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Core Mathematics 1

C1 was first introduced in 2004 as part of the Core series which replaced the old Pure system. It was created to help build a bridge between GCSE maths and A level maths, expanding mainly on what is dealt with at Higher Level GCSE. The topics that are new include differentiation and integration, both of which are covered on a very simple level. C1 aims to teach you the basics of this topics, so that when you move onto the later units (C2,C3,C4) you will have a basic understanding. Note that C1 is a non-calculator paper, as it is partly aimed to build and develop your mental maths skills.

Textbook Answers

Chapter 1 - Algebra and Functions:

  • Ex 1B - 12

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Contents

Below is a list of the topics that are included in the Edexcel Core Mathematics 1 unit.


1. Algebra and functions

  • Simplyfing expressions .
  • The laws of indices.
  • Expanding an expression.
  • Factorising an expression.
  • Uses and manipulation of surds.
  • Rationalising/simplifying surds.


2. Quadratic Functions

  • Plotting quadratic functions
  • Factorising quadratic functions
  • Completing the square
  • Quadratic formula equation
  • Sketching the graphs of quadratics


3. Equations and inequalities

  • Solving simutaneous linear equations by elimination
  • Solving simutaneous linear equations by substitution
  • Solving simutaneous equations with one linear and one quadratic
  • Solving linear inequalities
  • Solving quadratic inequalities


4. Sketching curves

  • Sketching the curves of cubic functions
  • Sketching the reciprocal function
  • Using graphs to solve equations
  • Graph transformations of f(x+a)and f(x-a)
  • Graph transformations of f(ax) and af(x)
  • Reconizing and drawing transformations.


5. Coordinate geometry in the (x,y) plane

  • Equations of a straight line
  • The gradient of a straight line
  • Using 1 point and a gradient to find an equation
  • Conditions of paralell and perpendicular lines
  • Solving quadratic inequalities


6. Sequences and series

  • Introduction to sequences
  • Finding the 'nth' term of a sequence
  • Sequences generated by a recurrence relationship
  • Arithmetic sequences and the aritmetic series
  • Finding the nth term and sum up to 'n' of a series
  • Using the ∑ notation


7. Differentiation

  • Finding the derivative of f(x)
  • Relationship between the derivative and gradient of f(x)
  • Finding the gradient formula of functions
  • Expanding/simplifying functions in order to differentiate
  • Finding the 2nd order derivatives
  • Finding the rate of change of a function at a particular point
  • Finding the equation of the tangent and normal to a curve at a point


8. Integration

  • Relationship between integration and differentiation
  • Integrating a function f(x)
  • Simplifying expressions in order to integrate
  • Finding the constant of integration
  • Using the ∫ notation

Textbook

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