Topics which will be covered in this week

Week 1

Topics which will be covered in this week:

· Introducing Naturals, Integers, Quotients, Irrationals and Real numbers

· Bridging to Algebra and Algebraic Expressions – what they are, how to relate them to the everyday life activities then introducing equations and categorisation of them into two categories of linear and non-linear equations

· Non-linear equations main focus on Quadratics and Cubic equations. (solving quadratics by factorizing, completing the square and direct formula)

· Relationships between variables and functions

Learning outcomes:

Students should be able to

· Distinguish different sets of numbers

· Realise the use of letters instead of actual value of things in algebra

· Realise and simplify algebraic expressions by using their like term(s)

· Distinguish algebraic expressions from equations and also understand the concept of a function and its difference with an equation

· Simplify algebraic expressions (using their like terms and exponent rules)

· Distinguish non-linear and linear equation and solve first and second order equations

· Solve linear equations

· Solve quadratic equations (factorization, Completing the square, and using quadratic formula)

· Realise the difference between an equation and a function

Week 2

Topics which will be covered in this week

· Coordinate Geometry (Midpoint & Distance formulae)

· Graph of functions (in particular, Quadratic, Cubic and Quartic functions)

· Equation of straight lines (Point-slope form, Point-point form, Slope & y-intercept form)

· Parallel and perpendicular lines

Learning outcomes

Students should be able to:

· Recognise Cartesian plane, X-axis, Y-axis, Ordered pairs and their components, and four quadrants

· Find the distance between every two point in the plane and the midpoint between them

· Describe the concept of gradient (slope)

· Plot the graphs of straight lines

· Plot the graphs of quadratic functions

· Sketch the graphs of quadratic functions for different values and sign of discriminant of equations

· Sketch the graphs of Cubic functions

· Recognise parallel and perpendicular lines using their slopes

· Distinguish parallel and perpendicular lines by finding their slopes

Week 3

Topics which will be covered in this week

· Introducing transformation of functions

· How to shift the graph a function up, down, left and right

· Stretching and compressing the graphs

· Simultaneous equations – elimination, substitution and graphic methods

· Applications of simultaneous equations

· Learning outcomes

Students should be able to:

Week 4

Topics which will be covered in this week

· Introducing inequalities

· Double inequalities and their solution sets

· Introducing the solution sets of inequalities on the number line

· The remainder theorem

· The factor theorem

Learning outcomes

Students should be able to:

Week 5

Topics which will be covered in this week

· Introducing complex numbers and their properties,

· Non-real roots of quadratic equations

· Addition, subtraction , and product of complex numbers

· Comparing real & imaginary parts of the complex numbers

· Conjugate of a complex number and how to divide complex numbers

Learning outcomes

Students should be able to:

· Recognise an imaginary number

· Realise that a complex number is a combination of a real number and an imaginary number

· Find the non-real solution(s) of a quadratic equation with a negative discriminant

· Add, subtract, and multiply complex numbers

· Find the conjugate of a complex number and use it to divide complex numbers

· Recognise the Argand diagram, the imaginary and real axes on the complex plane and plot complex numbers on the complex plane

Week 6

Date: 2015-12-24; view: 799