Matrices and determinants, Matrix definition, Square matrices, Identity matrix, Vectors matrix, Transpose of matrix, Matrix addition and subtraction, Scalar multiplication of matrix, Matrix multiplication, Matrix vector product, Determinant of matrix, Expanding determinant by cofactors, Calculating value of determinant, Determinant of 2 X 2 matrix, Determinant of 3 X 3 matrix, Properties of determinants, Inverse of matrix, Systems of linear equations, Solving systems of equations using matrices, Inverse matrix method, Cramer's rule, Cramer's rule and inverse matrix method correlation, Use of Cramer's rule for solving systems of linear equations, Solving systems of linear equations using determinants, Solving systems of two equations in two unknowns using Cramer's rule, Solving systems of three equations in three unknowns using Cramer's rule, Method of expanding determinant of rank n by cofactors, Sequences and series, Arithmetic sequence or progression, General term of arithmetic sequence, Sum of first terms of arithmetic sequence, Sum of first n natural numbers, Arithmetic sequence examples, Geometric sequence, General term of geometric sequence, Sum of first n terms of finite geometric sequence, Geometric series, Geometric sequence examples, Recursive definition, Recursive formula, Series, Finite and infinite series, Convergent series, Divergent series, Sum of infinite geometric sequence, Infinite geometric series, Sum of infinite convergent geometric series, Sum of infinite convergent geometric series examples, Converting recurring decimals to fraction, Converting infinite decimals to fraction, Factorial, Binomial coefficients and Pascal's triangle, Sigma notation, Binomial expansion algorithm, Combinatorics, Combinatorial analysis, Permutations, Combinations, Variations, Permutations of n objects some of which are the same, Combination with repetition, Variations or permuted combinations, Permutations with repetition, Variations with repetition, Permuted combinations with repetition, Mathematical induction, Binomial theorem, Principle of mathematical induction, Proving statement theorem or formula, Mathematical induction examples

Pre-calculus Contents K

Matrices and Determinants

Matrix definition

Square matrices

The identity matrix

Vectors

The transpose of a matrix

Basic matrix operations

Matrix addition and subtraction

Scalar multiplication of a matrix

Matrix multiplication

The matrix-vector product

The determinant of a matrix

Expanding a determinant by cofactors

Calculating the value of a determinant

The determinant of a 2 ´ 2 matrix

The determinant of a 3 ´ 3 matrix

Properties of determinants

The inverse of a matrix

Systems of Linear Equations

Solving systems of equations using matrices

Inverse matrix method

Cramer’s rule

Cramer’s Rule and inverse matrix method correlation

Cramer’s rule (using the determinant) to solve systems of linear equations

Solving system of two equations in two unknowns using Cramer's rule

Solving system of three equations in three unknowns using Cramer's rule

Method of expanding a determinant of a rank n by cofactors

Sequences and Series

Sequences

Arithmetic sequence/progression

General term of an arithmetic sequence

The sum of the first n terms of an arithmetic sequence

The sum of the first n natural numbers

Arithmetic sequences examples

Geometric sequence/progression

General term of a geometric sequence

The sum of the first n terms of a finite geometric sequence, geometric series

Geometric sequences examples

Recursive definition and the recursion formula

Series

Finite and infinite, convergent and divergent series

Geometric series

The sum of an infinite geometric sequence, infinite geometric series

The sum of an infinite converging geometric series examples

Converting recurring decimals (infinite decimals) to fraction

Permutations, Combinations and Variations

Permutations

Permutations of n objects some of which are the same

Combinations

Combinations with repetition

Variations

Variations or permuted combinations (permutations without repetition)

Variations with repetition (or permuted combinations with repetition)

Mathematical Induction and The Binomial Theorem

The principle of mathematical induction

Proving a statement, a theorem or a formula

Mathematical induction examples

The Binomial Theorem

Factorial

Binomial coefficients and Pascal's triangle

The binomial theorem, sigma notation and binomial expansion algorithm

The binomial theorem and binomial expansion algorithm examples

Pre-calculus Contents