Examples, and questions with solutions

Partial Fractions, Factor Theorem, Remainder Theorem, Simplifying Algebraic Fractions. With brief solutions.

Component vectors, i and j vectors, revision of vectors

Scalar triple product including applications to volumes

Examples and Questions

A quotient rule jigsaw puzzle that doesn’t need differentiation of trig functions or of e^x and lnx

With brief solutions

Includes integration which results in inverse hyperbolics and inverse trig functions. (I've chosen to do this with definite integration instead of indefinite integration, so that the students can't solve the puzzle by differentiation of the solutions, they must integrate)

Working out the third side in a right-angled triangle. In this puzzle, a and b are always the shorter sides, and c the hypotenuse. Non-exact answers are given to 3 s.f.

Taken together, these three give a first lesson on eigenvectors and eigenvalues (not diagonalising)

This worksheet looks in more detail at why cosh x = a has 2 solutions even though arcosh x is uniquely defined, and the different ways these 2 solutions can be expressed. Key words: hyperbolics, equations, inverse hyperbolic functions

Converting the practical problem to the classical problem

Hexagonal jigsaw for indices. The three pages make up one jigsaw.

An easier hexagonal jigsaw for indices, made up of 3 pages

Probability density functions and cumulative distribution functions

In 2D and 3D

Graphs, revision notes, p greater than a half

PMCC, product moment correlation coefficient

Algebraic fractions, partial fractions, factor theorem, remainder theorem

Surd forms for 30, 45, 60 etc