Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Prove that if α is a zero of multiplicity m, meeting the x -axis at A(α,0), then if m = 1, the curve crosses the x -axis at A at an acute or obtuse angle; if m > 1 is even, the curve is tangent to the x -axis at A and does not cross it; if m > 1 is odd, the curve has a horizontal inflection at A
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Conclude, for a continuous function y = f(x) on the interval a ≤ x ≤ b, that ∫abf(x)dx = (area of regions between curve and x -axis lying above the x -axis) - (area of regions between curve and the x -axis lying below the x -axis)
Mathematics Advanced 11–12 – Year 12 · Integral calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Model and solve practical problems involving integrals and areas of regions bounded by a curve and the x -axis, or by a curve and the y -axis, involving functions within the scope of the Mathematics Advanced course
Mathematics Advanced 11–12 – Year 12 · Integral calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Use the fact that the graphs of y = a^x and y = log_ax are reflections of each other in the line y = x to solve problems involving areas between the x -axis or y -axis and a curve involving either an exponential or logarithmic function
Mathematics Advanced 11–12 – Year 12 · Integral calculus Draft mapping
No checked resources on this prerequisite dot point yet.