Summer maths: ready for Year 13
Week 1 Algebra
- Index laws, fractional indices and surds
- Expanding, factorising and simplifying algebraic fractions
- Logarithms: what they mean and the log laws
Check week 1
Week 2 Equations
- Quadratic equations: solving, and forming from the roots
- The discriminant: how many roots, and what kind
- Simultaneous equations: two lines, or a line and a curve
Check week 2
Week 3 Graphs
- Families of graphs
- Transforming graphs
- Exponential growth and decay: interest, depreciation, half-life
Check week 3
Week 4 Differentiation
- The derivative: what the gradient function means
- Differentiating polynomials, fractions and all
- Equation of a tangent to a curve, step by step
Check week 4
Week 5 Calculus in use
- Turning points: finding and proving max or min
- Optimisation with calculus: the biggest box
- Anti-differentiation and why you need + c
- Kinematics: displacement, velocity and acceleration
Check week 5
Week 6 Trigonometry and chance
- The sine and cosine rules
- Radians, arcs and sectors
- Probability: when to add and when to multiply
- The normal distribution: probabilities and z-values