Additional Arithmetic

• Proportions

Mensuration

• Volume and Surface Area of Solids

Algebra

• Linear Graphs and Simultaneous Linear Equations
• Expansion of Algebraic Expressions
• Factorisation of Algebraic Expressions
• Quadratic Equations and Graphs
• Algebraic Fractions and Manipulations

Geometry

• Congruency and Similarity
• Maps and Scales
• Trigonometry
• Pythagoras Theorem
• Trigonometric Ratios and Applications

Probability

• Probability

Statistics

• Data Handling
• Data Analysis
• Data Analysis of Grouped Data

Equation and Inequalities

1.1. Simultaneous Equations
1.1.1. Solve a pair of simultaneous linear and non-linear equations
1.1.2. Find the point(s) of intersection of two graphs algebraically
1.1.3. Formulate and solve simultaneous equations to model real-world
problems
1.2. Sum and Product of Roots
1.2.1. Use the formulae for the sum and product of roots of a quadratic
equation
1.2.2. Form a quadratic equation from its roots
1.3. Discriminant, Roots and x-intercepts
1.3.1. Sketch quadratic graphs
1.3.2. Use discriminant to determine the nature of roots
1.3.3. Use discriminant to determine the number of points of intersection of
two graphs.
1.4. Quadratic Inequalities
1.4.1. Solve quadratic inequalities graphically
1.4.2. Solve inequality problems involving the discriminant, roots and x-
intercepts
1.4.3. Solve simultaneous inequalities

Surds and Indices

2.1. Surds
2.1.1. Simplify surds
2.1.2. Rationalise fractions with surds in their denominators
2.1.3. Solve equations involving surds
2.2. Indices
2.2.1. Simplify expressions using the definition and properties of indices
2.2.2. Evaluate expressions involving indices and surds to find unknowns
2.3. Equations Involving Indices
2.3.1. Use the property (ax=ay x = n) to solve equations involving indices
2.3.2. Use substitution to solve equations involving indices
2.4. Exponential Functions
2.5. Sketch graphs of exponential functions
2.6. Use exponential functions in real-world contexts

Polynomials and partial fraction

3.1. Polynomial and identities
3.1.1. Identify polynomials
3.1.2. Add and subtract polynomials
3.1.3. Multiply polynomials
3.1.4. Find the unknowns in an identity
3.2. Division of Polynomials
3.2.1. Divide two polynomials
3.2.2. Express the result of division in terms of quotient, divisor and
remainder
3.3. The Remainder Theorem
3.3.1. Use the remainder theorem to find remainder
3.3.2. Use the remainder theorem to find unknown coefficients or find the
relationship between unknown coefficients.
3.4. The Factor Theorem
3.4.1. Apply the factor theorem to find factors of a polynomial
3.4.2. Apply the factor theorem to find unknown coefficients or the
relationship between unknown coefficients
3.4.3. Factorise expressions of the form a 2 +b 2 and a 2 – b 2
3.5. Cubic Polynomials and Equations
3.5.1. Factorise or determine factors of cubic expressions
3.5.2. Solve cubic expressions
3.6. Partial Fractions
3.6.1. Express a proper algebraic fraction into its partial fractions
3.6.2. Identify whether an algebraic fraction is a proper or an improper
fraction
3.6.3. Express an improper algebraic fraction in partial fractions

The Modulus and Power Functions

4.1. Modulus Functions and Their Graphs
4.1.1. Simplify and evaluate modulus expressions
4.1.2. Solve equations involving modulus
4.1.3. Sketch graphs of y=If(x)l
4.2. Graph of Power Functions
4.2.1. Sketch graphs of power functions
4.2.2. Solve problems on intersections of curves with one power graph

Binomial Theorem

5.1. The Binomial Expansion of (1+b) n
5.1.1. Use the notations n! and ( )
5.1.2. Expand (1+b) n where n is a positive integer
5.2. The Binomial Expansion of (a+b) n
5.2.1. Expand (a+b) n
5.2.2. Use the general term formula to find specific terms, coefficients and unknown values.

Points Lines and Shapes

6.1. Mid-point of a line segment
6.1.1. Use the mid-point formula
6.1.2. Apply the mid-point formula to solve geometric problems
6.2. Parallel Lines
6.2.1. Relate gradient to the angle of inclination
6.2.2. Find hoe the gradients of two parallel lines are related
6.2.3. Find the equation of a line that is parallel to a given line
6.3. Perpendicular Lines
6.3.1. Find how the gradients of two perpendicular lines are related
6.3.2. Find the equation of a line that is perpendicular to a given line
6.3.3. Find the equation of a perpendicular bisector of a line segment
6.4. Areas of Triangles and Quadrilaterals
6.4.1. Use the formulae for the area of a triangle
6.4.2. Use the formulae for the area of a quadrilateral

Logarithms

7.1. Introduction to Logarithms
7.1.1. State what a logarithm is and use logarithmic notations
7.1.2. Use the equivalence of y=ax and x=logaY
7.1.3. Evaluate special logarithmic values
7.1.4. Apply the concept of logarithm to solve equations
7.2. Laws of logarithms
7.2.1. Use the power, product and quotient laws to manipulate logarithms
7.2.2. Use the change-of-base law to manipulate logarithms
7.3. Logarithmic Equations
7.3.1. Apply the law for the same base to solve logarithmic equations
7.3.2. Apply the change-of-base law to solve equations
7.4. Logarithms and Equations of the Form a x =b
7.4.1. Use logarithms to solve equations of the for, ax=b
7.5. Graphs and Applications of Logarithmic Function
7.5.1. Draw graphs of logarithmic functions
7.5.2. Solve real-world problems on logarithmic functions

Application of Straight Lines Graphs

8.1. Reducing Equations to Linear Form
8.1.1. Reduce equations to linear form and plot straight line graphs
8.1.2. Obtain non-linear equations from straight line equations or graphs
8.2. Linear Laws
8.2.1. Sketch and interpret lines of closest fit
8.2.2. Solve real-world problems on linear law

Parabola and Circles

9.1. Graph of Parabolas of the Formy 2 =kx
9.1.1. Sketch parabolic graphs of the form y2=kx
9.1.2. Solve geometric problems involving the intersection of lines and curves
9.2. Coordinates Geometry of Circles
9.2.1. Find the equation, the center and the radius of a circle
9.2.2. Solve geometric problems involving the intersection of lines and circles.