
Precalculus
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
matrixvector 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

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 









Precalculus Contents 



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