International A levels Mathematics Edexcel

This subject is broken down into 52 topics in 7 modules:

  1. Mechanics 1 10 topics
  2. Pure 1 5 topics
  3. Pure 2 8 topics
  4. Pure 3 6 topics
  5. Pure 4 12 topics
  6. Statistics 1 6 topics
  7. Statistics 2 5 topics
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  • 7
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  • 52
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  • 20,033
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  • 2+
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This page was last modified on 28 September 2024.

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Mathematics

Mechanics 1

Quantities and units in mechanics

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Quantities and units in mechanics

Basic Principles

  • Understand the concept of physical quantities; these are anything that can be measured (mass, length, time, etc.) in mechanics.
  • Every physical quantity has a unit of measurement linked to it (kilograms, metres, seconds, etc.).
  • Learn to identify scalar quantities (only magnitude) and vector quantities (both magnitude and direction).

Mechanic Quantities and their Units

  • Mass (M): This is a scalar quantity. The unit of mass is the kilogram (kg).
  • Length (L): This can be a scalar or vector quantity. The unit of length is the meter (m).
  • Time (T): A scalar quantity. The unit of time is the second (s).
  • Speed/ Velocity (V): Speed is a scalar quantity while Velocity is a vector quantity. Both have units of meter per second (m/s).
  • Acceleration (a): Vector quantity. Unit is meter per second squared (m/s²)
  • Force (F): Vector quantity. Unit is Newton (N) or kg.m/s².
  • Momentum (p): Vector quantity. Unit is kg. m/s.
  • Work done (W), Energy (E), and Power (P): Scalar quantities. Units are Joules (J) for work done and energy, and Watt (W) for power.

The Importance of Dimensions

  • Understand the concept of dimensions, which are the powers to which the basic quantities must be raised to represent a derived quantity.
  • Dimensions are always written in square brackets, e.g. [L] for length.
  • Might be required to provide the dimensions for a physical quantity in questions.

Conversions

  • Learn to convert different units, like km/h to m/s, kg to g, etc.
  • Practice dimensional analysis, which is a method of checking the likely correctness of an equation by considering the dimensions of the quantities on each side of it.

Significant Figures

  • Learn to present answers to an appropriate number of significant figures.
  • Distinguish between the absolute error, fractional error, and percentage error in measurements.

Implications of Errors in Mechanics

  • Understand the implications of errors in calculations, how quantities are affected by small changes, and how these changes propagate through calculations.
  • Practice understanding the mechanics of real-world objects where small variations can have significant impacts.

Course material for Mathematics, module Mechanics 1, topic Quantities and units in mechanics

Mathematics

Pure 3

Diffrenciation

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Diffrenciation

Differentiation

Basic principles of differentiation

  • Grasp the concept of a derivative as the rate of change of a function.
  • Understand how to find the derivative or gradient of a function using the power rule, including when to use the chain rule or product rule.
  • Apply the quotient rule when differentiating fractions.
  • Be familiar with the derivatives of basic functions such as sin(x), cos(x), tan(x), e^x and natural logarithm functions.

Applications of differentiation

  • Interpret the gradient at a point geometrically as the slope of the tangent to the graph of the function at that point.
  • Use differentiation to find tangents and normals to curves.
  • Utilise differentiation to solve problems involving rates of change, in various fields like physics, economics, and engineering.
  • Understand and determine maximum and minimum points, as well as points of inflection of a function.

Differentiation of trigonometric, exponential and logarithmic functions

  • Be capable of differentiating trigonometric functions and their reciprocals, and understand their respective derivatives.
  • Understand how to differentiate exponential functions, such as a^x, and natural logarithmic functions.
  • Use chain rule, product rule and quotient rule efficiently in differentiation of these functions.

Higher derivatives and implicit differentiation

  • Become proficient in finding higher order derivatives.
  • Comprehend implicit differentiation, and use it to find derivatives where explicit differentiation isn't simple or possible.

Course material for Mathematics, module Pure 3, topic Diffrenciation

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