How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
If y = x sinx, find dy/dx when x = π/2.
-π/2
-1
1
π/2
Correct answer is C
y = x sin x
dy/dx = 1 x sinx + x cosx
= sinx + x cosx
At x = π/2, = sin (π/2) + (π/2) cos (π/2)
= 1 + (π/2) x (0) = 1
Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1
12π
4π
24π
8π
Correct answer is B
Volume of sphere, V = 4/3 x πr3
Rate of change of V = dv/dr
Thus if V = 4/3 x πr3,
=> dv/dr = 4πr2
At r = 1, Rate = 4 x π x 1 = 4π
Find the area bounded by the curves y = 4 - x2 and y = 2x + 1
20(1/3) sq. units
20(2/3) sq. units
10(2/3) sq. units
10(1/3) sq. units
Correct answer is C
y = 4 - x\(^2\) and y = 2x + 1
=> 4 - x2 = 2x + 1
=> x2 + 2x - 3 = 0
(x+3)(x-1) = 0
thus x = 1 or x = -3.
Integrating x\(^2\) + 2x - 3
Differentiate \((2x+5)^{2} (x-4)\) with respect to x.
4(2x+5)(x-4)
4(2x+5)(4x-3)
(2x+5)(2x-13)
(2x+5)(6x-11)
Correct answer is D
\(y = (2x + 5)^{2} (x - 4)\)
\(\frac{\mathrm d y}{\mathrm d x} = (2x + 5)^{2} (1) + (x - 4)(2)(2)(2x + 5)\)
= \((2x + 5)(2x + 5 + 4x - 16)\)
= \((2x + 5)(6x - 11)\)
Evaluate \(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\)
3/5(2x-3)5/3 + k
6/5(2x-3)5/3 + k
2x-3+k
2(2x-3)+k
Correct answer is A
\(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\)
Let \(u = 2x - 3\)
\(\mathrm d u = 2 \mathrm d x\)
= \(\int u^{\frac{2}{3}} \mathrm d u\)
= \(\frac{u^{\frac{5}{3}}}{\frac{5}{3}} + k\)
= \(\frac{3}{5} (2x - 3)^{\frac{5}{3}} + k\)