Singapore · SEABSyllabus
Maths syllabus, dot point by dot point
Every dot point in the Singapore Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Coordinate Geometry and Vectors
Module overview →- Given two points or a point and a gradient, how do we find the equation of the straight line through them?Find the gradient of a line through two points and determine the equation of a straight line in the form y = mx + c8 min answer →
- Given two points, how do we find the length of the segment joining them and the coordinates of its midpoint?Calculate the length of a line segment using the distance formula and find the midpoint of a line segment8 min answer →
- What is a vector, and how do we add vectors and multiply them by a number?Represent a vector as a column vector, add and subtract vectors, and multiply a vector by a scalar8 min answer →
Equations and Inequalities
Module overview →- How do we solve a linear equation by keeping it balanced, and how do we turn a word problem into one?Solve linear equations in one unknown, including those with brackets and fractions, and form linear equations from word problems8 min answer →
- How do we solve a linear inequality, and why does the inequality sign sometimes flip?Solve simple linear inequalities in one unknown and represent the solution on a number line8 min answer →
- How do we solve a quadratic equation, where the unknown appears squared, by factorising or using the formula?Solve quadratic equations of the form ax^2 + bx + c = 0 by factorisation and by the quadratic formula9 min answer →
- How do we find the pair of values that satisfies two linear equations at the same time?Solve a pair of simultaneous linear equations in two unknowns by elimination and by substitution, and form them from word problems9 min answer →
Functions and Graphs
Module overview →- How does a distance-time graph describe a journey, and how do we read speed from its gradient?Interpret and draw distance-time graphs, find speed from the gradient, and describe stationary and return stages of a journey8 min answer →
- How do we plot a straight-line graph, and what do its gradient and intercept tell us?Plot and draw graphs of linear functions y = mx + c, and interpret the gradient and y-intercept8 min answer →
- What shape does a quadratic function make, and how do we read its turning point and intercepts?Draw graphs of quadratic functions y = ax^2 + bx + c, identify the shape, the turning point and the x-intercepts9 min answer →
Geometry and Circle Properties
Module overview →- What special angle rules hold inside a circle, such as the angle in a semicircle and the radius-tangent angle?Use the basic angle properties of the circle, including the angle in a semicircle and the angle between a tangent and a radius8 min answer →
- What angle rules let us find unknown angles on lines, at points, and between parallel lines?Use angle properties on a straight line, at a point, and between parallel lines to find unknown angles8 min answer →
- When are two figures congruent or similar, and how do we use similarity to find missing lengths?Identify congruent and similar figures, and use the ratio of corresponding sides of similar figures to find unknown lengths8 min answer →
- What are the angle and side properties of triangles and the common quadrilaterals?Use the angle sum of a triangle and a quadrilateral, the exterior angle property, and the properties of special triangles and quadrilaterals8 min answer →
Mensuration and Trigonometry
Module overview →- How do we find the perimeter and area of rectangles, triangles, circles and shapes made from them?Calculate the perimeter and area of rectangles, triangles, parallelograms, trapeziums and circles, and of composite figures8 min answer →
- In a right-angled triangle, how are the three sides related, and how do we find a missing side?Apply Pythagoras' theorem to find a missing side in a right-angled triangle and to solve simple problems8 min answer →
- How do sine, cosine and tangent connect the angles and sides of a right-angled triangle?Use the sine, cosine and tangent ratios to find unknown sides and angles in right-angled triangles9 min answer →
- How do we find the volume and surface area of cuboids, prisms and cylinders?Calculate the volume and surface area of cuboids, prisms and cylinders, and solve problems involving capacity8 min answer →
Number and Algebra
Module overview →- How do we simplify algebraic expressions, expand brackets, and factorise to reveal common factors?Simplify expressions by collecting like terms, expand single and double brackets, and factorise using a common factor8 min answer →
- How do we work confidently with whole numbers, fractions and decimals using the four operations and the correct order?Carry out the four operations on integers, fractions and decimals, apply the order of operations, and round answers sensibly8 min answer →
- How do we calculate percentages, percentage change, and everyday money problems such as discounts and simple interest?Find a percentage of a quantity, express one quantity as a percentage of another, calculate percentage change, and solve money problems including discount, profit and simple interest8 min answer →
- How do we compare quantities with ratio, work with rates, and solve direct proportion problems?Express and simplify ratios, divide a quantity in a given ratio, work with rates, and solve direct proportion problems8 min answer →
Statistics and Probability
Module overview →- What do the mean, median and mode each measure, and how do we calculate them?Calculate the mean, median and mode of a set of data, find the range, and choose an appropriate average8 min answer →
- How do we measure how likely an event is, and how do we calculate the probability of a single event?Find the probability of a single event as a fraction, decimal or percentage, and use the fact that probabilities sum to one8 min answer →
- How do we organise data and choose the right statistical diagram to display it?Organise data into tables and display it using bar charts, pictograms and pie charts, and read information from such diagrams8 min answer →