JAMB Mathematics Past Questions & Answers - Page 263

% error in Area = \(\frac{\pi(5.1)^2 - \pi(5)^2 \times 100%}{\pi(5)^2}\)

= \(\frac{\pi 26.01 - 25 \times 100%}{\pi(25)}\)

= \(\frac{1.01}{25}\) x 100%

= 4.04%

To find n if 34n = 10011₂, convert both sides to base 10

= 3n + 4 = (1 x 2⁴) + (0 x2³) + (0 x 2²) + (1 x 2¹) + 1 x 2^o

= 3n + 4 = 16 + 0 + 0 + 2 + 1

3n + 4 = 19

3n = 15

n = 5

Chance of x = \(\frac{1}{2}\)

Change of Y = \(\frac{2}{3}\)

Chance of Z = \(\frac{1}{4}\)

Chance of Y and Z only occurring

= Pr (Y ∩ Z ∩ Xc)

where Xc = 1 - Pr(X)

1 - \(\frac{1}{2}\) = \(\frac{1}{2}\)

= Pr(Y) x Pr(Z) x Pr(Xc)

= \(\frac{2}{3}\) x \(\frac{1}{4}\) x \(\frac{1}{2}\)

= \(\frac{1}{12}\)

\(\begin{array}{c|c} x & x - x & (x - x)^2\\ \hline 7 & -3 & 9\\8 & -2 & 4 \\9 & -1 & 1\\10 & 0 & 1\\11 & 1 & 1\\ 12 & 2 & 4\\13 & 3 & 9\\ \hline & & 28\end{array}\)

S.D = \(\sqrt{\frac{\sum(x - x)^2}{N}}\)

= \(\sqrt{\frac{\sum d^2}{N}}\)

= \(\sqrt{\frac{28}{7}}\)

= \(\sqrt{4}\)

= 2

Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Prime numbers has only two factors

itself and 1

The prime numbers among the group are 23, 29. Probability of choosing a prime number

= \(\frac{\text{Number of prime}}{\text{No. of total Possible Outcomes}}\)

= \(\frac{2}{11}\)