Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Estimate limits from tables or graphs; formal analytic limit methods are not required. • Interpret derivative as gradient function and rate of change. • Use notation dy/dx, f'(x), dV/dr and ds/dt.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Interpret f'(x)>0, f'(x)=0 and f'(x)<0 graphically. • Identify intervals where functions are increasing or decreasing.
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Learning objective
• Differentiate f(x)=ax^n to f'(x)=anx^(n-1), n in Z. • Differentiate sums of integer-power terms.
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Learning objective
• Find tangents and normals at a given point and their equations. • Use analytic methods and technology.
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Learning objective
• Integrate polynomial-type functions as anti-derivatives. • Use boundary conditions to determine constants. • Connect anti-derivatives, definite integrals and area under curves.
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Learning objective
• Differentiate x^n (n in Q), sin x, cos x, e^x and ln x. • Use sum/multiple rules, chain rule, product rule and quotient rule.
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Learning objective
• Use second derivative notation d2y/dx2 and f''(x). • Relate graphs of f, f' and f''; use technology where useful.
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Learning objective
• Find local maxima/minima using first-derivative sign changes or second derivative tests. • Solve optimization problems in contexts such as profit, area and volume. • Identify points of inflexion and concavity.
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Learning objective
• Use displacement s, velocity v, acceleration a and total distance travelled. • v=ds/dt and a=dv/dt=d2s/dt2. • Displacement is integral of velocity; distance is integral of speed |v(t)|.
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Learning objective
• Integrate x^n, sin x, cos x, 1/x and e^x. • Use composites with linear functions and reverse chain rule/substitution by inspection.
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Learning objective
• Use definite integral analytically: integral_a^b g'(x) dx = g(b)-g(a). • Find areas under curves and between curves, accounting for sign. • Write correct integral expressions before calculating.
Start with the concept explanation, then practise to create mastery evidence.