Summary Pure Mathematics Revision Notes (Mathematics Edexcel A-Level)

Pure

Pure Mathematics
Quadratics
Domain: The set of possible input values for a function.

Range: The set of possible output values for a function.

Roots: The values of x for which f(x) = 0.


Graphs and transformations
Cubic graphs
Positive Negative



Minimum - positive
Maximum - negative




Quartic graphs
Positive Negative




This graph instead, has two
repeated roots so one curve
just touches the x-axis


Reciprocal graphs
Positive Negative




Page 1 of 12 A Level Mathematics

, Pure
Points of In ection
Curvature: Second derivative/rate of change of the gradient (f’’(x))

Convex function: When f’’(x) > 0

Concave function: When f’’(x) < 0

Point of in ection: When the graph switches from convex to concave (or vice versa) or
when f’’(x) changes sign

Translating graphs
• Translations
• Stretches
• Re ections

Functions and graphs
Mapping
• Functions can only either be one-to-one or many-to-one




Composite functions
• When two or more functions are combined to make a new function




Inverse functions
• The domain of f(x) is the range of f⁻¹(x)
• The range of f(x) is the domain of f⁻¹(x)

Combining transformations




Page 2 of 12 A Level Mathematics


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