Mathematics Practice Tests (SS1 – SS3) – Calculus (Differentiation and Integration)

Hello and Welcome to Mathematics Practice Tests (SS1 - SS3) - Calculus (Differentiation and Integration)

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Find the maximum value of y in the equation y = 1 - 2x - 3x2

A. $\frac{5}{4}$      B. $\frac{5}{3}$      C. $\frac{3}{4}$      D. $\frac{4}{3}$

Evaluate $\int_{0}^{1}&space;(3&space;-&space;2x)&space;dx$

A. 3     B.5     C. 2     D. 6

lf  $\frac{dy}{dx}$  = 2x - 3 and y = 3 when x = 0, find y in terms of x.

A. 2x2 - 3x      B. x2 - 3x      C. x2 - 3x - 3       D. x2 - 3x + 3

Evaluate $\int_{\frac{\pi&space;}{2}}^{0}sin\:&space;2xdx$

A. 1    B. 0     C. $-\frac{1}{2}$    D. –1

Differentiate (cos θ — sin θ)2 with respect to θ

A. -2 cos 2θ    B. -2 sin 2θ     C. 1 - 2 cos 2θ    D. 1 - 2 sin 2θ

If y = x cos x, find  $\frac{dy}{dx}$

A. sin x - x cos x     B. sin x + x cos x     C. cos x + x sin x     D. cos x - x sin x

Given y = x3 − x2 − 4,  find  $\frac{dy}{dx}$  at  x  =  4

A. 38    B. 39    C. 40   D. 41

Given y = x3 − x2 − 4, find  $\frac{dy}{dx}$  at  x =  0

A. 0     B. 1    C. 2    D. 3

The distance travelled by a particle from a fixed point is given as s = (t3 - t2 - t + 5) cm. Find the minimum distance that the particle can cover from the fixed point.

A. 2.3 cm    B. 4.0 cm    C. 5.2 cm    D. 6.0 cm

Find the minimum value of y = x2 + 6x - 12

A. -21     B. -12     C. -6     D. -3

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