Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Differentiate sin x, cos x, tan x, e^x, ln x and x^n for n in Q. • Use chain, product and quotient rules. • Solve related rates problems.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use second derivative notation and second derivative test for maxima/minima. • Interpret concavity and points of inflexion in context.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Integrate x^n, sin x, cos x, sec^2 x and e^x. • Use integration by inspection or substitution of the form integral f(g(x))g'(x) dx.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Find areas enclosed by curves and x- or y-axes, including negative integrals. • Find volumes of revolution about the x-axis or y-axis.
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Learning objective
• Use displacement, velocity and acceleration with v=ds/dt and a=dv/dt=d2s/dt2. • Use a=v dv/ds where appropriate. • Displacement is integral of velocity; total distance is integral of speed.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Set up differential equations from contexts. • Solve separable differential equations; exponential models solve dy/dx=ky. • Know the term general solution.
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Learning objective
• Use and interpret slope fields and their diagrams.
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Learning objective
• Use Euler's method for numerical solutions of first-order differential equations. • Use technology/spreadsheets for approximations. • Numerically solve coupled first-order systems such as predator-prey models.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use phase portraits for coupled systems dx/dt=ax+by, dy/dt=cx+dy. • Analyse future paths using real, complex and imaginary eigenvalues. • Identify equilibrium points, stable populations, saddle points, spirals and circles/ellipses.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Solve second-order differential equations numerically with Euler's method. • Rewrite as coupled first-order equations dx/dt=y and dy/dt=f(x,y,t). • Use phase portrait ideas for suitable second-order systems.
Start with the concept explanation, then practise to create mastery evidence.