| Form | Topic | Objectives and Subjects | Assessment
|
|---|
| 4 | Algebra
| Real number system -- Addition and subtraction of polynomials -- Multiplication and division of polynomials -- Factorization of polynomials -- Dividing a polynomial by a polynomial -- Remainder Theorem -- Factor Theorem
| Quiz or test
|
| Quadratics
| Quadratic equation -- Method of factorization -- Quadratic formula -- Completing the square -- Determining the values of h and k -- Maximum or minimum and range of a quadratic function -- Graph of a quadratic function -- nature of the roots of a quadratic equation -- Equation reducible to a quadratic equation -- Relationships between roots and coefficients of a quadratic equation -- Simultaneous equations: one linear and one quadratic
| Quiz or test
|
| Inequalities
| Definition and properties of inequalities -- Quadratic inequalities in one unknown -- Rational inequalities with linear factors
| Quiz or test
|
| Functions
| Relation -- Function -- Determining the range of a function -- Funtion: one-to-one or many-to-one -- Inverse of a function -- Composition of two functions -- Composition of a function and its inverse
| Quiz or test
|
| Surds, indices and logarithms
| Surds -- Addition and subtraction of surds -- Multiplication of surds -- Rationalization of the denominator of a surd -- Laws of indices -- Zero, negative and rational indices -- Exponential equation with one unknown -- Relationship between indices and logarithms -- Laws of logarithms -- Logarithmic equations -- Equations of the form a to the power of x = b -- Transformation of a relationship to linear form
| Quiz or test
|
| Sequences and series
| Sequence -- Series and summation notation -- Arithmetic series -- Geometric series -- Divergent and Convergent series -- Investments
| Quiz or test
|
| Geometry
| Gradient of a line segment -- Equation of a straight line -- Parallel lines -- Perpendicular lines -- Point of intersection of two lines -- Equations of a circle -- Equations of tangents and normal to a circle -- Point(s) of intersection of a circle and a straight line
| Quiz or test
|
| Vectors
| Scalar quantities and vector quantities -- Representing a vector -- Column vectors -- Equal vectors -- Addition of vectors -- Subtraction of vectors -- Multiplication of a vector by a scalar -- Unit vectors -- Position and displacement vectors -- Scalar product of two vectors
| Quiz or test
|
| 5 | Trigonometry
| Radian -- Arc length and area of sector -- Trigonometric ratios and general angles -- Trigonometric ratios of a general angles -- Graphs of sine, cosine and tangent function -- Fundamental trigonometric identities -- Compound angle formulae -- Double angle formulae -- Solutions of simple trigonometric equations
| Quiz or test
|
| Differentiation
| Gradient of a curve at a point -- Derivative as a limit -- Derivative of x to the power of n -- Derivative of a multiple of a function -- Derivatives of a sum and difference of two functions -- Deriatives of sin x and cos x -- Product rule -- Quotient rule -- Chain rule -- Rate of change -- Stationary points -- Second derivative of a function -- Second derivative test for maxima and minima -- Equations of a tangent and normal to a curve
| Quiz or test
|
| Integration
| Integration of a indefinite integral -- Integral of x to the power of n -- Integral of a multiple of a function -- Integral of a sum and a difference of two functions -- Integral of a product -- Integral of a quotient -- Integral of (ax + b) to the power of n -- Integrals of sin x and cos x -- Evaluation of a definite integral -- Formulating the equation of a curve -- Area bounded by a curve and two lines parallel to the y-axis -- Volume of a solid of revolution
| Quiz or test
|
| Data representation and analysis
| Statistics -- Types of variables and data -- Measures of central tendency from raw data -- Measures of dispersion from raw data -- Stem-and-leaf diagram (stemplot) -- Back-to-back stemplots -- Measures of central tendency for ungrouped data -- Measures of dispersion for ungrouped data -- Measures of central tendency for grouped data -- Measures of dispersion for grouped data
| Quiz or test
|
| Probability
| Classical probability and relative frequency -- Basic laws of probability -- Non-mutually exclusive events -- Mutually exclusive events -- Conditional probability and dependant events -- Independent events -- Possibility space diagram, Venn diagram and Tree diagram
| Quiz or test
|
| Kinematics of motion along a straight line
| Kinematics -- Scalar and vector quantities -- Displacement-time graphs -- Velocity-time graphs -- Equations of motion of a particle moving in a straight line -- Vertical motion under gravity -- Variable motion of a particle
| Quiz or test
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