1992 - JAMB Mathematics Past Questions and Answers - page 4

(\frac{dm}{dt}) = 4 - 0.6t

(\int)dm = (\int)(4 - 0.6t)dt

m = 4t - 0.3t² + c, when t = 0, m = 2g

∴ c = 2

m = 4t - 0.3t² + 2, when t = 5 minutes

m = 4(5) - 0.3(5)² + 2 = 20 - 7.5

= 14.5

f(x) = x³ - 12x + 11

(\frac{df(x)}{dx)}) = 3x² - 12 = 0

∴ 3x² - 12 = 0 (\to) x²m = 4

x = (\pm)2, f(+2) = 8 - 24 + 11 = -15

= f(-2) = (-8) + 24 + 11

= 35 - 8 = 27

∴ maximum value = 27

(\frac{dv}{dt}) = (\pi)(20 - t²)cm²S^-1

(\int)dv = (\pi)(20 - t²)dt

V = (\pi) (\int)(20 - t²)dt

V = (\pi)(20 (\frac{t}{3}) - t³) + c

when c = 0, V = (20t - (\frac{t^3}{3}))

after t = 2 seconds

V = (\pi)(40 - (\frac{8}{3})

= (\pi)(\frac{120 - 8}{3})

= (\frac{112}{3})

= 37.33(\pi)

let I = (\int^{\frac{\pi}{4}}_{\frac{\pi}{12}}) 2 cos 2x dx

= 2(sin 2x)^{(\frac{\pi}{4})} (sin 2x)^{(\frac{\pi}{4})}_{(\frac{\pi}{12})}

(2)(\frac{\pi}{12})

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

= (\frac{1}{2})

H will represent (\frac{108}{720}) x (\frac{360^o}{1}) = 54^o

Mean (\bar{x}) = (\frac{\sum fx}{\sum f})

= (\frac{5.2}{1})

= (\frac{8 + 4y + 36 + 40}{4 + y + 6 + 5})

= (\frac{5.2}{1})

= (\frac{84 + 4y}{15 + y})

= 5.2(15 + y)

= 84 + 4y

= 5.2 x 15 + 5.2y

= 84 + 4y

= 78 + 5.2y

= 84 = 4y

= 5.2y - 4y

= 84 - 78

1.2y = 6

y = (\frac{6}{1.2})

= (\frac{60}{12})

= 5

(x) = (\frac{5 + 6 + 7}{3})

= (\frac{18}{3})

= 6

(\begin{array}{c|c} scores(X) & \text{d = (x - x) deviation} & (deviation)^2\hline 5 & 5 - 6 & 1\ 6 & 6 - 6 & 0 \ 7 & 7 - 6 & 1\ \hline & & 2\end{array})

S.D (\sqrt{\frac{\sum d^2}{n}}) where d = deviation = (x - x)

= (\sqrt{\frac{2}{3}})