Calculus - Mathematics Jamb Past Questions and Answers

Question 1 :

• JAMB 2019

If \(y = 6x^3 + 2x^{-2} - x^{-3}\), find \(\frac{\mathrm d y}{\mathrm d x}\).

A. \(\frac{\mathrm d y}{\mathrm d x} = 15x^2 - 4x^{-2} - 3x^{-2}\)
B. \(\frac{\mathrm d y}{\mathrm d x} = 6x + 4x^{-1} - 3x^{-4}\)
C. \(\frac{\mathrm d y}{\mathrm d x} = 18x^2 - 4x^{-3} + 3x^{-4}\)
D. \(\frac{\mathrm d y}{\mathrm d x} = 12x^2 + 4x^{-1} - 3x^{-2}\)

Question 2 :

• JAMB 2019

\(\frac{d}{dx} [\log (4x^3 - 2x)]\) is equal to

A. \(\frac{12x - 2}{4x^2}\)
B. \(\frac{43x^2 - 2x}{7x}\)
C. \(\frac{4x^2 - 2}{7x + 6}\)
D. \(\frac{12x^2 - 2}{4x^3 - 2x}\)

Question 3 :

• JAMB 2019

Integrate \(\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x\)

A. \(4\frac{1}{2}\)
B. \(3\frac{1}{2}\)
C. \(7\frac{1}{2}\)
D. \(5\frac{1}{4}\)

Question 4 :

• JAMB 2019

If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.

A. 50 units per sec
B. 35 units per sec
C. 22 units per sec
D. 13 units per sec

Question 5 :

• JAMB 2019

If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).

A. \(\frac{\pi h}{3} (2R + r)\)
B. \(2R + r + \frac{\pi h}{3}\)
C. \(\frac{\pi h}{3} (2R^2 + r + 2r)\)
D. \(\frac{2R^2}{3} \pi h\)