Pre-calculus Contents K
Matrices and Determinants
      Matrix definition
         Square matrices
         The identity matrix
      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
      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
      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 of n objects some of which are the same
      Combinations with repetition
      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
      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
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