# A Level Maths

Need some A Level Maths help?
We have a collection of videos, solutions, activities, worksheets and past year papers that are suitable for A Level Maths. Some materials here are also relevant for IGCSE/GCSE Additional Mathematics.

In these lessons, we will look at:
• Worked solutions for some A-level maths past year examinations.
• Concepts that you will need to know for the A-level Maths: Algebra, Transformation of Graphs, Functions, Indices, Logarithms & Exponential, Polynomials, Geometry. Coordinate Geometry, Differentiation, Integration, Sequences & Series, Binomial Expansion, Trigonometry, Vectors, Statistics & Probability, Mechanics and Further Pure Mathematics.

Edexcel has redeveloped their AS/A level in Mathematics for international centres, called Edexcel International AS/Advanced Level in Mathematics. Students sitting exams from January 2014 will be awarded the new qualification.

What are the changes to the International Advanced Level in Mathematics specification?

• The Core units have been combined.
C1 and C2 have been combined to create one unit.
C3 and C4 have been combined to create one unit.

• Further Pure Mathematics 1 has been updated with some new content.

• Application units available include:
- Statistics 1, 2, and 3
- Mechanics 1, 2 and 3
- Decision Mathematics 1.

• Further Pure Mathematics units available are Further Pure Mathematics 1, 2 and 3.

#### Questions and Answers for Edexcel Core Mathematics C1 January and May

 Step by step Solutions Step by step Solutions May 2017 May 2016 May 2015

#### Questions and Answers for Edexcel Core Mathematics C2 January and May

 Past Papers (C2) Step by step Solutions May 2015 May 2015

#### Questions and Answers for Edexcel Core Mathematics C1 January and June

 Past Papers (C1) Mark Schemes Step by step Solutions May 2014 May 2014 May 2014 June 2013 June 2013 June 2013 January 2013 January 2013 January 2013 June 2012 June 2012 June 2012 January 2012 January 2012 January 2012 June 2011 June 2011 June 2011 January 2011 January 2011 January 2011 June 2010 June 2010 June 2010 January 2010 January 2010 January 2010 June 2009 June 2009 June 2009 January 2009 January 2009 January 2009 June 2008 June 2008 June 2008 January 2008 January 2008 January 2008 June 2007 June 2007 June 2007 January 2007 January 2007 January 2007

#### Questions and Answers for Edexcel Core Mathematics C2 January and June

 Past Papers (C2) Mark Schemes Step by step Solutions May 2014 May 2014 May 2014 June 2013 June 2013 June 2013 January 2013 January 2013 January 2013 June 2012 June 2012 June 2012 January 2012 January 2012 January 2012 June 2011 June 2011 June 2011 January 2011 January 2011 January 2011 June 2010 June 2010 June 2010 January 2010 January 2010 January 2010 June 2009 June 2009 June 2009 January 2009 January 2009 January 2009 June 2008 June 2008 June 2008 January 2008 January 2008 January 2008 June 2007 June 2007 June 2007 January 2007 January 2007 January 2007

#### Questions and Answers for Edexcel Core Mathematics C3 January and June

 Past Papers (C3) Mark Schemes Step by step Solutions May 2014 May 2014 May 2014 June 2013 June 2013 June 2013 January 2013 January 2013 January 2013 June 2012 June 2012 June 2012 January 2012 January 2012 January 2012 June 2011 June 2011 June 2011 January 2011 January 2011 January 2011 June 2010 June 2010 June 2010 January 2010 January 2010 January 2010 June 2009 June 2009 June 2009 January 2009 January 2009 January 2009 June 2008 June 2008 June 2008 January 2008 January 2008 January 2008 June 2007 June 2007 June 2007 January 2007 January 2007 January 2007

#### Questions and Answers for Edexcel Core Mathematics C4 January and June

 Past Papers (C4) Mark Schemes Step by step Solutions May 2014 May 2014 May 2014 June 2013 June 2013 June 2013 January 2013 January 2013 January 2013 June 2012 June 2012 June 2012 January 2012 January 2012 January 2012 June 2011 June 2011 June 2011 January 2011 January 2011 January 2011 June 2010 June 2010 June 2010 January 2010 January 2010 January 2010 June 2009 June 2009 June 2009 January 2009 January 2009 January 2009 June 2008 June 2008 June 2008 January 2008 January 2008 January 2008 June 2007 June 2007 June 2007 January 2007 January 2007 January 2007

#### Practice test and answers for Core 1 A-level Examination

 A-level Examination Q1 - Q5 A-level Examination Q6 - Q10 A-level Examination Paper 2 Q1 - Q4 A-level Examination Paper 2 Q5 - Q8

#### Questions and Answers for OCR 4721 Core Mathematics 1

 Questions for Jan 2010 Core Mathematics 1 January 2010 Q1-Q4 Core Mathematics 1 January 2010 Q5-Q8 Core Mathematics 1 January 2010 Q9-Q11

 Additional Maths 2008 Q1 - Q4 Additional Maths 2008 Q5 - Q8 Additional Maths 2008 Q9 - Q13

## GCSE Review

#### Bridging the gap between GCSE Maths and A-level Maths

 Fractions and Indices Surds Straight Line Graphs, Parallel & Perpendicular Lines Linear Algebra, Simultaneous Equations, Rearranging Equations Factoring & Solving Quadratic Equations, Completing the Square Solving Quadratics with Fractions, Simultaneous Equations (Linear & Non-Linear) Graph Sketching & Transformations Pythagoras Theorem, Sine Rule, Cosine Rule, Area of non-right Triangle

## Pure Mathematics

### Transformation of Graphs

 Graph Transformations (Translation, Reflection, Stretch) Graph Transformations- Proofs Sketch Quadratic Graphs by Completing the Square Exponential Graphs Sketching Exponential Graphs Modulus Graphs I Modulus Graphs II Graph Sketching Transformation of Trig. Graphs I Transformation of Trig. Graphs II More Graph Transformations Graph Transformation Exam Questions

### Functions

 Functions: Domain, Range, Mappings Inverse Functions Domain and Range of Inverse Functions Combined or Composite Functions Composite Function Exam Questions Even and Odd Functions Modulus Functions Function Exam Questions I Function Exam Questions II Function Exam Questions III Function Exam Questions IV Inverse and Self-Inverse Functions Exam Questions

### Indices

 Rules of Indices (Review) Simplifying Indices Indices Exam Questions Indices and Differentiation Exam Questions

### Surds

 Surds Tutorial I Surds Tutorial II Surds Tutorial III Surds Tutorial IV

### Logarithms and Exponential Functions

 Logarithms Tutorial Solving Logarithmic Equations Solving Logarithmic Equations Solving Logarithmic Inequalities Change of Base Log Equations Logarithm Simplification More Logarithm Simplification Quadratic Log Equations Solving Equations using Logs Logs and Exponential Equations I Logs and Exponential Equations II Logarithmic Equations Exam Questions ln(x) and ex equations I ln(x) and ex equations II Exponential Growth and Decay

### Polynomials

 Adding and Subtracting Polynomials Multiplying Polynomials Dividing Polynomials (Algebraic Long Division) Solving Cubics using Polynomial Long Division The Remainder Theorem Remainder Theorem Exam Questions The Factor Theorem Factorising Cubics using the Factor Theorem I Factorising Cubics using the Factor Theorem II Factor Theorem Exam Questions Using the Remainder Theorem and Factor Theorem Remainder and Factor Theorem I Remainder and Factor Theorem II

### Geometry

 Pythagoras' Theorem (Review) Trigonometric Ratios (Review) Three-dimensional Applications (Review) Sine Rule Cosine Rule The Ambiguous Case for the Sine Rule Area of a Triangle using Sine Trigonometric Questions with Bearings Area of Quadrilaterals (Review) Area of Circle (Review) Radian, Area of Sector & Segment Area of Sectors and Triangles Area of Circles, Sectors and Triangles Questions on Triangles I Questions on Triangles II

### Coordinate Geometry

 Midpoint and Distance Formula Parallel and Perpendicular Lines Equation of a Line I Equation of a Line II Distance of a Point from a Line Intersection of two straight lines Angle between two straight lines Equation of Circle Tutorial 1 Equation of Circle Tutorial 2 Equation of Circle Tutorial 3 Equation of Circle Tutorial 4 Find Equation of a Circle given Centre and Radius Find Centre and Radius given the Equation of a Circle Find Equation of a Circle given Three Points at the Circumference Equation of Circle and Distance Formula Equation of a Tangent to a Circle Equation of a Circle and the Tangent Equation of Circle Problems I Equation of Circle Problems II Centre of Circles and Chords Intersection of Two Circles

### Differentiation

 Differentiate axn DifferentiationChain Rule DifferentiationProduct Rule DifferentiationQuotient Rule Using the Chain Rule: Exponential, Log and Trig Functions Chain Rule (Core 3) Differentiate the Natural Log Product Rule Examples Quotient Rule Examples Chain Rule Examples Differentiation Combining Chain, Product and Quotient Rules I Differentiation Combining Chain, Product and Quotient Rules II Differentiation Combining Chain, Product and Quotient Rules III Product Rule to find Tangents and Normals Quotient Rule Stationary Points, Tangents and Normals Second Derviatives Tangents and Normal I Tangents and Normal II Increasing and Decreasing Functions Stationary Points I Stationary Points II Differentiation Lessons I Differentiation Lessons II Differentiation Lessons III Differentiation Exam Questions I Differentiation Exam Questions II Differentiation Exam Questions III Differentiation Exam Questions IV Differentiation Exam Questions V Differentiation: Connected Rates of Change Differentiation: Rates of Change Problems Differentiation: Maximum Volume Differentiation: Optimisation Lessons on Implicit Differentiation Differentiate Implicit Equations Implicit Differentiation Exam Questions Cubic Differentiation Tangents and Stationary Points to Implicit Curves Differentiating y = ax Parametric Equations I Parametric Equations II Parametric Equations and Cartesian Differentiate Parametric Equations Differentiate Parametric Equations I Differentiate Parametric Equations II Differentiate Parametric Equations III Differential Equations I Differential Equations II Differential Equations III

### Integration

 Introduction to Integration Basic Integration Exam Questions Integration Help I Integration Help II Integration Help III Integration Help IV Integration by Substitution Tutorial I Integration by Substitution Tutorial II Integration by Substitution Exam Questions Integration by Parts Tutorial Integration by Parts Exam Questions I Integration by Parts Exam Questions II Trapezium Rule Trapezium or Trapezoid Rule Integration of Exponential and Natural Log Functions Integration of Trigonometric Functions I Integration of Trigonometric Functions II Integration: Mixed Examples I Integration: Mixed Examples II Definite Integral Area bounded by a Curve I Area bounded by a Curve II Integration: Area under a Graph Questions I Integration: Area under a Graph Questions II Integration: Area under a Graph Questions III Area within a Parametric Graph Volume of Revolution I Volume of Revolution II Parametric Integration

### Sequences and Series

 Recurrence Relations Tutorial Sequences: Recurrence Relations Sigma Notation Arithmetic Sequences and Series Tutorial Arithmetic Progressions Arithmetic Sequences and Series I Arithmetic Sequences and Series II Arithmetic Sequences and Series III Arithmetic Sequences and Series IV Geometric Series Tutorial Geometric Sequences and Series Tutorial I Geometric Sequences and Series Tutorial II Geometric Sequences and Series Tutorial III Geometric Sequences Geometric Series I Geometric Series II Geometric Series III Geometric Series IV Geometric Series V Geometric Series VI Geometric Sequences and Series

### Binomial Expansion

 Binomial Expansion Beginners Tutorial I Binomial Expansion Beginners Tutorial II Binomial Expansion Beginners Tutorial III Binomial Expansion Tutorial Binomial Expansion Formula Finding Terms in a Binomial Expansion Binomial Expansion C2 Exam Questions I Binomial Expansion C2 Exam Questions II Binomial Expansion C2 Exam Questions III Binomial Expansion C4 Exam Questions I Binomial Expansion C4 Exam Questions II Binomial Expansion Approximations and Estimations Binomial Expansions with Surds Binomial Expansion Examples I Binomial Expansion Examples II

### Trigonometry

 Trigonometry Tutorial 1 Trigonometry Tutorial 2 Trigonometry Tutorial 3 Trigonometry Tutorial 4 Trigonometry Tutorial 5 Quadrant Method Solving Sin θ = + value Solving Sin θ = − value Solving Cos θ = + value Solving Cos θ = − value Solving Tan θ = + value Solving Tan θ = − value Solving Sin 2x = + value Trig Ratios for multiples of 30, 45 and 60 degrees Trigonometric Basics - Reciprocal Functions Trigonometric Equations - Factorising Types Trigonometric Equations - Identity Types Trigonometric Equations - Double Angle Identity Types Trig. Equations Examples using CAST Diagrams Solving Equations using Identities Trig. Equations : A sin x - B cos x = C Type Solving equations using reciprocal trig identities More Reciprocal Trig Identities Trig Identities Examples Evaluating Inverse Trig Values Quadratic Trigonometric Equations Proof of A sin x + B cos x = R sin (x + alpha) Proof of A cos x + B sin x = R cos (x - alpha) Proof of A sin x - B cos x = R sin (x - alpha) Proof of A cos x - B sin x = R cos (x + alpha) Proving Trig Identities I Proving Trig Identities II Proving Trig Identities III Proving Trig Identities IV Proving Trig Identities V Trigonometry C2 Exam Questions I Trigonometry C2 Exam Questions II Trigonometry C2 Exam Questions III Trigonometry C3 Exam Questions I Trigonometry C3 Exam Questions II Trigonometry C3 Exam Questions III Trigonometry C3 Exam Questions IV

### Vectors

 Vector Equation of a Line Vectors: Shortest Distance between point and line Vector Exam Questions I Vector Exam Questions II Vector Exam Questions III

## Statistics and Probability

#### Questions and Answers for A-level Edexcel GCE Statistics S1 June 2007

 Questions for S1 June 2007 A-Level Edexcel S1 June 2007 Q1 Correlation A-Level Edexcel S1 June 2007 Q2 Box Plots A-Level Edexcel S1 June 2007 Q3 Regression A-Level Edexcel S1 June 2007 Q4 Venn Diagrams A-Level Edexcel S1 June 2007 Q5 Histogram A-Level Edexcel S1 June 2007 Q6 Normal Distribution A-Level Edexcel S1 June 2007 Q7 Discrete Random Variables

 Permutation and Combination Tutorial Conditional Probability and Probability Tree Diagrams Probabilty and Venn Diagrams Probability Density Functions Correlation and Regression Continuous Random Variable: Mode, Mean and Variance Continuous Random Variable: Median, Quartiles and Percentiles Normal Distribution: Mean and Standard Deviation Normal Distribution: Probability in a given range Normal Distribution: Probability Example Using Normal Distribution to find Probabilities Using Normal Distribution as an Approximation to Binomial Distribution Cumulative Distribution Function Probability Distribution Table Discrete Random Variables Binomial Distribution Tutorial Binomial Distribution: Cumulative Probability Tables Poisson Approximation to the Binomial Distribution Binomial Distribution: Hypothesis Testing Binomial Distribution: Find Critical Values Poisson Distribution Tutorial Poisson Distribution: Hypothesis Testing Probability Exam Questions: Conditional Probability & Tree Diagrams Statistics Exam Questions: Correlation and Regression Statistics Exam Questions: Grouped Frequency Table Statistics Exam Questions: Normal Distribution Statistics Exam Questions: Discrete Probability Distribution

## Mechanics

 Mechanics TutorialForce and Moments MechanicsNewton's Law of Motion, F=ma Resolving ForcesSplitting a Force into Components Mechanics Exam QuestionsForces Mechanics Exam QuestionsForce Vectors Mechanics Exam QuestionsGravity and Acceleration Inclined Planes Finding Coefficient of Friction & Missing Angles Conservation of Momentum Mechanics Exam QuestionsImpulse, Momentum Mechanics Exam QuestionsMoments I Mechanics Exam QuestionsMoments II Mechanics Exam QuestionsVelocity-Time Graphs Mechanics Exam QuestionsConnected Particles I Mechanics Exam QuestionsConnected Particles II Mechanics Exam QuestionsConnected Particles III Friction, Limiting Equilibrium, Coefficient of Friction Mechanics Exam QuestionsFriction Mechanics Exam QuestionsPosition and Velocity Vectors Mechanics Exam QuestionsVelocity Vectors Kinematics SUVAT equations I Kinematics SUVAT equations II Kinematics SUVAT equations III Kinematics SUVAT equations IV Kinematics Vertical Motion I Kinematics Vertical Motion II Kinematics Acceleration-Time and Speed-Time Graphs I Kinematics Acceleration-Time and Speed-Time Graphs II Moments 1 Basic example of taking moments Equilibrium - taking moments Moments 2 Example of non-uniform rod Finding the centre of a non-uniform rod Hanging a non-uniform bar Moments 3 Taking moments at an angle Sum of moments about a point Hanging rod in equilibrium

## Further Pure Mathematics

 Proof by Induction I Summation of series, Divisibility Proof by Induction II Recurrence Relations, Matrices Matrices Dimensions, Adding and Subtracting Matrices Matrices Scalar, Multiplying Matrices Matrices Basic Linear Transformations Matrices Finding Linear Transformations Matrices Multiple Linear Transformations Matrices Inverse and Determinants Matrices Area of image using determinants Matrices 2x2 Matrix to solve simultaneous equations Summing Finite Series I with limits, with geometric series, proof by induction Summing Finite Series II logs, unknown coefficients, finding 2n

 Complex Numbers 1 Adding & subtracting complex numbers Simplifying purely imaginary parts Quadratics with complex roots Complex Numbers 2 Powers of i Multiplying Complex Numbers Complex Numbers 3 Conjugates Dividing Complex numbers Solving Equation with conjugate Complex Numbers 4 Sum and product of roots Complex Numbers 5 Plotting Argand Diagram Complex Numbers 6 Argand Diagram modulus Argand Diagram parallelogram law Finding Modulus & Argument Basics Complex Numbers 7 Polar Form r(cos0 + isin0) Polar Form to rectangular form Complex Numbers 8 Comparing imaginary numbers Square roots of a complex number Complex Numbers 9 Finding a quadratic Finding a cubic Complex Numbers 10 Finding a quartic equation Quartic equation on Argand Diagram

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