2013 - JAMB Mathematics Past Questions and Answers - page 1

(\begin{array}{c|c}

3 & \text{27 rem 0} \

\hline

3 & \text{ 9 rem 0} \

\hline

3 & \text{ 3 rem 0} \

\hline

3 & \text{ 1 rem 1}\

\hline

& 0

\end{array})

Hence the correct answer is 1000₃

The sum, S of ratio is S = 5 + 3 + 2 = 10.

But highest share = (\frac{5}{10} \times T), where T is the total number of apples.

Thus, (40 = \frac{5}{10} \times T),

given 40 x 10 = 5T,

(T = \frac{40 \times 10}{5} = 80)

Hence the smallest share = (\frac{2}{10} \times 80)

= 16 apples

(\frac{1.25 \times 0.025}{0.05})

( = \frac{125 \times 10^{-2} \times 25 \times 10^{-3}}{5 \times 10^{-2}})

= 125 x 5 x 10^-3

= 625 x 0.001

= 0.625

= 0.6 Approx to 1 d.p.

Using (S.I =\frac{P \times T \times R}{100})

(600 =\frac{3000 \times T \times 8}{100})

(T =\frac{600 \times 100}{3000 \times 8})

(\frac{20}{8})

= 2(\frac{1}{2}) years

(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1})

(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)})

(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)})

(3^{-5n - 2(1-n) + 3(n + 1)})

(3^{-5n - 2 + 2n + 3n + 3})

(3^{-5n + 5n + 3 - 2})

(3^{1})

= 3

log₁₀4^1/3 = 1/3 log₁₀4

= 1/3 x 0.6021

= 0.2007

(\frac{\sqrt{5}(\sqrt{147} - \sqrt{12}}{\sqrt{15}})

(\frac{\sqrt{5}(\sqrt{49 \times 3} - \sqrt{4 \times 3}}{\sqrt{5 \times 3}})

(\frac{\sqrt{5}(7\sqrt{3} - 2\sqrt{3}}{\sqrt{5} \times \sqrt{3}})

(\frac{\sqrt{3} (7 - 2}{\sqrt{3}})

= 5

S = (\sqrt{t^2 - 4t + 4})

S² = t² - 4t + 4

t² - 4t + 4 - S² = 0

Using (t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a})

Substituting, we have;

Using (t = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(4 - S^2)}}{2(1)})

(t = \frac{4 \pm \sqrt{16 - 4(4 - S^2)}}{2})

(t = \frac{4 \pm \sqrt{16 - 16 + 4S^2}}{2})

(t = \frac{4 \pm \sqrt{4S^2}}{2})

(t = \frac{2(2 \pm S)}{2})

Hence t = 2 + S or t = 2 - S

Let f(x) = x² - x - k

Then by the factor theorem,

(x - 4): f(4) = (4)² - (4) - k = 0

16 - 4 - k = 0

12 - k = 0

k = 12