Home » Mathematics Theory (a) Simplify : ((frac{x^{2}}{2} – x + frac{1}{2})(frac{1}{x – 1})) (b) A point P is…

Mathematics Theory (a) Simplify : ((frac{x^{2}}{2} – x + frac{1}{2})(frac{1}{x – 1})) (b) A point P is…

(a) Simplify : ((frac{x^{2}}{2} – x + frac{1}{2})(frac{1}{x – 1}))

(b) A point P is 40km from Q on a bearing 061°. Calculate, correct to one decimal place, the distance of P to (i) north of Q ; (ii) east of Q.

(c) A man left N5,720 to be shared among his son and three daughters. Each daughter’s share was (frac{3}{4}) of the son’s share. How much did the son receive?

Explanation

(a) ((frac{x^{2}}{2} – x + frac{1}{2})(frac{1}{x – 1}))

(frac{x^{2}}{2} – x + frac{1}{2} = frac{x^{2} – 2x + 1}{2})

= (frac{(x – 1)^{2}}{2})

(therefore (frac{x^{2}}{2} – x + frac{1}{2})(frac{1}{x – 1}) = (frac{(x – 1)^{2}}{2})(frac{1}{x – 1}))

= (frac{x – 1}{2})

(b) 

(i) TQ = PR (North of Q)

(implies sin 29 = frac{PR}{40})

(PR = 40 sin 29 = 19.39 km)

(ii) QR = East of Q

(frac{QR}{40} = cos 29)

(QR = 40 cos 29)

= 34.98km

(approxeq) 35km.

(c) Let the son’s share = x.

Each daughter’s share = (frac{3}{4}x)

For the three daughters = (3 times frac{3}{4} = frac{9}{4})

(x + frac{9}{4}x = 5720 implies frac{13}{4}x = 5720)

(x = frac{5720 times 4}{13} = N1760)