Indices and logarithms
- Prove laws of logarithms
- Solve equations of logarithms and induces
- Convert logarithms from one base to another
Series
- Define finite and infinite series
- Use sigma notation in writing series
- Find the sum of the 1st n squares and cubic natural number
Proof mathematical induction
- State the principle of mathematical induction
- Use the principle of mathematical induction to prove mathematical statement
Roots of a polynomial functions
- Determine the roots of a polynomial functions
- Establish the relationship between roots and coefficients of a cubic equations
- Form equations from known roots
Remainder theorem
- Determine the remainder of a polynomial functions by using remainder theorem and synthetic method
Inequalities
- Solve quadratic inequalities
- Solve inequalities involving rational functions
- Solve absolute values inequalities
Matrices
- Calculate the determinant of a 3×3 matrix
- Use Cramer’s rule to solve three equations with three unknowns
- Find the inverse of a 3×3 matrix
- Apply the knowledge of the inverse of s matrix to solve three linear equations with three unknowns simultaneously
Binomial theorem
- Develop Pascal's triangle
- Use Pascal's triangle to expand a binomial expression
- Apply binomial theorem to solve problems
- Use factorial notation to Express binomial theorem
Partial functions
- Use partial fractions to decompose a rational function