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Eight original Paper 3 investigations to support problem solving skills to prepare for the Paper 3 Higher Level paper. These investigations also are excellent for coursework explorations. Full markschemes also included.
Description
Eight original Paper 3 investigations to support problem solving skills to prepare for the Paper 3 Higher Level paper. These investigations also are excellent for coursework explorations. Full markschemes also included.
Questions included are:
Rotating curves.
The mathematics used here is trigonometry (identities and triangles), functions and transformations. Students explore the use of parametric and Cartesian equations to rotate a curve around the origin.
Who killed Mr. Potato?
The mathematics used here is logs laws, linear regression and solving differential equations. Students explore Newton’s Law of Cooling to predict when a potato was removed from an oven.
Graphically understanding complex roots
The mathematics used here is complex numbers (finding roots), the sum and product of roots, factor and remainder theorems, equations of tangents. Students explore graphical methods for finding complex roots.
Avoiding a magical barrier
The mathematics used here is creating equations, optimization and probability. Students explore a scenario that requires them to solve increasingly difficult optimization problems.
Circle packing density
The mathematics used here is trigonometry and using equations of tangents. Students explore different methods of filling a space with circles to find different circle packing densities.
A sliding ladder investigation
The mathematics used here is trigonometry and differentiation. Students find the general equation of the midpoint of a slipping ladder and calculate the length of the astroid formed.
Exploring the Si(x) function
The mathematics used here is Maclaurin series, integration, summation notation, sketching graphs. Students explore methods for approximating non-integrable functions
Volume optimization of a cuboid
The mathematics used here is optimization, graph sketching, extended binomial series, limits to infinity. Students start with a simple volume optimization problem but extend this to a general case.