JAMB Mathematics Past Questions & Answers - Page 16

Area of a circle (A) = \(\pi r^2\)

Given

\(\frac{dA}{dt} = 1.5cm^2s^{-1}\)

\(\frac{dr}{dt}\) = ?

A = 2cm\(^2\)

Now

2 = \(\pi r^2\)

= r\(^2 = \frac {2}{\pi}\)

r = \(\sqrt \frac {2}{\pi}\) cm = 0.798cm

\(\frac {dr}{dt} = \frac {dA}{dt} \times \frac {dr}{dt}\)

\(\frac {dA}{dr} = 2\pi r\) (differentiating A = \(\pi r^2)\)

\(\frac {dr}{dA} = \frac {1}{2\pi r}\)

\(\frac {dr}{dt} = 1.5 \times \frac {1}{2\times \pi \times 0.798} = 1.5 \times 0.199\)

\(\frac {dr}{dt} = 0.299cms^{-1}\) (to 3 s.f)

An interior angle of a regular polygon = \(\frac{(2n-4)\times 90}{n}\)

An exterior angle of a regular polygon = \(\frac{360}{n}\)

\(\frac{(2n-4)\times 90}{n}\) =5 \(\times\)  \(\frac{360}{n}\) (Given)
= (2n-4) x 90 = 5 x 360
= 180n - 360 = 1800
= 180n = 1800 + 360
= 180n = 2160
= n = \(\frac{2160}{180}\) = 12
The polygon has 12 sides which is dodecagon

\(\int_0^1 4x - 6^3\sqrt x^2\) dx
=\(\int_0^1 4x - 6x^{2/3}\) dx
=\((2x^2 - \frac{8x^{5/3}}{5})_0^1\)
=\((2(1)^2 - \frac{18(1)^{5/3}}{5}) - (2(0)^2 - \frac{18(0)^{5/3}}{5}\)
= - \(\frac{8}{5}\) - 0
    - \(\frac{8}{5}\)

16\(^{0.16}\) × 16\(^{0.04}\) × 2\(^{0.2}\)
=2\(^{4(0.16)}\) × 2\(^{4(0.04)}\) × 2\(^{0.2}\)
=2\(^{0.64}\) × 2\(^{0.16}\) × 2\(^{0.2}\)
=2\(^{0.64\times0.16\times0.2}\)
=2\(^1\)
  2

√24 + √96 - √600 = y√6

convert all to basic surds

√24 = 2√6

√96 = 4√6

- √600 = -10√6

2√6 + 4√6 - 10√6 = -4√6

value of y = -4