AS Level Edexcel Topics

1. Pure Mathematics

This makes up a large part of the course. Key topics include:

• Algebra and Functions
  • Simplifying expressions, solving equations (linear, quadratic), and inequalities.
  • Understanding and using functions, including domain, range, inverse functions, and composite functions.
• Coordinate Geometry
  • Straight-line equations, distance between points, midpoints, and gradients.
  • Circles: equations of a circle and tangents to circles.
• Polynomials
  • Division of polynomials, factor theorem, and remainder theorem.
  • Solving cubic equations.
• Quadratics
  • Completing the square, using the quadratic formula.
  • Solving quadratic inequalities and equations.
• Binomial Expansion
  • Expanding powers of binomials using Pascal’s Triangle and the binomial theorem for positive integer powers.
• Trigonometry
  • Working with radians, solving trigonometric equations, and using identities such as sin⁡2(x)+cos⁡2(x)=1\sin^2(x) + \cos^2(x) = 1sin2(x)+cos2(x)=1.
  • Sine and cosine rule, graphs of sine, cosine, and tangent functions.
• Exponential and Logarithms
  • The laws of logarithms, solving exponential equations, and understanding the logarithmic form.
  • The function exe^xex and natural logarithms.
• Differentiation
  • Finding derivatives of polynomials, exponentials, and trigonometric functions.
  • Differentiating using the chain rule, product rule, and quotient rule.
  • Applications: Finding gradients, tangents, normals, and solving problems involving maxima and minima.
• Integration
  • Basic integration (reverse of differentiation).
  • Definite integrals and finding the area under curves.
  • Integration of simple functions like polynomials, exponentials, and trigonometric functions.
• Vectors
  • Basic vector operations (addition, scalar multiplication).
  • Magnitude and direction, vector equations of lines.

2. Statistics

This part involves analysing data and probability:

• Data Representation and Interpretation
  • Histograms, box plots, cumulative frequency diagrams.
  • Measures of central tendency (mean, median, mode) and spread (variance, standard deviation).
• Probability
  • Laws of probability, including independent and mutually exclusive events.
  • Conditional probability and Venn diagrams.
• Statistical Distributions
  • Binomial distribution: properties and application.
  • Normal distribution: mean, standard deviation, and applications.
• Statistical Hypothesis Testing
  • Formulating and testing hypotheses using the binomial distribution.
  • Understanding significance levels and p-values.

3. Mechanics

Mechanics is the application of maths to physical problems:

• Kinematics
  • Using equations of motion to solve problems involving constant acceleration.
  • Graphs of motion (displacement-time, velocity-time, acceleration-time).
• Forces and Newton’s Laws
  • Newton’s three laws of motion.
  • Resolving forces, equilibrium, and friction.
• Momentum
  • Calculating momentum and understanding the principle of conservation of momentum.
  • Using impulse and collisions.
• Statics
  • Using vectors to solve problems involving forces in equilibrium.