2004 - WAEC Mathematics Past Questions and Answers - page 4

First four prime numbers greater than 10 are 11, 13, 17, 19
The average \(= \frac{11+13+17+19}{4}=15\)

\(\sqrt{128} +\sqrt{18}-\sqrt{k}=7\sqrt{2}\
\sqrt{2\times 64}+\sqrt{9\times 2} - \sqrt{k} = 7\sqrt{2}\
8\sqrt{2} + 3\sqrt{2} - \sqrt{k} = 7\sqrt{2}; 11\sqrt{2} - \sqrt{k} = 7\sqrt{2}\
-\sqrt{k}=7\sqrt{2}-11\sqrt{2}; -\sqrt{k} = -4\sqrt{2}; \sqrt{k}=4\sqrt{2}\
=\sqrt{4^2\times 2} = \sqrt{16\times 2}; \sqrt{k}=\sqrt{32}; k = 32\)

MPQ = PQM = 3x; ∆MPQ
MPQ + PQM + PMQ = 180^o; 3x + 3x + 30^o = 180^o
6x \times 30^o = 180^o; 6x + 180^o - 30^o; 6x + 150^o
\(x = \frac{150}{6} = 25^{\circ}\)

Median = 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5
Median mark = \(\frac{3+3}{2} = \frac{6}{2} = 3\)

Prob (2 or 3) = prob(2) + prob(3)
Prob (mark 2) \(=\frac{7}{22}\) + Prob(mark 3) = \(\frac{5}{22}\)
Prob(2 or 3) \(=\frac{7}{22}+\frac{5}{22}=\frac{12}{22}=\frac{6}{11}\)

\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\
\frac{3(x+2)-4(x+1)>6}{12}; 3x + 6 – 4x – 4 > 6\
-x +2>6; -x > 4; x < -4\)

\(Average \hspace{1mm}speed = \frac{Distance}{Time\hspace{1mm} taken}\
Distance = 800m = \frac{800}{1000}km = 0.8km\
Time\hspace{1mm}taken = 20\hspace{1mm}minutes = \frac{20}{60}hr=\frac{1}{3}hr\Average \hspace{1mm} speed = \left(0.8\div \frac{1}{3}\right)km/hr = (0.8\times3)km/hr\=2.4km/hr\)

Simplify \(\frac{2}{a+b}-\frac{1}{a-b}; \frac{2(a-b)-1(a+b)}{(a+b)(a-b)}\)

= \(\frac{2a-2b-a-b}{(a+b)(a-b)}\)

= \(\frac{a-3b}{a^2 - ab + ab - b^2}\)

= \(\frac{a-3b}{a^2-b^2}\)

x² + 3x – 4 = 0 has roots value at the curve makes touches with the x – axis. The curve contact is at x = -4 and +1.