## Objectives

Everything you need to know for your C2 exam in one place.

Textbook Chapter
Topic
Learning Outcomes
Students should be able to:
More details
Chapter 7
Sequences and Series
Understand the definitions and notation used to describe sequences Arithmetic sequences, geometric sequences, oscillating sequences and periodic sequences.
Interpret arithmetic sequences and series Notation and sum to n terms
Interpret geometric sequences and series Notation, sum to n terms, infinite geometric series.
Chapter 8
Differentiation
Find the gradient of a curve Tangents and Chords, first principles, the gradient of a function.
Use alternative notation Standard derivatives, sums and differences of functions.
Find tangents and normals Relates back to y = mx + c in C1
Find maximum and minimum points Gradient at a turning point, increasing and decreasing functions
Find stationary points
Find higher derivatives Using the 2nd derivative, points of inflexion
Apply differentiation Applications to business, mechanics etc
Chapter 9
Integration
Reverse differentiation Particular solutions, integrating $x^n$
Find the area under a curve Notation, area as the limit of a sum, definite and indefinite integrals
Find areas below the x axis
Find the area between two curves
Find the area between a curve and the y axis
Use numerical integration The trapezium rule
Chapter 10
Trigonometry
Use trigonometrical functions Angles of elevation and depression, bearings, special cases, positive and negative angles, identities for sinθ, cosθ and tanθ, graphs of sine, cosine and tangent, solving equations using the graphs.
Deal with triangles without right angles The sine rule
Use the cosine rule
Find the area of a triangle
Model curves Relationships in the form $y = kx^n$, exponential relationships
Differentiate more functions $kx^n$
Integrate more functions $kx^n$, differential equations