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

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Find

A.     B.     C.     D.

The derivative of (2x + 1)(3x + 1) is _____

A. 12x + 1     B. 6x + 5    C. 6x + 1    D. 12x + 5

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

Evaluate ∫ sec2 θ dθ.

A. sec θ tan θ + k     B. tan θ + k     C. 2sec θ + k     D. sec θ + k

If y = 2x cos x- sin 2x, find when x =

A. π     B. - π     C.     D.

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

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

Find the value of x for which the function 3x3 — 9x2 is minimum.

A. 0    B. 2    C. 3    D. 5

The maximum value of the function f(x) = 2 + x - x2 is ______

A. -\frac{9}{4}     B. -\frac{7}{4}     C. -\frac{3}{2}     D. -\frac{1}{2}

If y = 3 cos 4x, \frac{dy}{dx} equals _____

A. 6 sin 8x     B. -24 sin 4x     C. 12 sin 4x     D. -12 sin 4x

Differentiation and Integration

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}

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