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Diploma in Mathematics
Want to improve your math skills? This course will guide you through math’s most important concepts and principles.
Take this certificate on your own.
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Description
The course covers a comprehensive range of key subjects in mathematics. Starting with calculus and geometry, the course guides you through the mathematics behind shapes and design principles. Next, the course moves through functions, vectors, and data distributions. These are highly important principles used in rocket science, the military, and aerospace engineering. The course will then introduce you to algebra and trigonometry, which are core to a future in any mathematics-oriented career.
Next, you’ll learn how to confidently create graphs and make advanced calculations such as straight-line calculations, kinematics, motion, and quadratic functions. Finally, for the gamblers amongst you, you will learn about probability and statistics, including an overview of the relationship between the graphs of functions and their antiderivatives. This section will also show you how to use binomial expansions for problem solving, so the next time you play poker you will have a real edge over your competitors.
By the end of this course, you will have gained math skills that can open up a range of careers, and will be much better prepared for your next math exam. Math skills are in great demand from international employers, and almost every student in the world needs to learn them. Despite this, very few people have strong math skills. With this free course, and less than 5 hours of work, you’ll stand above the crowd. So why wait? Make Math easier, today.
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Modules
Introduction to triangles
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Introduction to triangles
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Triangle letter names
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Equilateral triangles
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Isosceles triangles
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Scalene triangles
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Acute-angled triangles
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Right-angled triangles
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Obtuse-angled triangles
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Quiz on triangle names
Angle types
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Angle types
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Angles in a circle
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Angles as numbers
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Measuring angles with a protractor
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Complementary and supplementary angles
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Angles in circles, rectangles and triangles
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Vertically opposite angles
Angle sizes and sums in triangles
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Angle sizes and sums in triangles
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Angle sum demonstration
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Practice questions on sum of angles in a triangle
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Quiz on sum of angles in a triangle
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Exterior angles of a triangle
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Quiz on exterior angles of triangles
Triangles - Similiarity and congruence
Corresponding angles
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Corresponding angles
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Parallel lines
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Alternate and co-interior angles
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General angles quiz
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Quiz on angles and parallel lines
Introduction to quadrilaterals
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Introduction to quadrilaterals
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Equal sides, equal angles and parallel lines
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Properties of a square
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Properties of a rectangle
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Properties of a parallelogram
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Properties of a rhombus
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Properties of a trapezium
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Properties of a kite
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Properties of basic quadrilaterals
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Quiz on properties of quadrilaterals
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Properties of an isosceles trapezium
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Properties of a rectangle
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Properties of a parallelogram
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Properties of a rhombus
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Properties of a trapezium
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Properties of an isosceles trapezium
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Properties of a kite
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Properties of basic quadrilaterals
Quadrilaterals
Introduction to polygons
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Introduction to polygons
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What are polygons?
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Regular polygons
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Naming of polygon types
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Rotational symmetry in polygons
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Line symmetry in polygons
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Quiz on polygons
Polygons
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Polygon interior angle sum
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Regular polygon interior angle sizes
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Sum of exterior angles of polygons
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Regular polygon exterior angle sizes
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Quiz on polygon angle sizes
Geometrical solids
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Geometrical solids
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Prisms
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Prisms quiz
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Pyramids and cones
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Spheres, hemispheres and toruses
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Quiz on geometrical solids
Transformations
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Introduction to transformations
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Translations, reflections and rotations
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Translations and coordinate geometry
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Translations and coordinate geometry quiz
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Reflections
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Reflections
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Reflections and coordinate geometry
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Rotations
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Rotations and coordinate geometry
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Quiz on transformations
Univariate data
Univariate data 2
Bivariate data
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Introduction
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Dependent and independent variables
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Percentaged tables
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Parallel boxplots
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Back-to-back stemplots
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Graphical display of bivariate data – in summary
Summary statistics
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Summary statistics
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The mean
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The median – definition
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Cumulative frequency
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Cumulative frequency graph
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The mode
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Advantages and disadvantages of the mean
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The median for even data sets
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Advantages and disadvantages of the median
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The mean - example
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The median - example
Range
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The soccer activity
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The range
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The interquartile range
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The interquartile range - example 1
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The interquartile range - example 2
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The standard deviation
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Boxplots
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Boxplots - example
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Using your calculator
Symmetry
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Symmetry and skew of a distribution
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Negative skew
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Positive skew
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Probability intervals
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Probability interval examples
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Comparing sample and population
Calculating a seasonal index
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Calculating a seasonal index
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Interpreting seasonal indices
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Seasonal movements
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Deseasonalising the data
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Deseasonalising the data – example
Coefficient
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Scatterplots
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Scatterplots: using your calculator
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Pearson's product moment correlation coefficient, r
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Calculating r
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The coefficient of determination
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Practice question
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Strength of association
Regression line
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Introduction
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Finding the equation of a regression line
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Interpretation of slope and intercept
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Practice question
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The three-median regression line
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Using your calculator
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The three-median regression example
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The three-median regression practice questions
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The least squares regression line
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Making predictions from a regression line
Non-linear data
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Non-linear data
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Square transformation
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Log transformations
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Reciprocal transformation
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Example 1
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Example 2
Residual analysis
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Introduction
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Residual analysis - part 1
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Plotting the residuals
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Residual analysis - part 2
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Residual analysis - part 3
Trends
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Trends
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Cyclic patterns
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Random patterns
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Describing patterns in time series data
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Seasonal patterns
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Smoothing a time series
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Median smoothing
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Smoothing using moving averages
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Smoothing - example 1
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Smoothing - example 2
Arithmetic sequences
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Arithmetic sequences
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Find a particular term in an arithmetic sequence
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How many terms in this arithmetic sequence?
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Show that the sequence is arithmetic
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Solving arithmetic sequences simultaneously
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Summing up arithmetic sequences
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Is this an arithmetic sequence?
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Example (b)
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Example (c)
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Example (d)
Arithmetic series
Geometric sequences
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Geometric sequences
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Is this a geometric sequence?
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Find a term in an increasing geometric sequence
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Find a term in a decreasing geometric sequence
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Which term has that value?
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Example (b)
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Example (c)
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Example (d)
Geometric series
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Geometric series
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Infinite geometric series
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Find the sum of an increasing geometric sequence
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Find the sum of a decreasing geometric sequence
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How many terms until the sum exceeds 2000?
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Find the sum of an infinite geometric series
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Sum a geometric series to infinity
Difference equations 1
Difference equations 2
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Difference equations
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Generating a sequence from a difference equation
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Difference equations that represent arithmetic sequences
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Difference equations that represent geometric sequences
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Generate the first 4 terms of a sequence
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Generate the first 4 terms of another sequence
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Find a general expression for the nth term
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Find a general expression for the nth term
Difference equations 3
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Other first order difference equations
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Solving difference equations
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Find a general expression for the nth term
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Find the first term from a given term
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Find the first term from the second term
Geometry
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Intersection of half planes
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Finding maximum and minimum values
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Solving linear and programming problems
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Solving linear programming problems - example
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Example part (b)
Straight lines
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Straight line graphs
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The general equation of a straight line
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Finding the equation of a line
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Simultaneous equations
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Method 1 - elimination
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Method 2 - substitution
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Sketching linear equations
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Break even analysis
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Straight line graphs - gradient
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Finding the gradient given the coordinates of two points
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Elimination examples
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The break even example
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Sketching linear equations - example 1
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Sketching linear equations - example 2
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Straight line graphs - gradient example
Graphs
Power graphs
Trigonometry 1
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Trigonometry introduction
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Right-angled triangles
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Solving non right-angled triangles
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The sine rule
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The cosine rule
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The area of a triangle
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Example
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Example 2
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Cosine rule – Example 1
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Cosine rule – Example 2
Trigonometry 2
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Pythagoras' theorem
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Pythagoras in 3 dimensions
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Similar figures
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Surface area and volume
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Similar figures example
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Surface area and volume: example 1
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Surface area and volume: example 2
Pythagoras and bearings
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The tomb of Pythagoras activity
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Angles of elevation and depression
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Directions and bearings
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Contour maps
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Traverse surveys
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Compass bearings
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True Bearings
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Bearings application example
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Field survey example
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Field survey example continued
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Bearings yachting example
Ratio and proportion
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Ratio and proportion
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Simplifying ratios
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Expressing ratios as a percentage
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Dividing quantities in a given ratio
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Applications of ratio and proportion
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Map scales
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Dilution factors
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Photography
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Gears
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Finding x values in ratios
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Map scales: how far is that?
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Dilution: drug strength
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Photographing a tree
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Gearing up... gearing down
Ratio and proportion gears
Discrete random variables
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Random variables
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Discrete probability distribution
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The mean and variance of a discrete random variable
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Standard deviation as a measure of spread
Normal distribution
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The normal curve
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Continuous random variables and the normal distribution
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Calculation of probabilities for a normal distribution
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Approximating the binomial distribution with normal distribution
Binomial distribution
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Binomial probability function and distribution
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The number of successes in a given number of trials
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The effect of changing the parameter p
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The effect of changing the parameter n
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The mean and variance of a binomial random variable
Hypergeometric distribution
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Sampling without replacement
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The mean of a hypergeometric random variable
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The variance of a hypergeometric random variable
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The mean and variance of a hypergeometric random variable example
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The mean and variance of a hypergeometric random variable example 2
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The formula for calculating probabilities
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Calculating probabilities
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Relationship between hypergeometric and binomial distributions
Rules of integration
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Antidifferentiation
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Antiderivatives of basic functions
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Finding specific functions based on given information
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Indefinite integral
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Using related derivatives to find an integral
Integration applications
Rules of differentiation
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Basic functions
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Functions
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Rules of differentiation
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Rules for finding derivatives
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Linear combination of functions
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Product of two functions
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Quotient of two functions
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Function of a function
Applications of differentiation
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Applications of Differentiation
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Stationary Points
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Maximum or Minimum
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Maximum/Minimum Problems
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Equations of Tangents and Normals
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Examples
Factors of polynomials
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Factorising polynomials
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Polynomial notation and function manipulations
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Factorising polynomials
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Factorisation process for cubics
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Factorisation process for quartics
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Factor and remainder theorems
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Long division
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Synthetic division
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Factorising polynomials: example
Straight line graphs
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Activity
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Graphs of polynomial functions: the garden activity
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Introduction
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Graphs of polynomial functions
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Graphs derived from standard graphs
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Other standard graphs
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Certain special graphs
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Transformations
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Reflections
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Dilations
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Combinations of transformations
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Addition of ordinates
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Important graphs
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Important graphs: Type 1
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Important graphs: type 2
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Important graphs: type 3
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Important graphs: type 4
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Graphs of inverse functions
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Graphs of polynomial functions: examples
Graphs of ciruclar functions
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Introduction
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Graphs of the form y=Asin(a(x+b))+B and y=Acos(a(x+b))+B
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Solution of trigonometric equations
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Graphs of the form y = tan(ax)
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Equations of the form sin(ax)=B and cos(ax)=B
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Equations of the form sin(ax)=kcos(ax)
Inverse functions
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Inverse functions - many-to-one and one-to-many
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Inverse functions
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Further inverse functions
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Examples
Logarithms and index laws
The binomial theorem
Creating a frequency table from data
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Frequency and graphs - overview
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Nominal data
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Discrete data
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Continuous data
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Frequency tables with nominal data
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Frequency tables with discrete data
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Frequency tables - discrete data and summary statistics
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Mean from frequency tables - discrete data
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Interpreting column graphs
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Family size cumulative frequency
Differentiation - Product rule
Antiderivatives
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Review of Standard Antiderivatives
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Standard Antiderivative Types
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Type 2 - Hyperbolic Functions
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Type 3 - Partial Fractions
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Example 2
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Type 5 - Linear Substitution
Antiderivatives of circular functions
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Type 4 - Inverse Circular Functions
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Examples 1 and 2
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Examples 3 and 4
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Examples 5 and 6
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Type 6 - Odd and Even Powers
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Odd Powers
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Even Powers
Antiderivatives and their graphs
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Relationships Between Graphs of Functions and their Antiderivatives
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Original and Antiderivative Functions
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Graphs of Antiderivatives
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Examples 1 and 2
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Examples 3 and 4
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Examples 5 and 6
Conics (elipses and hyperbolae)
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Graphs of Ellipses
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Examples
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Graphs of Hyperbolae
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Example 1
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Example 2
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Example 3
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Example 4
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Transformations of hyperbolae
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Translations
Degrees and radians
Inverse circular functions
Polynomial equations
Reciprocal function graphs
Vectors in 2 and 3 dimensions
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Vector Definition
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Symbols Used to Represent Vectors
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Magnitude of a Vector
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Zero Vector
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Subtracting Vectors
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Equal vectors
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Parallel Vectors
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Vectors in Cartesian Form
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Position Vectors
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The Cartesian Plane
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Linear Dependence and Independence
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Unit Vector
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Multiplying by a Scalar
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Linear Dependence and Independence Example
Scalar products of vectors
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Scalar and vector resolutes
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Scalar resolutes
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Vector resolutes
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Vector resolute examples
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Scalar (or dot) Product
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Using the Dot Product in Vector Proofs
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Example 1
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Finding the Angle Between Two Vectors
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Example 2 (midpoints)
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Perpendicular Vectors
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Inclination to the x or y axis
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Example 3 (midpoints)
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Example 4 (Co-linear points)
Symmetry and periodicity
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Use of Symmetric, Periodic and Complementary Relationships of Circular Functions
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Symmetry Example 1
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Example 2
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Example 3
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Periodicity
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Complementary Relationships
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Complementary Relationship Examples
Trigonometric identities
Differential equations
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Introduction
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Order and degree of differential equations
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Verifying solutions
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Rates of change
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Rates of change - chain rule
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The rates of change example
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First order differential equations - type 1
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First order differential equations - type 2
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Second order differential equations
Second derivatives
Kinematics
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Introduction
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Finding displacement from velocity
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Solving differential equations (rectilinear motion) example
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Finding acceleration or velocity from displacement
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Constant acceleration - introduction
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Constant acceleration - example 1
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Velocity time graphs - introduction
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Finding the acceleration from the velocity time graph
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Finding the distance travelled from a velocity time graph
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Velocity time graphs - example
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Constant acceleration - example 2
Motion
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Introduction
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Newton's laws of motions
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Forces-weight
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Diagram of forces
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Basic equation of motion
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Resolution of forces
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Horizontal and vertical
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Equations of motion
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Parallel and perpendicular to a plane
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Equations of motion
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Moving down the slope
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Connected masses
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Motion under a constant force
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Motion under a constant force - example 1
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Motion under a constant force - example 2
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Motion under a variable force
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Motion under a variable force - example 1
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Motion under a variable force - example 2
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Motion under a variable force - example 3
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Momentum and impulse
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Momentum and impulse example
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Moving up the slope
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Motion under a constant force - example 1 continued
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Forces-normal reaction
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Forces-friction
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Forces-tension
Resolution of forces
Vectors
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Position vectors as functions of time (Parametric Equations)
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Finding cartesian equations from parametric equations
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Example 1
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Example 2
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Collision
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Example 3
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Using a graphic calculator with parametric equations
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Using a graphic calculator with two parametric equations to show a collision
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The closest distance to a path
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Example 4
Vectors 2
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The garden activity
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Notation used in vector calculus
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Differentiation and anti differentiation of vectors
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Example 1
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Example 2
Introduction to Algebra
Using Formulae 1
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Using formulae
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The XSIQ petrol pump
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Petrol stations
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Renting a car
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Get real rent-a-car deal
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Speed examples
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Speed
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Temperature
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Temperature examples
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Temperature converter
Using Formulae 2
Algebraic Expressions 1
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Simplifying algebraic expressions without using algebra blocks
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Verifying the simplified form of an algebraic expression
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Verifying the simplification using substitution - examples
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Verifying the simplification using a spreadsheet
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Adding and subtracting terms - practice questions 1
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Adding and subtracting terms - practice questions 2
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Mulitplying terms - Commutative Law
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Multiplying terms - rearranging 1
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Multiplying terms - rearranging 2
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Dividing terms - rearranging 1
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Dividing terms - rearranging 2
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Adding and subtracting like terms without using algebra blocks
Algebraic Expressions 2
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Expanding and simplifying algebraic expressions
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Distributive Law - algebra blocks
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Distributive Law - expansion
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Expanding and collecting like terms
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Expanding and simplifying algebraic expressions
Algebraic Fractions 1
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Introduction to algebraic fractions
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Adding simple algebraic fractions
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Subtracting algebraic fractions
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Fractions with letters in the denominators
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Binomials in denominator
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Speed and algebraic fractions
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The faster car takes less time
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Calculating the time difference
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Adding and subtracting algebraic fractions - practice questions
Algebraic Fractions 2
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Factorising algebraic expressions
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Factorising algebraic expressions
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Highest common factor
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More complex highest common factors
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Factorising algebraic expressions - practice questions
Algebraic Fractions 3
Terminology for Algebraic Expressions
Binomial Expressions 1
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Binomial expressions
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Binomial expansions with like and unlike terms
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Binomial expansions
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Binomial expansions and areas
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Using binomial expansions for problem solving
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Binomial expansions - reminder
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Binomial expansion with two variables
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Binomial expansions - practice questions
Binomial Expressions 2
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Binomial expansions with perfect and non-perfect squares
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Binomial expansions with non-perfect squares
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Expanding perfect squares - practice questions
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Binomial expansions with perfect squares
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Binomial expansions with perfect squares
Binomial Expressions 3
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Binomial expansions - Difference of perfect squares
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Difference of perfect squares (DOPS)
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Expanding and simplifying algebraic expressions - practice questions
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Expanding using the difference of perfect squares rule
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Difference of perfect squares rule
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Difference of perfect squares
Completing the Square
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Completing the square
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Factorising quadratic trinomials using the method of completing the square
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Process to factorise a quadratic trinomial by the method of completing the square
Perfect Squares
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Using the difference of perfect squares 1
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Using the difference of perfect squares 2
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Factorising using the difference of perfect squares (DOPS) expressions
Quadratic Trinomials
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What are quadratic trinomials?
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Factorising the general form by inspection
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Factorising quadratic trinomials
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Factorising algebraic expressions - quadratic trinomials
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Factorising quadratic trinomials
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Factorising quadratic trinomials
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Factorisation of quadratic trinomials
Substitution into Algebraic Expressions
Summary of Factorisation
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Summary of factorisation
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Practice question - Sally's patio
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Practice question - in the swim with algebra
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Practice question - algebra can be fishy
Summarising data
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Summarising data - overview
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Mode
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Mean
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Median
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Mode, mean, median
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Comparing mode, mean, median
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Range of data
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Inter-quartile range
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Review - summarising data
Frequency and graphs
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Frequency and graphs - overview
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Nominal data
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Discrete data
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Continuous data
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Frequency tables with nominal data
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Frequency tables with discrete data
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Frequency tables - discrete data and summary statistics
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Mean from frequency tables - discrete data
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Interpreting column graphs
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Family size cumulative frequency
Graphs of all kinds
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Graphs of all kinds
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Ice cream pictograph
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Column and bar graphs
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Examples of column graphs
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Pie charts
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Examples of pie charts
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Line graphs
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Temperature line graphs
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Types of graphs
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Interpreting column graphs
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Manchester flights bar graph
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Movie line graph
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Interpretation of a sports pie graph
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Review - graphs
Introduction to probability
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Introduction to probability
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Probability words
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Words describing chance
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Finding probabilities theoretically
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Probability with equally likely outcomes
Odds and probability
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Odds and probability
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Odds
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Odds on
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Odds and probability
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Fair or unfair?
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Deciding fairness using probability
Probability and relative frequency
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Probability and relative frequency
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Short-run coin tossing
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Short-run dice rolling
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Predicting from past experience
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Towards probability with coins
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Towards probability with dice
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Probability as long-run relative frequency
Assessment
Learning Outcomes
Alison's math course will greatly enhance your skills, giving you a greater understanding of core mathematics components such as geometry, trigonometry, calculus and more as well as expanding your knowledge base in areas such as chance, data distributions, statistics, probability, correlations and regression.
You will learn about using binomial expansions for problem solving and will understand the relationship between the graphs of functions and their anti-derivatives. You will be able to confidently create graphs and make advanced calculations such as straight-line calculations, kinematics, motion, vectors, algebra, binomial expressions, and quadratic functions.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Diploma course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Diploma course, you have the option to acquire an official Diploma, which is a great way to share your achievement with the world. Your Alison Diploma is:
Ideal for sharing with potential employers - include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Diplomas for completed Diploma courses:
Digital Diploma - a downloadable Diploma in PDF format, immediately available to you when you complete your purchase
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All Diplomas are available to purchase through the Alison Shop. For more information on purchasing Alison Diplomas, please visit our FAQs. If you decide not to purchase your Alison Diploma, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Diploma pricing, please visit our Pricing Page.