2012 - WAEC Mathematics Past Questions and Answers - page 5

\(\begin{array}{c|c} x & f & fx\ \hline 1 & 6 & 6 \
2 & 8 & 16\ 3 & 8 & 18\ 4 & 5 & 20\end{array}\)

mean x = \(\frac{\sum fx}{\sum f}\)

= \(\frac{60}{25}\)

x = 2.4

median = (\(\frac{N + 1}{2}\))th = (\(\frac{25 + 1}{2}\))th

= \(\frac{26th}{2}\)

= 13th

the 13th is 2

Reflex < POS = 2x (angle at centre is twice that at circumference)

reflex < POS + < POS = 350^o(angles at a point)

i.e. 2x + 8x = 360^o

10x = 360^o

x = \(\frac{360}{10}\)

= 36^o

< PRS = \(\frac{1}{2}\)

< POS(< at centre twice that circumference)

= \(\frac{1}{2}\) x 8x = 4x

4 x 36^o

< PRS = 144

< RSQ = < RPQ = 48^o (angle in the same segment)

< SQR < RSQ (Base angle of an isosceles \(\bigtriangleup\))

< SQR = 480

< QRS + < RSQ + < RSQ = 180^o(sum of interior angles of a \(\bigtriangleup\))

i.e. < QRS + 48^o + 48^o = 180

< QRS = 180 - (48 + 48) = 180 - 96 = 84^o

but < PRQ + < PRS = < QRS

< PRQ = < QRS - < PRS - 84 - 65

= 19^o

2x² - 5x - 3 = 0

2x² - 6x + x - 3 = 0

2x(x - 3) + 1(x - 3) = 0

(2x + 1)(x - 3) = 0

2x + 1 = 0

2x = -1

x = -\(\frac{1}{2}\)

x - 3 = 0

-\(\frac{1}{2}\) < x < 3

Sum of interior angles = 360²

i.e 3x + 2x + 2x + x + 4x = 360^o

12x = 360

x = \(\frac{360}{12}\)

x = 30^o

x + c = 180

30^o + c = 180

c = 180 - 30

c = 150^o