Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Use logarithm laws for products, quotients and powers. • In examinations, logarithm bases are 10 or e.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Simplify numerical and algebraic expressions with rational exponents. • Include negative and fractional powers.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Find sums of infinite geometric sequences. • Connect convergence to limits, fractals and Markov chains.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use i where i^2=-1 and Cartesian form z=a+bi. • Calculate sums, differences, products, quotients and powers of complex numbers. • Use Argand diagrams and complex roots of real-coefficient quadratics with negative discriminant.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use polar form z=r(cos theta+i sin theta)=r cis theta and Euler form z=re^(i theta). • Convert between Cartesian, polar and exponential forms. • Use products, quotients and integer powers; roots are not required. • Interpret complex operations geometrically and model sinusoidal phase shifts.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Use matrix terminology, order, equality, addition, subtraction, scalar multiplication and multiplication. • Know identity/zero matrices, determinants and inverses; hand calculation is limited to 2x2 inverses/determinants. • Write systems as Ax=b and solve with inverse matrices; apply matrices to coding, decoding and systems.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Find eigenvalues/eigenvectors and characteristic polynomial for 2x2 matrices. • Diagonalize 2x2 matrices with distinct real eigenvalues. • Use M^n=PD^nP^-1 for powers and applications such as population movement or predator-prey models.
Start with the concept explanation, then practise to create mastery evidence.