# Integrated Maths Scheme Book C2

A book of challenging problems from the Integrated Maths Scheme suitable for able key stage four and key stage five students. The book consists of four sections. Section one is a collection of twelve puzzles, section two, ten units exploring the mathematics behind computer graphics, section three, fifteen further challenging problems and section four contains the solutions.

Section One: Puzzles The mathematics in the puzzles includes finding the ratio of the shaded parts of overlapping circles, transforming shapes, a logic puzzle about the area of a carpet, a challenge to find a proof to show that a Damier, a French equivalent of a draughts board, cannot be split in a certain way, a topology problem, a geometry problem about the net of a dodecahedron, a repeating patterns and tessellation challenge, magic square, non-magic squares extended to hexagrams and pentagrams, a proportion problem involving the cautious gambler and Borel’s paradox.

Section Two: Graphics This section consists of ten units exploring the mathematics used in computer graphics. Areas of mathematics considered are vectors, trigonometry, Pythagoras’ rule, parametric equations, small angles, transformations, three dimensions, the equation of a sphere, equation of a plane, lines in three dimensions, rotations in three dimensions, using matrices to combine transformations, inverse matrices and perspective.

Section Three: Further Problems A collection of fifteen problems that is suitable for students studying advanced or further mathematics. Topics include solving simultaneous equations, forces in frameworks, the remainder theorem, binomial theorem, complex numbers, roots of equations, coding techniques, sums of series, difference equations, queuing theory and different dimensions.

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