IAL Mathematics

PURE MATH 1 Past Paper

Before 2018
2021 2020 2019 2018

PURE MATH 2 Past Paper

Before 2018
2021 2020 2019 2018

PURE MATH 3 Past Paper

Before 2018
2021 2020 2019 2018

PURE MATH 4 Past Paper

Before 2018

2021 2020 2019 2018

2019

Table of Contents

Chapter 1 Algebraic Expressions

  1. Index Laws
  2. Expanding Brackets
  3. Factorising
  4. Negative and Fractional Indices
  5. Surbs
  6. Rationalising denominators + Chapter review

Chapter 2 Quadratics

  1. Solving quadratic equations
  2. Completing the square
  3. Functions
  4. Quadratic graphs
  5. The discriminant +

Chapter review 2

Chapter 3 Equations and inequalities

  1. Linear Simultaneous equations
  2. Quadratic Simultaneous equations
  3. Simultaneous equations on graphs
  4. Linear inequalities
  5. Quadratic inequalities
  6. Inequalities on graphs
  7. Regions +

Chapter review 3

Chapter 4 Graphs and transformations

  1. Cubic graphs
  2. Reciprocal graphs
  3. Points of intersection
  4. Translating graphs
  5. Stretching graphs
  6. Transforming functions + Chapter Review 4

Review Exercise 1

Chapter 5 Straight Line graphs

  1. y=mx+c
  2. Equations of straight lines
  3. Parallel and perpendicular lines
  4. Length and area +

Chapter review 5

Chapter 6 Trigonometric Ratios

  1. The Cosine rules
  2. The Sine rule
  3. Areas of triangles
  4. Solving triangle problems
  5. Graphs of Sine, Cosine and Tangent
  6. Transforming Trigonometric graphs +

Chapter Review 6

Chapter 7 Radians

  1. Radian measure
  2. Arc Length
  3. Areas of sectors and segments +

Chapter Review 7

Chapter 8 Differentiation

  1. Gradients of curves
  2. Finding the derivative
  3. Differentiating x^n
  4. Differentiating quadratics
  5. Differentiating functions with two or more terms
  6. Gradients, Tangents and normals
  7. Second order derivatives + Chapter review 8

Chapter 9 Integration

  1. Integrating x^n
  2. Indefinite Integrals
  3. Finding Functions +

Chapter Review 9

Review Exercise 2

Exam Practice

Glossary

Answers

Index

2019

Table of Contents

Chapter 1 Algebraic Methods

  1. Algebraic Fractions
  2. Dividing Polynomials
  3. The Factor Theorem
  4. The Remainder Theorem
  5. Mathematical Proof
  6. Methods of Proof +

Chapter Review 1

Chapter 2 Coordinate Geometry in the (x,y) Plane

  1. Midpoints and perpendicular Bisectors
  2. Equation of a circle
  3. Intersections of Straight lines and circles
  4. Use Tangent and Chord Properties
  5. Circles and Triangles +


Chapter Review 2

Chapter 3 Exponentials and Logarithms

  1. Exponential functions
  2. Logarithms
  3. Laws of logarithms
  4. Solving equations using
  5. Changing the base of a logarithm +


Chapter review 3

Chapter 4 The Binomial Expansion

  1. Pascal's Triangle
  2. Factorial Notation
  3. The Binomial expansion
  4. Solving Binomial Problems
  5. Binomial Estimation +

Chapter Review 4

Review Exercise 1

Chapter 5 Sequences and Series

  1. Arithmetic sequences
  2. Arithmetic series
  3. Geometric sequences
  4. Geometric Series
  5. Sum to infinity
  6. Sigma Notation
  7. Recurrence relations
  8. Modelling with series +


Chapter Review 5

Chapter 6 Trigonometric Identities and Equations

  1. Angles in All four quadrants
  2. Exact Values of trigonometric ratios
  3. Trigonometric identities
  4. Solve Simple trigonometric equations
  5. Harder trigonometric equations
  6. Equations and identities +

Chapter Review 6

Chapter 7 Differentiation

  1. Increasing and decreasing functions
  2. Stationary points
  3. Sketching gradient functions
  4. Modelling with differentiation +


Chapter Review 7

Chapter 8 Integration

  1. Definite Integrals
  2. Areas under curves
  3. Areas under the x-AXIS
  4. Areas between curves and Lines
  5. Areas between two curves
  6. The Trapezium Rule +


Chapter Review 7

Review Exercise 2

Exam Practice

Glossary

Answers

Index

2019

Table of Contents

Chapter 1 Algebraic Methods

  1. Arithmetic Operations with Algebraic fractions
  2. Improper fractions +


Chapter Review 1




Chapter 2 Functions and graphs

  1. The modulus function
  2. Functions and Mappings
  3. Composite functions
  4. Inverse Functions
  5. y = I f(x) I and y = f (IxI)
  6. Combining transformations
  7. Solving modulus problems +

Chapter Review 2

Chapter 3 Trigonometric functions

  1. Secant, Cosecant and Cotangent
  2. Graphs of sec x, cosec x, and cot x
  3. Using sec x, cosec x and cot x
  4. Trigonometric identities
  5. Inverse trigonometric functions +


Chapter Review 3

Chapter 4 Trigonometric Addition Formulae

  1. Addition formulae
  2. Using the angle addition formulae
  3. Double-angle formulae
  4. Solving trigonometric equations
  5. Simplifying a cos x +/- b sin x
  6. Proving Trigonometric Identities +


Chapter review 4

Review Exercise 1

Chapter 5 Exponentials

  1. Exponential functions
  2. y = e^ax+b + c
  3. Natural logarithms
  4. Logarithms and Non-linear Data
  5. Exponential Modelling +


Chapter Review 5

Chapter 6 Differentiation

  1. Differentiating sin x AND cos x
  2. Differentiating exponentials and logarithms
  3. The Chain Rule
  4. The product rule
  5. The Quotient rule
  6. Differentiating Trigonometric functions +


Chapter Review 6

Chapter 7 Integration

  1. Integrating standard functions
  2. Integrating f(ax+b)
  3. Using Trigonometric identities
  4. Reverse Chain rule +


Chapter review 7

Chapter 8 Numerical Methods

  1. Locating Roots
  2. Fixed point iteration +


Chapter review 8

Review Exercise 2

Exam Practice

Glossary

Answers

Index

Graph Paper

2019

Table of Contents

Chapter 1 Proof

  1. Proof by Contradiction +


Chapter Review 1

Chapter 2 Partial Fractions

  1. Partial fractions
  2. Repeated factors
  3. Improper fractions +


Chapter review 2





Chapter 3 Coordinate geometry in the (x,y) plane

  1. Parametric equations
  2. Using trigonometric Identities
  3. Curve sketching +


Chapter Review 3

Chapter 4 Binomial Expansion

  1. Expanding (1+x) ^n
  2. Expanding (a+bx)^n
  3. Using partial fractions +

Chapter Review 4

Review Exercise 1

Chapter 5 Differentiation

  1. Parametric differentiation
  2. Implicit differentiation
  3. Rates of Change +


Chapter review 5

Chapter 6 Integration

  1. Finding the area under a curve defined parametrically
  2. Volumes of revolution around the x-AXIS
  3. Integration by substitution
  4. Integration by Parts
  5. Partial fractions
  6. Solving differential equations
  7. Modelling with differential equations +


Chapter review 6

Chapter 7 Vectors

  1. Vectors
  2. Representing vectors
  3. Magnitude and direction
  4. Vectors in 3D
  5. Solving geometric problems in two dimensions
  6. Solving Geometric problems in three dimensions
  7. Position vectors
  8. 3D Coordinates
  9. Equation of a line in three dimensions
  10. Points of intersection
  11. Scalar product +

Chapter review 7

Review Exercise 2

Exam Practice

Glossary

Answers

Index

OLD

C1

Edexcel Textbook


Unit 1: Algebra and functions
Unit 2: Quadratic functions
Unit 3: Equations and inequalities
Unit 4: Sketching curves





Review Exercise 1


Unit 5: Coordinate geometry in the (x,y) plane
Unit 6: Sequences and series
Unit 7: Differentiation
Unit 8: Integration



Review Exercise 2


Practice paper
Examination style paper
Formulae you need to remember
Lists of symbols and notation
Answers
Index









C2

Edexcel Textbook


Unit 1_Algebra and Functions
Unit 2_The Sine and Cosine rule
Unit 3_Exponential and Log
Unit 4_Coordinate Geometry in the (x,y) plane




Review Exercise 1


Unit 5_The Binomial expression
Unit 6_Radian measure and its applications
Unit 7_Geometric sequences and Series
Unit 8_Graphs of trigonometric functions

Review Exercise 2


Unit 9_Differentiation
Unit 10_Trigonometrical identities and simple equations
Unit 11_Integration

Review Exercise 3


Answers
Practice paper
Examination style paper
Formulae you need to remember
Lists of symbols and notation
Index

C3

Edexcel Textbook


Unit 1: Algebraic fractions
Unit 2: Functions
Unit 3: The exponential of log functions
Unit 4: Numerical methods




Review Exercise 1


Unit 5: Transforming graphs of functions
Unit 6: Trigonometry
Unit 7: Further trigonometric identities and their applications
Unit 8: Differentiation

Review Exercise 2


Practice paper
Examination style paper
Formulae you need to remember
List of symbols and notation
Answers
Index







C4

Edexcel Textbook


Unit 1: Partial fractions
Unit 2: Coordinate geometry in the (x,y) plane
Unit 3: The binomial expansion
Unit 4: Differentiation
Unit 5: Vectors
Unit 6: Integration

Review exercise


Practice paper
Examination style paper
Formulae you need to remember
List of symbols and notation
Answer
Index




















M Past Paper

before 2018
2021 2020 2019 2018

M Past Paper

before 2018
2021 2020 2019 2018

M Past Paper

before 2018
2021 2020 2019 2018

M Past Paper

before 2018
2021 2020 2019

M1

Edexcel Textbook


Unit 1: Mathematical models in mechanics
Unit 2: Kinematics of a particle moving in a straight line
Unit 3: Dynamics of particle moving in a straight line

Review Exercise 1


Unit 4: Statics of a particle
Unit 5: Moments
Unit 6: Vectors

Review Exercise 2


Examination style paper
Index


M2

Edexcel Textbook



Unit 1: Kinematics of a particle moving in a straight line or plane
Unit 2: Centres of mass
Unit 3: Work, energy and power

Review Exercise 1


Unit 4: Colisions
Unit 5: Statics of rigid bodies

Review Exercise 2


Practice exam paper
Answers
Index

M3

Edexcel Textbook



Unit 1: Further Kinematics
Unit 2: Elastic strings and springs
Unit 3: Further dynamics

Review Exercise 1


Unit 4: Motion in a circle
Unit 5: Statics of rigid bodies

Review Exercise 2


Examination style paper
Answers
Index

M4

Edexcel Textbook


Unit 1: Relative motion
Unit 2: Elastic collisions in two dimension
Unit 3: Resisted motion of a particle moving in a straight line

Review Exercise 1


Unit 4: Damped and forced harmonic motion
Unit 5: Stability

Review Exercise 2


Practice examination paper
Answers
Index

S Past Paper

Before 2018
2019 2018

S Past Paper

Before 2018
2019 2018

S Past Paper

Before 2018
2018

S Past Paper

Before 2018
2018

S1

Edexcel Textbook


Unit 1: Mathematical models in probability and statistics
Unit 2: Representation and summary of data - location
Unit 3: Representation and summary of data - measures of dispersion
Unit 4: Representation of data
Unit 5: Probability

Review Exercise 1


Unit 6: Correlation
Unit 7: Regression
Unit 8: Discrete random variables
Unit 9: The normal distribution

Review Exercise 2


Examination style paper
Appendix
Answers
Index



S2

Edexcel Textbook


Unit 1: Binomial distribution
Unit 2: Poisson distribution
Unit 3: Continuous random variables







Review Exercise 1


Unit 4: Continuous uniform distribution
Unit 5: Normal approximations
Unit 6: Population and samples
Unit 7: Hypothesis testing

Review Exercise 2


Examination practice paper
Appendix
Answers
Index



S3

Edexcel Textbook


Unit 1: COMBINATIONS OF RANDOM VARIABLES
Unit 2: Sampling
Unit 3: Estimation, confidence intervals and tests






Review Exercise 1


Unit 4: Goodness of fit and contingency tables
Unit 5: Regression and Correlation




Review Exercise 2


Examination style paper
Appendix
Answers
Index



S4

Edexcel Textbook


Unit 1: Quality of tests and estimators
Unit 2: One-sample procedures

Review Exercise 1


Unit 3: Two-sample procedures

Review Exercise 2


Examination style paper
Appendix
Answers





















D1

Edexcel Textbook



Unit 1: Algorithms
Unit 2: Graphs and networks
Unit 3: Algorithms on networks
Unit 4: Route inspection (Chinese postman problem)

Review Exercise 1


Unit 5: Critical path analysis
Unit 6: Linear programming
Unit 7: Matchings


Review Exercise 2


Examination style paper
Answers
Index

D2

Edexcel Textbook



Unit 1: Transportation problems
Unit 2: Allocation (assignment) problems
Unit 3: The travelling salesman problem
Unit 4: Further linear programming

Review Exercise 1


Unit 5: Game theory
Unit 6: Network flows
Unit 7: Dynamic programming



Review Exercise 2


Examination style paper
Answers
Index

FP1

Edexcel Textbook


Unit 1: Complex numbers
Unit 2: Number solutions of equations
Unit 3: Coordinate systems



Review Exercise 1


Unit 4: Matrix algebra
Unit 5: Series
Unit 6: Proof by mathematical induction


Review Exercise 2


Examination style paper
Answers
Index

FP2

Edexcel Textbook


Unit 1: Inequalities
Unit 2: Series
Unit 3: Further complex numbers




Review Exercise 1


Unit 4: First order differential equations
Unit 5: Second order differential equations
Unit 6: Maclaurin and Taylor series
Unit 7: Polar coordinates

Review Exercise 2


Examination style paper
Answers
Index

FP3

Edexcel Textbook


Unit 1: Hyperbolic functions
Unit 2: Further coordinate systems
Unit 3: Differentiation
Unit 4: Integration

Review Exercise 1


Unit 5: Vectors
Unit 6: Further matrix algebra

Review Exercise 2


Examination style paper
Answers
Index