C1 Tutorials – OCR A Level Maths

Contents for C1 OCR

Prior Knowledge
Algebra Basics
Pythagoras’ Theorem
Trigonometry
Number
Surds
Algebra and Functions
Indices
Functions
Factorising
Completing the Square
Polynomials
Simultaneous Equations
Quadratics
Quadratic Equations
Roots and Discriminant
Quadratic Graphs
Inequalities
Inequalities
Sketching Curves
Sketching Cubic and Reciprocal Curves
Graph Transformations and Asymptotes
Coordinate Geometry
Gradient
Lines
Intersection of Graphs
Exam Questions – Straight lines
Circles
Differentiation
Differentiation – Introduction
Tangents and Normals
Stationary Points
Increasing and Decreasing functions

Prior Knowledge

Algebra Basics

  1. Expanding a single bracket
  2. Expanding two or more brackets
  3. Squaring a bracket
  4. Terms in expressions and equations
  5. Identity or equation - what is the difference?
  6. Linear Equations with a positive x term
  7. Linear equations with a negative x-term
  8. Linear equations with two x-terms
  9. Linear equations with brackets
  10. Fractional linear equations
  11. f(x) notation
  12. Polynomials

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Polynomials

  1. Polynomials

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Pythagoras’ Theorem

  1. Pythagoras' theorem

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Trigonometry Introduction

  1. Introduction to trigonometry
  2. Finding the length of a side
  3. Finding an angle
  4. Mixed Exercise - Pythagoras and Trigonometry

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Number

Surds

  1. Surds - introduction & simplifying
  2. Addition and subtraction of surds
  3. Multiplying surds
  4. Dividing surds
  5. Rationalising surds
  6. Exam Questions - Surds

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Algebra and Functions

Indices

  1. Introduction to indices (exponents)
  2. Multiplication rules for indices
  3. Division rule for indices
  4. Negative indices
  5. Fractions raised to a negative index
  6. Rational (fractional) indices
  7. Simplifying terms with negative powers
  8. Expressing terms in the form axn
  9. Equations in which the power has to be found
  10. Summary of indices
  11. Exam Questions - Indices

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Functions

  1. f(x) notation

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Factorising

  1. Introduction to factorising
  2. Highest common factor (HCF)
  3. Factorising by grouping
  4. Factorising quadratic expressions
  5. Mixed Exercise - Factorising
  6. Exam Questions - Factorising

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Completing the Square

  1. Completing the square
  2. Applications of completing the square
  3. Exam Questions - Completing the square

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Simultaneous Equations

  1. Elimination method for linear equations
  2. Substitution method for linear and non-linear equations
  3. Exam Questions - Simultaneous equations

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Quadratics

Quadratic Equations

  1. Solve by factorising
  2. Solve by completing the square
  3. Solve by the quadratic formula
  4. Exam Questions - Solved by the quadratic formula
  5. Solving quadratic equations in some function of x

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Quadratic Equations – Roots and Discriminant

  1. Roots and discriminant of a quadratic equation
  2. Exam Questions - Roots and discriminant

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Quadratic Graphs

  1. Sketching quadratic graphs

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Inequalities

Inequalities

  1. Linear inequalities
  2. Rules for reversing the inequality sign
  3. Solving a linear type
  4. Solving a double inequality
  5. Exam Questions - Solving a double inequality
  6. Quadratic inequalities
  7. Exam Questions - Quadratic inequalities
  8. Exam Questions - Simultaneous inequalities

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Sketching Curves

Sketching Cubic and Reciprocal Curves

  1. Sketching cubic curves
  2. Sketching reciprocal curves of the form y = k/x

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Graph Transformations and Asymptotes

  1. Basic graphs used in transformations
  2. Translations of graphs
  3. Reflections of graphs
  4. Stretches of graphs
  5. Exam Questions - Graph transformations

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Coordinate Geometry

Gradient

  1. Line segment
  2. Parallel lines
  3. Perpendicular lines

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Lines

  1. Equation of a straight line: y=mx+c
  2. Equation of a line given the gradient and point
  3. Mid-point of a line segment
  4. Equation of a parallel line
  5. Equation of a perpendicular bisector

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Intersection of Graphs

  1. Intersection of two straight lines
  2. Intersection of a straight line and a parabola
  3. Intersection of a straight line and a hyperbola
  4. Nature of the intersection

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Exam Questions – Straight Lines

  1. Exam Questions - Straight lines

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Circles

  1. Equation of a circle
  2. Finding the centre and radius
  3. Circle properties
  4. Equation of a tangent to a circle
  5. Equation of a circle through 3 points
  6. Exam Questions - Circles

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Differentiation

Differentiation – Introduction

  1. The gradient function dy/dx
  2. Differentiation - terms of the form axn
  3. The second derivative
  4. Exam Questions - Differentiation: introduction

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Tangents and Normals

  1. Equations of tangents and normals
  2. Exam Questions - Tangents and normals

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Stationary Points

  1. Stationary points
  2. Nature of a stationary point
  3. Exam Questions - Stationary points
  4. Applications of stationary points
  5. Exam Questions - Applications of stationary points

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Increasing and Decreasing functions

  1. Increasing and decreasing functions
  2. Exam Questions - Increasing and decreasing functions

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