IB Math Applications & Interpretation Higher Level

This subject is broken down into 26 topics in 5 modules:

  1. Numbers & Algebra 5 topics
  2. Functions 4 topics
  3. Geometry & Trigonometry 7 topics
  4. Statistics & Probability 6 topics
  5. Calculus 4 topics
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  • 26
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  • 9,613
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This page was last modified on 28 September 2024.

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Math Applications & Interpretation

Numbers & Algebra

Number Skills

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Number Skills

Number Skills

Understanding the Number System

  • Understand and use positive and negative integers
  • Understand and use decimals and fractions
  • Appreciate the difference between discrete numbers and continuous numbers
  • Use order of operations, including brackets, exponents, multiplication and division, addition and subtraction

Calculation Techniques

  • Understand and use the four operations (+, -, x, ÷) in calculation
  • Understand and use exponentiation and root extraction
  • Understand and use percentage changes, including increase and decrease
  • Calculate with money, using all operations and percentages
  • Use estimation and rounding as a check on calculations

Expressing Quantities

  • Understand and use ratios and proportions in context (e.g. sharing amounts, comparing quantities, similarity and congruence)
  • Understand and use scale factors, maps and plans
  • Use rates and pricing, including unit pricing and cumulative cost calculations
  • Understand and use proportional change, including fractional growth and decay

Dealing with Error and Uncertainty

  • Understand and use range as an indication of spread
  • Understand and use significant figures and decimal places as limits to accuracy and precision
  • Understand and use standard form to express very large or very small numbers in contexts such as scientific notation
  • Use and interpret bounds of values given rounded data

Algebraic Skill

  • Understand and use algebraic notation
  • Use and interpret substitution into algebraic expressions
  • Understand and apply the concepts of equality and inequality
  • Understand and apply the laws of indices for numerical and algebraic expressions involving integer and fractional powers.

Remember, practice makes perfect. Work through examples and non-examples to solidify your understanding of these number skills.

Course material for Math Applications & Interpretation, module Numbers & Algebra, topic Number Skills

Math Applications & Interpretation

Geometry & Trigonometry

Geometric Transformations

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Geometric Transformations

Geometric Transformations

Translation

  • A translation moves a shape to a different position without altering its size or orientation.
  • To describe a translation, you need a vector. A vector [a b] moves points a units horizontally and b units vertically.
  • In a translation, all points of the shape move the same distance in the same direction.

Rotation

  • A rotation turns a shape around a fixed point, called the centre of rotation.
  • To describe a rotation, you need the centre of rotation, the angle of rotation (how much it turns) and the sense of rotation (clockwise or anticlockwise).
  • A point's distance from the centre of rotation remains the same.

Reflection

  • A reflection flips a shape over a line, called the mirror line or line of reflection.
  • The distance from any point to the line of reflection equals the distance from the line of reflection to the image of that point.
  • A reflection changes the orientation of a shape.

Enlargement

  • An enlargement changes the size of a shape but not its shape.
  • The centre of enlargement is a fixed point and all lines through the centre of enlargement to or from a point and its image are in the same direction.
  • If the scale factor is greater than 1, the shape gets larger. If it's between 0 and 1, the shape gets smaller.
  • A negative scale factor shows the image is also a reflection in a point.

Combined Transformations

  • The sequence of transformations matters. Performing translation then rotation, for example, can give a different result to performing rotation then translation.
  • An object can undergo more than one transformation. The result of a transformation is called the image, with the original object termed the pre-image.

Remember, familiarity with the effects of geometric transformations and the ability to describe transformations accurately is vital. The ability to perform and describe transformations is key to solving many geometry problems.

Course material for Math Applications & Interpretation, module Geometry & Trigonometry, topic Geometric Transformations

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