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301 questions found · practise this subject as a set
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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 51 | At how many points is f(x) = |x − 1| + |x − 2| not differentiable? | Mathematics/Applied Mathematics Continuity and differentiability |
Hard |
| 52 | The derivative of tan⁻¹x with respect to x is | Mathematics/Applied Mathematics Derivatives of special functions |
Easy |
| 53 | The derivative of log(sin x) is | Mathematics/Applied Mathematics Derivatives of special functions |
Easy |
| 54 | If x = at² and y = 2at, then dy/dx equals | Mathematics/Applied Mathematics Derivatives of special functions |
Medium |
| 55 | For the curve x² + y² = 25, the value of dy/dx at the point (3, 4) is | Mathematics/Applied Mathematics Derivatives of special functions |
Medium |
| 56 | If y = x^x for x > 0, then dy/dx equals | Mathematics/Applied Mathematics Derivatives of special functions |
Hard |
| 57 | If y = x³ − 2x, then d²y/dx² equals | Mathematics/Applied Mathematics Second-order derivatives |
Easy |
| 58 | The second derivative of y = sin x is | Mathematics/Applied Mathematics Second-order derivatives |
Easy |
| 59 | The function y = e^(3x) satisfies which of the following? | Mathematics/Applied Mathematics Second-order derivatives |
Medium |
| 60 | If y = log x, the value of d²y/dx² at x = 2 is | Mathematics/Applied Mathematics Second-order derivatives |
Medium |
| 61 | If x = a cos t and y = a sin t, then d²y/dx² equals | Mathematics/Applied Mathematics Second-order derivatives |
Hard |
| 62 | The rate of change of the area of a circle with respect to its radius r, when r = 5 cm, is | Mathematics/Applied Mathematics Rate of change |
Easy |
| 63 | A particle moves so that s = t³ − 3t metres after t seconds. Its velocity at t = 2 s is | Mathematics/Applied Mathematics Rate of change |
Easy |
| 64 | The radius of a circle increases at 0.5 cm/s. How fast is its area increasing when the radius is 4 cm? | Mathematics/Applied Mathematics Rate of change |
Medium |
| 65 | Each side of a cube increases at 3 cm/s. At what rate is the volume increasing when a side is 10 cm? | Mathematics/Applied Mathematics Rate of change |
Medium |
| 66 | Air is pumped into a spherical balloon so that its volume increases at 900 cm³/s. How fast is the radius incr… | Mathematics/Applied Mathematics Rate of change |
Hard |
| 67 | The function f(x) = 3x + 7 is | Mathematics/Applied Mathematics Increasing and decreasing functions |
Easy |
| 68 | On which interval is f(x) = x² strictly decreasing? | Mathematics/Applied Mathematics Increasing and decreasing functions |
Easy |
| 69 | The function f(x) = x³ − 3x is strictly decreasing on | Mathematics/Applied Mathematics Increasing and decreasing functions |
Medium |
| 70 | The function f(x) = 2x³ − 9x² + 12x + 1 is strictly decreasing on | Mathematics/Applied Mathematics Increasing and decreasing functions |
Medium |
| 71 | For which values of a is f(x) = x³ + ax + 5 strictly increasing on all of R? | Mathematics/Applied Mathematics Increasing and decreasing functions |
Hard |
| 72 | The minimum value of x² + 4x + 9 is | Mathematics/Applied Mathematics Maxima and minima |
Easy |
| 73 | If f′(c) = 0 and f″(c) > 0, then at x = c the function f has | Mathematics/Applied Mathematics Maxima and minima |
Easy |
| 74 | The local maximum value of f(x) = x³ − 3x is | Mathematics/Applied Mathematics Maxima and minima |
Medium |
| 75 | Two positive numbers have a sum of 20. What is the largest possible value of their product? | Mathematics/Applied Mathematics Maxima and minima |
Medium |
| 76 | The absolute maximum value of f(x) = 2x³ − 15x² + 36x + 1 on the interval [1, 5] is | Mathematics/Applied Mathematics Maxima and minima |
Hard |
| 77 | ∫ x⁴ dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Easy |
| 78 | ∫ sec²x dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Easy |
| 79 | ∫ (2x + 3/x) dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Medium |
| 80 | ∫ e^(2x) dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Medium |
| 81 | If F′(x) = 3x² + 2x and F(1) = 5, then F(x) equals | Mathematics/Applied Mathematics Indefinite integrals |
Hard |
| 82 | To evaluate ∫ 2x cos(x²) dx, the most useful substitution is | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 83 | ∫ x eˣ dx equals | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 84 | ∫ dx/[x(x + 1)] equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 85 | ∫ log x dx equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 86 | ∫ dx/(x² − 9) equals | Mathematics/Applied Mathematics Methods of integration |
Hard |
| 87 | The value of ∫₀² x dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 88 | The value of ∫ from −1 to 1 of x³ dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 89 | The value of ∫₀^(π/2) cos x dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 90 | The value of ∫₀^(π/2) sin x/(sin x + cos x) dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 91 | The value of ∫₀¹ x(1 − x)⁴ dx is | Mathematics/Applied Mathematics Definite integrals |
Hard |
| 92 | The area bounded by the line y = x, the x-axis and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 93 | The area enclosed by the ellipse x²/a² + y²/b² = 1 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 94 | The area under y = x² from x = 0 to x = 3, above the x-axis, is | Mathematics/Applied Mathematics Applications of integrals |
Medium |
| 95 | The area of the part of the circle x² + y² = 16 lying in the first quadrant is | Mathematics/Applied Mathematics Applications of integrals |
Medium |
| 96 | The area of the region bounded by the parabola y² = 4x and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Hard |
| 97 | The order of the differential equation d³y/dx³ + 2 d²y/dx² + dy/dx = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Easy |
| 98 | The degree of (d²y/dx²)² + (dy/dx)³ + y = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Easy |
| 99 | The degree of the differential equation d²y/dx² + sin(dy/dx) = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Medium |
| 100 | How many arbitrary constants appear in the general solution of a differential equation of order 3? | Mathematics/Applied Mathematics Differential equations: basics |
Medium |