1. Integration: Solving definite integrals and simplifying the result. 2. Function Simplification: Simplifying expressions in terms of other variables. 3. Line Equation: Finding the gradient of a line and the equation of a perpendicular line. 4. Curve and Region: Identifying inequalities that define regions bounded by curves. 5. Differentiation: Solving equations based on first and second derivatives. 6. Graphing: Sketching curves, finding points of intersection, and solving for coordinates.