# Reinforcing KS5 Maths Resources 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.

All resources are in English and Welsh.

Here you can find the original bilingual cover notes, worksheets and solutions for each session;
Click on the titles below to see each video.

**A: Problem Solving (2 videos)**

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;
Video
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.
Video
**B: Reinforcing AS-level Maths (6 videos)**

B1: Algebra (25 minutes) Surds, indices, factorising, algebraic fractions, completing the square,
remainder and factor theorems, simultaneous equations.Video
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. Video
B3: Algebraic Proof (50 minutes) Worked examples of deductive algebraic proofs, including using the
method of exhaustion. Video
B4: Differential Calculus (45 minutes) Differentiating simple expressions, equation of a
tangent to a curve, finding and identifying stationary points, differentiation from first principles.Video
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. Video
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.Video
**C: Tasting Further Mathematics (3 videos)**

C1: FM Pure Maths taster (55 minutes) Manipulating matrices, transformations using matrices,
summing series, Euler’s formula.Video
C2: Complex number taster (45 minutes) The idea of i =√(-1), the Argand diagram and manipulating
complex expressions in Cartesian x+iy form. Video
C3: FM Applied Maths taster (35 minutes) Regression lines and collisions.Video
Any questions or feedback, please contact fmspwales@swansea.ac.uk