Matrix Calculations

Algebra

Expressions: An expression is a collection of terms, with terms being comprised of numbers and letters combined via multiplication or division.
Equations: An equation shows that two expressions are equal. Remember: what you do to one side, you must do to the other to keep an equation balanced.
Factorisation: Factorising is expressing an algebraic expression as the product of its factors. To factorise an expression, take out the common factor.
Expanding: To expand, multiply the term outside of the bracket with each term inside the bracket.

Simplifying: To simplify an algebraic fraction, factorise the numerator and the denominator and ‘cancel’ common factors.
Adding or subtracting: To add or subtract algebraic fractions, find the common denominator and change each fraction to an equivalent fraction with the common denominator.

Completing the square is a method of rewriting a quadratic equation. Perfect squares are helpful because they can be solved by taking square roots.
Quadratics that have “a” values of 1 can be rewritten in the form (x-h)² + k by using the Completing the Square process.

Linear Equations: A linear equation is an equation in which each term is either a constant or the product of a constant and a variable.
Quadratic Equations: A quadratic equation is of the form ax²+bx+c = 0, and can be solved by factoring, completing the square, or using the quadratic formula.

Basic Trigonometric Ratios: The basic trigonometric ratios include sine (sin), cosine (cos), and tangent (tan).
Trigonometric identities: Fundamental trigonometric identities include sin² θ + cos² θ = 1 and tan θ = sin θ / cos θ.
Inverse Trigonometric functions: The inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) can be used to find an angle from a trigonometric value.