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Topics which will be covered in this weekWeek 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: 849
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