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WAEC 2009 · Paper 2 · Q1

  1. (a)

    Simplify, without using tables or a calculator, 313÷114−493\frac13 \div 1\frac14 - \frac49.

  2. (b)

    Simplify, without using tables or a calculator, 2+96−4(6−1)22 + \sqrt{96} - 4(\sqrt6 - 1)^2, and express your answer in the form m+n6m + n\sqrt6, where mm and nn are real numbers.

Worked solution (try it first)

(a)

  1. Change to improper fractions: 313=1033\frac13 = \frac{10}{3} and 114=541\frac14 = \frac54.
  2. Divide first (BODMAS): 103÷54=103×45\frac{10}{3} \div \frac54 = \frac{10}{3} \times \frac45
    =83= \frac83.
  3. Subtract with denominator 9: 249−49=209\frac{24}{9} - \frac49 = \frac{20}{9}
    =229= 2\frac29.

(b)

  1. Simplify the surd: 96=16×6=46\sqrt{96} = \sqrt{16 \times 6} = 4\sqrt6.
  2. Expand the square: (6−1)2=6−26+1(\sqrt6 - 1)^2 = 6 - 2\sqrt6 + 1
    =7−26= 7 - 2\sqrt6.
  3. Multiply by 4: 4(7−26)=28−864(7 - 2\sqrt6) = 28 - 8\sqrt6.
  4. Combine: 2+46−28+86=−26+1262 + 4\sqrt6 - 28 + 8\sqrt6 = -26 + 12\sqrt6.

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