MATH06069 2013 Mathematics 1

Add, subtract, divide Natural Numbers, Integers, Rational Numbers and Real Numbers and demonstate knoweledge of the indice rules and riles of logs

Solve linear, quadratic and simultaneous equations; expand (a+b)ⁿ for n between 2 and 8; Solve equations with fractions; Manipulate formulae; State, prove and use the factor theorem.

Use the ratio’s sine, cosine and tangent to calculate the side or an angle of a right angled triangle; Use pythagoras’ Theorem to calculate a side of a right angle d triangle; Become familiar with the sine, cosine and tangent of 30,45,60,90,180 etc. ; Use sine and cosine rule to calculate sides and angles of a triangle; Become familiar with standard trigonometric identities; Become familiar with compound and double angle formulae; Convert Degree’s to Radians and Radians to Degree’s.

Add, subtract, divide complex numbers; calculate the complex conjugate, modulus and argument of a complex number; Be familiar with polar and exponential form;  Multiply and divide complex numbers in polar form; Use De Moivre’s Theorem to calculate (a+bi)^n and find roots.

Add, subtract, scalar multiply and multiply matrices. Become familiar with the Zero and Identity matrix and their properties.  Invert 2x2. Solve equations with matrices and a system of linear equations.

Become familiar with the basic rules of diferentations (xⁿ,  e^x,sin(x), cos(x), ln(x), etc.);Differentiate using 1^st principles; Be able to differentiate using the product, quotient and chain rule; Calculate the equation of a tangent to a curve; Use differentiation to find the Max/Min of a function.

Add, subtract and scalar multiply vectors; Calculate the length and unit vector of a vector; Be familiar with their properties.

1. Revision of computation, algebraic operations, transposition of formulae, solution of algebraic equations, laws of indices and logs
2. Elementary set theory, relations, functions and their graphs
3. Solution of right-angled and other triangles, sin and cos rules, trigonometric identities, degrees and radians, area and circumference of circles
4. Addition and subtraction of vectors and scalar multiples of vectors. Lengths and unit vectors of a vector.
5. Addition, subtraction and multiplication of matrices. Scalar multiples of a matrix. The Zero and Identity matrix and their properties. Inversion of 2x2 matrices. Solution a system of linear equations with matrices.
6. Add, subtract, divide complex numbers, and calculate the complex conjugate modulus and argument of a complex number. Be familiar with polar and exponential form. Multiply and divide complex numbers in polar form, DE Moivre’s Theorem
7. Differentiation of polynomial, trigonometric, exponential and logarithmic functions. Differentiation using first principles. Differentiation using the product, quotient and chain rules. Equation of a tangent to a curve. Maxima and minima of a function. Rates of change, velocity and acceleration as derivatives.