Ten questions on differentiation, integration, logarithms, the circle, vectors, the remainder theorem, trigonometric equations and recurrence limits…
10 questions • Zestly
• Find the coordinates of the stationary point of the curve $y = x^2 - 6x + 5$ and classify it.
• Find the area enclosed between the curve $y = 4 - x^2$ and the x-axis from $x = 0$ to $x = 2$.
• Solve for $x$ in the equation $3^{x+1} = 27$.
• Find the centre and radius of the circle with equation $x^2 + y^2 - 4x + 6y - 3 = 0$.
• Given vectors $u = (1, 2, -1)$ and $v = (3, 0, 2)$, find their scalar product $u \cdot v$.
• Find the remainder when $P(x) = 2x^3 - x^2 + 4$ is divided by $(x - 2)$.
• Solve $\sin(x) = 0.5$ for $0 \le x < 2\pi$.
• A sequence is defined by $u_{n+1} = 0.5u_n + 3$. Find the limit as $n \to \infty$.
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