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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 4301 | For AX = B, suppose |A| = 0 and (adj A)B ≠ O. Then the system | Mathematics/Applied Mathematics Solving systems of linear equations |
Medium |
| 4302 | For which value of k does the system kx + 2y = 3, 2x + y = 5 have no solution? | Mathematics/Applied Mathematics Solving systems of linear equations |
Medium |
| 4303 | The system x + y + z = 6, y + 3z = 11, x − 2y + z = 0 has the solution | Mathematics/Applied Mathematics Solving systems of linear equations |
Hard |
| 4304 | If f(x) = kx + 1 for x ≤ 2 and f(x) = 3x − 1 for x > 2, for which value of k is f continuous at x = 2? | Mathematics/Applied Mathematics Continuity and differentiability |
Easy |
| 4305 | At x = 0, the function f(x) = |x| is | Mathematics/Applied Mathematics Continuity and differentiability |
Easy |
| 4306 | The derivative of sin(x²) with respect to x is | Mathematics/Applied Mathematics Continuity and differentiability |
Medium |
| 4307 | If f(x) = x² for x ≤ 1 and f(x) = ax + b for x > 1 is differentiable at x = 1, then (a, b) equals | Mathematics/Applied Mathematics Continuity and differentiability |
Medium |
| 4308 | At how many points is f(x) = |x − 1| + |x − 2| not differentiable? | Mathematics/Applied Mathematics Continuity and differentiability |
Hard |
| 4309 | The derivative of tan⁻¹x with respect to x is | Mathematics/Applied Mathematics Derivatives of special functions |
Easy |
| 4310 | The derivative of log(sin x) is | Mathematics/Applied Mathematics Derivatives of special functions |
Easy |
| 4311 | If x = at² and y = 2at, then dy/dx equals | Mathematics/Applied Mathematics Derivatives of special functions |
Medium |
| 4312 | 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 |
| 4313 | If y = x^x for x > 0, then dy/dx equals | Mathematics/Applied Mathematics Derivatives of special functions |
Hard |
| 4314 | If y = x³ − 2x, then d²y/dx² equals | Mathematics/Applied Mathematics Second-order derivatives |
Easy |
| 4315 | The second derivative of y = sin x is | Mathematics/Applied Mathematics Second-order derivatives |
Easy |
| 4316 | The function y = e^(3x) satisfies which of the following? | Mathematics/Applied Mathematics Second-order derivatives |
Medium |
| 4317 | If y = log x, the value of d²y/dx² at x = 2 is | Mathematics/Applied Mathematics Second-order derivatives |
Medium |
| 4318 | If x = a cos t and y = a sin t, then d²y/dx² equals | Mathematics/Applied Mathematics Second-order derivatives |
Hard |
| 4319 | 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 |
| 4320 | 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 |
| 4321 | 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 |
| 4322 | 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 |
| 4323 | 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 |
| 4324 | The function f(x) = 3x + 7 is | Mathematics/Applied Mathematics Increasing and decreasing functions |
Easy |
| 4325 | On which interval is f(x) = x² strictly decreasing? | Mathematics/Applied Mathematics Increasing and decreasing functions |
Easy |
| 4326 | The function f(x) = x³ − 3x is strictly decreasing on | Mathematics/Applied Mathematics Increasing and decreasing functions |
Medium |
| 4327 | The function f(x) = 2x³ − 9x² + 12x + 1 is strictly decreasing on | Mathematics/Applied Mathematics Increasing and decreasing functions |
Medium |
| 4328 | 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 |
| 4329 | The minimum value of x² + 4x + 9 is | Mathematics/Applied Mathematics Maxima and minima |
Easy |
| 4330 | If f′(c) = 0 and f″(c) > 0, then at x = c the function f has | Mathematics/Applied Mathematics Maxima and minima |
Easy |
| 4331 | The local maximum value of f(x) = x³ − 3x is | Mathematics/Applied Mathematics Maxima and minima |
Medium |
| 4332 | Two positive numbers have a sum of 20. What is the largest possible value of their product? | Mathematics/Applied Mathematics Maxima and minima |
Medium |
| 4333 | The absolute maximum value of f(x) = 2x³ − 15x² + 36x + 1 on the interval [1, 5] is | Mathematics/Applied Mathematics Maxima and minima |
Hard |
| 4334 | ∫ x⁴ dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Easy |
| 4335 | ∫ sec²x dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Easy |
| 4336 | ∫ (2x + 3/x) dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Medium |
| 4337 | ∫ e^(2x) dx equals | Mathematics/Applied Mathematics Indefinite integrals |
Medium |
| 4338 | If F′(x) = 3x² + 2x and F(1) = 5, then F(x) equals | Mathematics/Applied Mathematics Indefinite integrals |
Hard |
| 4339 | To evaluate ∫ 2x cos(x²) dx, the most useful substitution is | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 4340 | ∫ x eˣ dx equals | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 4341 | ∫ dx/[x(x + 1)] equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 4342 | ∫ log x dx equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 4343 | ∫ dx/(x² − 9) equals | Mathematics/Applied Mathematics Methods of integration |
Hard |
| 4344 | The value of ∫₀² x dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 4345 | The value of ∫ from −1 to 1 of x³ dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 4346 | The value of ∫₀^(π/2) cos x dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 4347 | The value of ∫₀^(π/2) sin x/(sin x + cos x) dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 4348 | The value of ∫₀¹ x(1 − x)⁴ dx is | Mathematics/Applied Mathematics Definite integrals |
Hard |
| 4349 | The area bounded by the line y = x, the x-axis and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 4350 | The area enclosed by the ellipse x²/a² + y²/b² = 1 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |