Secondary 4 Mathematics

Students will differentiate between relations and functions, identifying domain and range from various representations.

Students will review linear functions, their equations, and graphical properties, including gradient and intercepts.

Students will explore quadratic functions, their graphs (parabolas), and key features like vertex and axis of symmetry.

Students will explore the graphs of simple reciprocal functions (e.g., y = k/x) and identify their key features, including asymptotes.

Students will understand the characteristics of exponential growth and decay, and their real-world applications.

Students will use intersection points of multiple graphs to solve complex equations that are difficult to handle algebraically.

Students will analyze how translations, reflections, and stretches affect the graphs of various functions.

Students will review fundamental concepts of angles, parallel lines, and transversals, applying theorems to solve problems.

Students will investigate the sum of interior and exterior angles of polygons and properties of regular polygons.

Students will apply congruence and similarity criteria to triangles and other polygons to solve geometric problems.

Students will apply the Pythagorean theorem to solve problems involving right-angled triangles in 2D and 3D contexts.

Students will define and apply sine, cosine, and tangent ratios to find unknown sides and angles in right-angled triangles.

Students will calculate surface area and volume of prisms, cylinders, pyramids, cones, and spheres.

Students will investigate the geometric relationships between tangents, chords, and angles within circles.

Students will sketch and interpret the graphs of sine, cosine, and tangent functions for angles between 0° and 360°.

Students will apply the sine rule and cosine rule to solve non-right-angled triangles.

Students will calculate the area of any triangle using A = ½ab sinC, where the sine of the included angle is applied directly — distinct from the Sine Rule (a/sinA = b/sinB = c/sinC), which is used to find unknown sides and angles.

Students will apply bearings to solve navigation problems involving distances and directions.

Students will apply sine and cosine rules alongside bearings to solve complex spatial navigation problems.

Students will understand the concept of the gradient of a curve at a point and estimate it using tangents.

Students will learn various methods of collecting data and representing it using tables, bar charts, and pie charts.

Students will calculate and interpret mean, median, and mode for various datasets.

Students will calculate and interpret range and interquartile range to describe the spread of data.

Students will use measures of spread to compare different datasets and evaluate consistency.

Students will construct and interpret box-and-whisker plots to visualize data distribution and compare datasets.

Students will construct and interpret scatter diagrams to identify relationships between two variables.

Students will draw lines of best fit by eye on scatter diagrams and use them to make estimations and predictions.

Students will define basic probability concepts, including sample space, events, and calculating simple probabilities.

Students will calculate probabilities for independent and dependent events using tree diagrams and Venn diagrams.

Students will differentiate between mutually exclusive and independent events and apply appropriate rules for calculating probabilities.

Students will understand matrices as a way to organize data and perform basic matrix operations.

Students will perform matrix multiplication for 2x2 matrices and understand its conditions and applications.

Students will identify identity matrices and calculate the inverse of a 2x2 matrix.

Students will use inverse matrices to solve systems of two linear simultaneous equations.

Students will perform and describe translations of shapes on a Cartesian plane using vector notation.

Students will perform and describe reflections of shapes across lines (x-axis, y-axis, y=x, y=-x).

Students will perform and describe rotations of shapes about a point (origin or other) through various angles.

Students will perform and describe enlargements of shapes from a center of enlargement with a given scale factor.

Students will perform and describe sequences of multiple geometric transformations.

Students will apply algebraic equations and inequalities to solve real-world problems.

Students will use ratios, rates, and proportions to solve problems involving scaling, comparisons, and direct/inverse variation.

Students will solve problems involving percentages, profit and loss, simple and compound interest, and taxation.

Students will apply geometric theorems and measurement formulas to solve practical problems involving shapes and solids.

Students will use statistical measures and probability concepts to analyze data and make predictions in real-world contexts.

Students will apply linear equations to model real-world situations involving constant rates of change.

Students will use quadratic functions to model situations involving parabolic trajectories or optimization problems.