# Specification for the Edexcel A’Level Mathematics

## Paper 1 and Paper 2: Pure Mathematics

1. Proof

2. Algebra and Functions

1. Indices?
2. Surds? and Rationalising the Denominator?
• Completing the Square?
• Discriminant?
4. Simultaneous Equations?
5. Inequalities?
6. Polynomials?
• Factorisation?
• Algebraic Division?
• Factor Theorem?
• Algebraic Fractions?
7. Graphs? including reciprocals? and the modular function?
8. Composite functions? and Inverse Functions?
9. Transformations of Graphs?
10. Partial Fractions?
11. Modelling? using functions
3. Coordinate Geometry in the $(x,y)$-Plane

1. Equation of a Straight Line?, including Parallel? and Perpendicular?
2. Equation of a Circle?
3. Parametric Functions?
4. Modelling using parametric functions
4. Sequences and Series

1. Binomial Expansion?
2. Sequences?
3. Sigma Notation?
4. Arithmetic Series?
5. Geometric Series?
6. Modelling using sequences and series
5. Trigonometry

1. Trigonometry?
3. Small Angle Approximation?
4. Trigonometric Graphs?
5. Inverse Trigonometric Functions? and Reciprocal Trigonometric Functions?
6. Trigonometric Identities?
7. Compound Angle Formula?
8. Trigonometric Equations?
9. Proofs involving trigonometric functions
10. Modelling using trigonometric functions
6. Exponentials and Logarithms

1. Exponential Functions? including e^x?
2. Derivative of the Exponential Function?
3. Logarithm Functions? including ln?
4. Laws of Logarithms?
5. Solving equations using logarithms
6. Logarithmic Graphs?
7. Modelling using Exponential Functions?
7. Differentiation

1. Derivative? as gradient of a function
2. Differentiation of Powers?, of trigonometric functions?, and of exponential and logarithmic functions?
3. Using differentiation to find the equations of Tangents? and Normals?
4. The Chain Rule?, The Product Rule?, and The Quotient Rule?
5. Implicit Differentiation? and Parametric Differentiation?
6. Differential Equations?
8. Integration

1. Fundamental Theorem of Calculus?
2. Integration of Powers?, of reciprocals?, of trigonometric functions?, and of exponential and logarithmic functions?
3. Definite Integration?
4. Riemann Sums?
5. Integration by Substitution? and Integration by Parts?
6. Integration of Partial Fractions?
7. Solve simple Differential Equations?
8. Modelling using differential equations
9. Numerical Methods

1. Change of Sign Test?
2. Iteration Methods?
3. Newton-Raphson?
4. Numerical Integration?
5. Solving problems by numerical methods
10. Vectors

1. Vectors?
2. Magnitude? and Direction? of a vector
4. Position Vectors?

## Paper 3: Statistics and Mechanics

1. Statistical Sampling

1. Statistical Sampling?
2. Data Presentation and Interpretation

1. Interpreting diagrams, including Histograms?, Frequency Polygons?, Box and Whisker Plots? (including Outliers?) and Cumulative Frequency Diagrams?
2. Scatter Diagrams? and Regression Lines?, Correlation?
3. Measures of central tendency: Mean, Median, and Mode. Measures of variation: Variance?, Standard Deviation?, Range?, Interpercentile Ranges?
4. Outliers?
3. Probability

1. Mutually Exclusive? and Independent? events, discrete? and continuous? distributions
2. Conditional Probability?, Venn Diagrams?, and Tree Diagrams?
3. Modelling with Probability
4. Statistical Distributions

1. Discrete Probability Distributions? including Uniform Distribution? and Binomial Distribution?
2. Normal Distribution?
3. Modelling using distributions
5. Statistical Hypothesis Testing

1. Statistical Hypothesis Testing?
2. Conduct a statistical hypothesis test using the Binomial distribution
3. Conduct a statistical hypothesis test using the Normal distribution
6. Quantities and Units in Mechanics

1. Quantities and Units in Mechanics?
7. Kinematics

1. Language of Kinematics?
2. Graphs in Kinematics?
3. Constant Acceleration?
4. Calculus Methods in Kinematics?
5. Projectile Mechanics?
8. Forces and Newton’s Laws

1. Forces? and Newton's First Law?
2. Newton's Second Law?
3. Motion Under Gravity?
4. Newton's Third Law?
5. Algebra of Forces?
6. Friction?
9. Moments

1. Moments?

category: specifications
category: edexcel
category: alevel
category: ks5