Curved Graphs

IGCSE 0580

Topic: Algebra and graphs

Core: C2.10 C2.11

Construct tables of values, and draw, recognise and interpret graphs for functions of the following
forms:
• ax^n (includes sums of no more than three of these)
• ab^x + c
Solve associated equations graphically, including finding and interpreting roots by graphical methods.
Recognise, sketch and interpret graphs of the following functions:
(a) linear
(b) quadratic

Extended: E2.10, E2.11, E2.12, E.13

Everything in Core.
Draw and interpret graphs representing exponential growth and decay problems.
Recognise, sketch and interpret graphs of the following functions:
(a) linear, (b) quadratic, (c) cubic, (d) reciprocal, (e) exponential.
Estimate gradients of curves by drawing tangents.
Use the derivatives of functions of the form ax^n, where a is a rational constant and n is a positive
integer or zero, and simple sums of not more than three of these.
Apply differentiation to gradients and stationary points (turning points).
Discriminate between maxima and minima by any method.
Understand functions, domain and range and use function notation.
Understand and find inverse functions.
Form composite functions as defined by gf(x) = g(f(x)).