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
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
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