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 →- How do we work with the equation of a straight line in the coordinate plane?Find the equation of a straight line from given conditions, and use gradients to test for parallel and perpendicular lines8 min answer →
- How do we find the length, midpoint and gradient of a line segment between two points?Calculate the distance between two points, the midpoint of a segment, and the gradient, and apply them to geometric problems8 min answer →
- How do position vectors and the route method let us prove geometric facts?Use position vectors and the relationship between points to express vectors, and apply parallel and ratio properties in geometry9 min answer →
- What is a vector, and how do we add, subtract and scale vectors in two dimensions?Represent vectors in column form, add and subtract them and multiply by a scalar, and find the magnitude of a vector8 min answer →
Equations and Inequalities
Module overview →- How do we solve linear equations and pairs of simultaneous linear equations?Solve linear equations in one unknown, including those with fractions, and solve simultaneous linear equations by substitution and elimination8 min answer →
- How do we solve linear inequalities and represent the solution set?Solve linear inequalities in one variable, represent solutions on a number line, and find integer values that satisfy an inequality7 min answer →
- How do we solve quadratic equations by factorisation, and what do the solutions mean?Solve quadratic equations by factorisation and interpret the solutions, including equations that must first be rearranged into standard form8 min answer →
- How do we solve quadratics that do not factorise, using the formula and completing the square?Solve quadratic equations using the quadratic formula and by completing the square, and express a quadratic in completed-square form9 min answer →
- How do we turn a worded situation into equations and solve it?Formulate linear and quadratic equations from worded problems, solve them, and interpret the solution in context8 min answer →
Functions and Graphs
Module overview →- What do the gradient and the area under a travel graph tell us about motion?Interpret distance-time and speed-time graphs, using the gradient and the area under the graph to find speed, acceleration and distance8 min answer →
- How do we use graphs to solve equations, and how do we read solutions off a curve?Solve equations graphically by finding intersection points, and estimate solutions and gradients from a drawn curve8 min answer →
- How do we recognise and sketch the standard non-linear graphs in the syllabus?Recognise and sketch graphs of cubic, reciprocal and exponential functions, and describe their main features8 min answer →
- What does the equation of a straight line tell us, and how do we find it?Interpret and use the equation y = mx + c, find the gradient and intercept, and determine the equation of a straight line8 min answer →
- What does the graph of a quadratic function look like, and how do we find its key features?Sketch the graph of a quadratic function, find the intercepts and the turning point, and use the line of symmetry9 min answer →
Geometry and Properties of Circles
Module overview →- What angle rules govern lines, triangles and polygons, and how do we use them?Apply angle properties of parallel lines, triangles and polygons, including interior and exterior angle sums, to find unknown angles8 min answer →
- What angle relationships hold inside a circle, and how do tangents and chords behave?Apply the circle theorems relating angles at the centre and circumference, angles in a semicircle and the same segment, cyclic quadrilaterals, and tangent properties10 min answer →
- When are two figures congruent or similar, and how do scale factors work?Identify congruent and similar figures, apply the conditions for congruence and similarity, and use scale factors for lengths, areas and volumes9 min answer →
- How do we construct accurate figures and describe the set of points satisfying a condition?Construct triangles, angle bisectors and perpendicular bisectors with compasses, and describe and draw simple loci8 min answer →
- How does Pythagoras theorem relate the sides of a right-angled triangle?Apply Pythagoras theorem to find an unknown side in a right-angled triangle and to test whether a triangle is right-angled7 min answer →
Mensuration and Trigonometry
Module overview →- How do we find the length of an arc and the area of a sector of a circle?Calculate arc length and sector area as fractions of a circle, and find the perimeter and area of segments8 min answer →
- How do we find the area and perimeter of standard plane figures and composite shapes?Calculate the perimeter and area of triangles, quadrilaterals and circles, and of composite plane figures8 min answer →
- How do we find sides and angles in triangles that are not right-angled?Apply the sine rule and the cosine rule to find sides and angles in any triangle, and find the area using the sine formula9 min answer →
- How do the sine, cosine and tangent ratios let us find sides and angles in right-angled triangles?Use sine, cosine and tangent to find unknown sides and angles in right-angled triangles, including angles of elevation and depression9 min answer →
- How do we find the volume and surface area of prisms, cylinders, cones, pyramids and spheres?Calculate the volume and surface area of prisms, cylinders, pyramids, cones and spheres, and of composite solids9 min answer →
Number and Algebra
Module overview →- How do we expand, factorise and simplify algebraic expressions reliably?Expand products, factorise expressions including quadratics and the difference of two squares, and simplify algebraic fractions9 min answer →
- How do the laws of indices work, and how do we write very large or small numbers in standard form?Apply the laws of indices including zero, negative and fractional powers, and express and calculate with numbers in standard form8 min answer →
- How do we work confidently with integers, fractions, decimals and the order of operations?Carry out the four operations on integers, fractions and decimals, apply the order of operations, and use approximation and estimation8 min answer →
- How do we calculate with percentages and apply them to money problems?Calculate percentages, percentage change and reverse percentages, and apply them to profit, loss, discount, taxation and simple and compound interest9 min answer →
- How do we compare quantities using ratio, and handle direct and inverse proportion?Use ratio to share and compare quantities, work with rates, and solve problems involving direct and inverse proportion8 min answer →
Statistics and Probability
Module overview →- How do we summarise data with an average and describe how spread out it is?Calculate the mean, median and mode, including from frequency tables, and find the range as a measure of spread8 min answer →
- How do we use a cumulative frequency curve to find the median, quartiles and spread?Construct a cumulative frequency curve and use it to estimate the median, quartiles, interquartile range and percentiles9 min answer →
- How do we organise and display data, and read information from statistical diagrams?Construct and interpret bar charts, pie charts, line graphs, histograms and stem-and-leaf diagrams, and choose an appropriate display8 min answer →
- How do we calculate the probability of single events and of combined events?Calculate the probability of single events, and of combined events using the addition and multiplication rules with tree diagrams9 min answer →