Sequences, Functions and Graphs

Worked examples (5)

• 1$n$th term of an arithmetic sequence
• 2Use the $n$th term to find a specific term
• 3$n$th term of a quadratic sequence
• 4Geometric sequence
• 5Recursive (Fibonacci-style) sequence

Worked examples (4)

• 1Evaluate a function
• 2Composite functions $fg(x)$
• 3Find an inverse function
• 4Evaluate a composite

Worked examples (5)

• 1Find gradient and y-intercept
• 2Equation from two points
• 3Parallel line through a point
• 4Perpendicular line
• 5Midpoint of two points

Worked examples (4)

• 1Sketch a quadratic
• 2Sketch a cubic
• 3Reciprocal graph
• 4Exponential graph

Worked examples (4)

• 1Distance-time graph: speed from gradient
• 2Speed-time graph: distance from area
• 3Acceleration from speed-time graph
• 4Conversion graph

Worked examples (4)

• 1Vertical translation $y = f(x) + a$
• 2Horizontal translation $y = f(x + a)$
• 3Reflections
• 4Stretches

Worked examples (4)

• 1Differentiate a power
• 2Differentiate a polynomial
• 3Find gradient at a specific point
• 4Find stationary points