# Teacher Guide

These are a series of eleven videos with accompanying question sheets and solutions, produced by FMSP Wales in Summer 2020, to help students transition from GCSE to A-level maths.

##### A: Problem Solving

A1: Mathematical Investigation (35 minutes)

An investigation of dates with no repeated digits; an investigation of numbers with digits summing to 8, or other values.

A2: Problems and Algorithms (35 minutes)

An introduction to the idea of algorithms, including calculating the day of the week from the date; and a look at some problems.

##### B: Reinforcing AS-level Maths

B1: Algebra (25 minutes)

Surds, indices, factorising, algebraic fractions, completing the square, remainder and factor theorems, simultaneous equations

B2: Coordinate Geometry (35 minutes)

Midpoints, distance, gradient, parallel and perpendicular lines, equation of line given gradient and a point, intersection a quadratic and line

B3: Algebraic Proof (50 minutes)

Worked examples of deductive algebraic proofs, including using the method of exhaustion.

B4: Differential Calculus (45 minutes)

Differentiating simple expressions, equation of a tangent to a curve, finding and identifying stationary points, differentiation from first principles.

B5: Integral Calculus (25 minutes)

Integrating simple expressions, finding equation of a curve from the gradient function and a point, finding the area under a graph.

B6: Introduction to Applied Maths (40 minutes)

Statistics: variance and standard deviation, Venn diagrams, distributions, hypothesis testing; Mechanics: vectors, motion equations with constant acceleration, Newton’s second law, planar motion

##### C: Tasting Further Mathematics

C1: FM Pure Maths taster (55 minutes)

Manipulating matrices, transformations using matrices, summing series, Euler’s formula.

C2: Complex number taster (45 minutes)

The idea of i =√(-1), the Argand diagram and manipulating complex expressions in Cartesian x+iy form

C3: FM Applied Maths taster (35 minutes)

Regression lines and collisions