Year 11 Maths Advanced MAV-11-06 Checkpoint 1

Checkpoint Quiz 1

This checkpoint covers Average and Instantaneous Rates of Change, Limits, the Derivative as the Gradient of a Tangent, Differentiation Rules, and the Chain Rule (Lessons 1–6).

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Quick Review

  • Average rate of change: $\dfrac{f(b)-f(a)}{b-a}$, the gradient of the secant line joining $(a, f(a))$ and $(b, f(b))$. Shrinking the interval estimates the instantaneous rate at a point.
  • Limits: $\lim_{x \to a} f(x)$ is the value $f(x)$ approaches as $x$ gets arbitrarily close to $a$. Factor and cancel to evaluate limits that give $\frac{0}{0}$ on direct substitution.
  • Derivative from first principles: $f'(x) = \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$, the exact gradient of the tangent at a point. The normal at that point has gradient $-\dfrac{1}{f'(a)}$.
  • Differentiation rules: Power rule $\dfrac{d}{dx}(x^n) = nx^{n-1}$; constants pass through unchanged, $\dfrac{d}{dx}(cf(x)) = cf'(x)$; differentiate sums and differences term by term.
  • Chain rule: For a composite function $y = f(g(x))$, let $u = g(x)$ so $y = f(u)$, then $\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}$.
MC

Multiple Choice

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