Secondary 2 Mathematics

Reviewing fundamental concepts of ratios, rates, and unit rates, and their application in everyday contexts.

Investigating direct proportion through data tables and graphical representations, identifying the constant of proportionality.

Formulating and solving direct proportion problems using algebraic equations, including real-world scenarios.

Exploring inverse proportion through data tables and graphical representations, identifying the constant product.

Formulating and solving inverse proportion problems using algebraic equations, including real-world scenarios.

Plotting linear equations on a Cartesian plane and interpreting key features like intercepts.

Understanding the geometric interpretation of rate of change as the steepness of a line and calculating it.

Deriving and applying the equation of a straight line in the form y=mx+c from given information.

Applying proportional reasoning to solve problems involving maps, scale models, and architectural drawings.

Solving real-world problems involving currency exchange rates, percentage increase/decrease, and simple interest.

Revisiting fundamental algebraic operations, combining like terms, and the distributive law.

Applying the distributive law to expand expressions with a single bracket.

Using the distributive law (FOIL method) to expand products of two binomials.

Recognizing and applying special identities such as (a+b)^2, (a-b)^2, and (a^2-b^2).

Reversing the expansion process by identifying and extracting common factors from expressions.

Factoring quadratic expressions of the form ax^2+bx+c where a=1.

Factoring expressions using the special identities: difference of squares, and perfect squares.

Applying the technique of grouping terms to factorise expressions with four or more terms.

Performing operations on algebraic fractions, including addition, subtraction, multiplication, and division.

Changing the subject of a formula to express one variable in terms of others.

Reviewing the concept of a linear equation in one variable and its solution.

Understanding what simultaneous linear equations are and what their solution represents.

Identifying the solution to a pair of equations as the coordinates of their intersection point.

Mastering the substitution technique to find exact solutions for systems of equations.

Mastering the elimination technique to find exact solutions for systems of equations.

Developing strategies to select the most efficient algebraic method (substitution or elimination) for a given system.

Translating simple word problems into systems of equations to solve real-world dilemmas.

Solving more complex word problems involving simultaneous equations, including those with cost, revenue, and mixture scenarios.

Reviewing translations, reflections, and rotations as foundational concepts for congruence.

Defining congruence and identifying corresponding parts of congruent figures.

Defining and proving congruence in triangles using specific geometric criteria (Side-Side-Side, Side-Angle-Side, Angle-Side-Angle).

Extending congruence proofs to include Angle-Angle-Side and Right-angle-Hypotenuse-Side criteria.

Understanding the relationship between corresponding angles and the ratio of corresponding sides in similar figures.

Proving similarity in triangles using Angle-Angle, Side-Side-Side, and Side-Angle-Side similarity criteria.

Using similar triangles to solve real-world problems involving indirect measurement of heights and distances.

Exploring how the area of a shape scales when it is enlarged or reduced by a given scale factor.

Exploring how the volume of a 3D shape scales when it is enlarged or reduced by a given scale factor.

Identifying properties of right-angled triangles and their components (hypotenuse, opposite, adjacent).

Developing and applying the relationship between the sides of a right-angled triangle, including visual proofs.

Using the theorem to find unknown side lengths in right-angled triangles and identifying Pythagorean triples.

Extending the application of Pythagoras Theorem to find lengths in three-dimensional figures.

Understanding and applying scale to represent real-world objects and distances on paper.

Using given scales to calculate the actual lengths or distances from a scale drawing.

Determining the scale of a drawing or map when both the actual and drawing lengths are known.

Investigating the relationship between areas and volumes of similar figures and their scale factors.

Solving practical problems involving scale drawings in contexts such as maps, blueprints, and models.

Understanding different types of data (discrete, continuous) and methods for collecting and organizing raw data.

Constructing frequency tables for both ungrouped and grouped data, and understanding class intervals.

Creating and interpreting histograms for continuous data and bar charts for discrete data.

Creating and interpreting stem and leaf plots and pie charts for various data sets.

Calculating and interpreting the mean for ungrouped and grouped data.

Calculating and comparing median and mode for various data sets, including grouped data.

Calculating and interpreting the range as a measure of data variability and its limitations.

Understanding the concept of randomness and calculating the likelihood of single outcomes.

Exploring the probability of combined events using tree diagrams and systematic listing of sample spaces.

Applying probability concepts to solve problems in everyday contexts, such as games of chance or risk assessment.