#### Reinforcement for A-level Mathematics & Further Mathematics

These are a series of eleven videos with accompanying question sheets and solutions, produced by FMSP Wales 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