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301 questions found · practise this subject as a set
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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 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 |