Secondary 3 Mathematics

Reviewing basic algebraic terms, operations, and the order of operations (BODMAS/PEMDAS) with variables.

Exploring the distributive law to expand products of linear expressions, including binomials.

Exploring the expansion of algebraic products and the three fundamental algebraic identities.

Identifying and extracting common factors from algebraic expressions, including binomial factors.

Developing strategies for factorising expressions with four terms by grouping them into pairs.

Mastering the cross method to factorise quadratic expressions of the form ax^2 + bx + c.

Applying the difference of squares and perfect squares identities to factorise expressions.

Practicing a variety of factorisation techniques, including combinations of methods.

Revisiting techniques for solving linear equations with one unknown, including those with fractions.

Solving equations using the factorisation method and understanding the zero product property.

Solving quadratic equations by transforming them into a perfect square trinomial.

Deriving and applying the quadratic formula to solve any quadratic equation, including those with irrational or no real solutions.

Solving and representing linear inequalities on a number line.

Solving and representing compound linear inequalities involving 'and' or 'or'.

Using algebraic tools to solve word problems involving real life constraints.

Solving real-world problems that require setting up and solving linear inequalities.

Defining functions, domain, range, and using function notation to represent relationships.

Reviewing gradient, y-intercept, and different forms of linear equations (y=mx+c, ax+by=c).

Investigating the properties of parabolas including symmetry and turning points.

Plotting quadratic functions by creating tables of values and identifying key features.

Exploring the characteristics and graphical representation of power functions, including y=ax^3 and y=ax^n for simple integer values of n.

Investigating the properties of reciprocal functions (y=k/x) and the concept of asymptotes.

Investigating simple exponential relationships (e.g., compound interest, population growth/decay) and their graphical representation.

Solving equations by finding the intersection of multiple graphs.

Analyzing and interpreting various types of graphs to extract information and draw conclusions from real-world data.

Defining and identifying parts of a circle: radius, diameter, chord, arc, sector, segment, tangent, secant.

Investigating angles at the center and circumference subtended by the same arc.

Exploring angles in a semicircle and angles in the same segment.

Understanding the properties of angles in cyclic quadrilaterals.

Studying the perpendicular property of tangents and radii.

Investigating the properties of tangents drawn from an external point to a circle.

Studying the perpendicular properties of chords and the line from the center.

Investigating the properties related to tangents and chords, including the angle between a tangent and a chord.

Applying multiple circle theorems to solve complex geometric problems.

Revisiting sine, cosine, and tangent ratios for right-angled triangles and solving for sides and angles.

Extending trigonometry to solve for sides and angles in any triangle using the Sine Rule.

Applying the Cosine Rule to solve for sides and angles in any triangle.

Calculating the area of any triangle using the formula involving the sine of an included angle.

Solving problems involving angles of elevation and depression in two dimensions.

Understanding and applying bearings in navigation problems.

Solving problems involving angles of elevation, depression, and bearing in three dimensions.

Calculating arc lengths and sector areas using degree measures.

Solving more complex problems involving arc length and sector area, including segments and composite shapes, using degree measure.

Calculating surface areas and volumes of composite 3D shapes involving cylinders, cones, and spheres.

Revisiting histograms, bar charts, pie charts, and stem-and-leaf plots for data visualization.

Calculating and interpreting mean, median, and mode for grouped and ungrouped data.

Calculating and interpreting range and interquartile range for grouped and ungrouped data.

Constructing and interpreting cumulative frequency curves.

Constructing and interpreting box plots from cumulative frequency data.

Defining probability, outcomes, events, and calculating simple probabilities.

Using tree diagrams and possibility diagrams to calculate probabilities for multiple independent events.

Calculating probabilities for multiple dependent events, including 'without replacement' scenarios.

Understanding and applying the concepts of mutually exclusive and exhaustive events.

Solving complex probability problems from various real-world contexts.