015 · May/June · Further Maths · Paper 2

Topics include Binary operations, Indices, logarithms & surds.

Our copy of this paper is missing questions 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

Sit this paper

Answer every question in order, timed if you like (suggested 15 min). You're marked when you hand in, then you see where to focus and the working for each question.

Sit it as an examPractise it, marked as you go

Or read it here: every question below has a worked solution.

Question 1

  1. (a)

    A binary operation Δ\Delta is defined on the set of real numbers R\mathbb R by a Δ b=a3−b3a\,\Delta\,b = a^3 - b^3. Without using a calculator, find the value of (3+2) Δ (3−2)(\sqrt3 + \sqrt2)\,\Delta\,(\sqrt3 - \sqrt2), leaving the answer in surd form.

Worked solution (try it first)
  1. By the definition, the answer is (3+2)3−(3−2)3(\sqrt3 + \sqrt2)^3 - (\sqrt3 - \sqrt2)^3.
  2. Expand with (a+b)3=a3+3a2b+3ab2+b3(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3: (3)3=33(\sqrt3)^3 = 3\sqrt3, 3(3)22=923(\sqrt3)^2\sqrt2 = 9\sqrt2, 33(2)2=633\sqrt3(\sqrt2)^2 = 6\sqrt3 and (2)3=22(\sqrt2)^3 = 2\sqrt2.
  3. So (3+2)3=33+92+63+22(\sqrt3 + \sqrt2)^3 = 3\sqrt3 + 9\sqrt2 + 6\sqrt3 + 2\sqrt2
    =93+112= 9\sqrt3 + 11\sqrt2.
  4. With a minus sign, the terms with an odd power of 2\sqrt2 change sign: (3−2)3=93−112(\sqrt3 - \sqrt2)^3 = 9\sqrt3 - 11\sqrt2.
  5. Subtract: (93+112)−(93−112)=222(9\sqrt3 + 11\sqrt2) - (9\sqrt3 - 11\sqrt2) = 22\sqrt2.

Report a problem with this question