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Singapore · SEABSyllabus
Additional Mathematics syllabus, dot point by dot point
Every dot point in the Singapore Additional Mathematicssyllabus, 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.
Algebra: Surds, Indices and Polynomials
Module overview →- What are the laws of indices, and how do we use them to simplify expressions and solve index equations?State and apply the laws of indices, including zero, negative and fractional indices, to simplify expressions and solve simple index equations8 min answer →
- How do the remainder and factor theorems let us find remainders and factors of a polynomial without long division?Apply the remainder theorem and the factor theorem to find remainders, test for factors, and factorise a cubic polynomial9 min answer →
- How do we simplify surds and rewrite a fraction so that there is no surd in the denominator?Simplify surds, perform the four operations with surds, and rationalise denominators of the form a over root b and a over (b plus root c)8 min answer →
Binomial Theorem and Partial Fractions
Module overview →- How do we find one specific term, such as the term in x cubed, in a binomial expansion without writing out the whole thing?Find a specific term or coefficient in a binomial expansion using the general term formula8 min answer →
- How do we split a single algebraic fraction into the sum of simpler fractions?Express a proper algebraic fraction with linear factors in the denominator as a sum of partial fractions8 min answer →
- How does the binomial theorem let us expand a power of a bracket like (a plus b) to the n without multiplying it out by hand?Use the binomial theorem to expand (a plus b) to the power n for a positive integer n, using binomial coefficients8 min answer →
Coordinate Geometry and Circles
Module overview →- How do we find the gradient, length and midpoint of a line segment and write the equation of a straight line?Find the gradient, length and midpoint of a line segment, and find the equation of a straight line through given points8 min answer →
- How do the gradients of parallel and perpendicular lines relate, and how do we use this to find their equations?Use the gradient conditions for parallel and perpendicular lines to find equations of lines and solve geometry problems8 min answer →
- How do we write the equation of a circle and find its centre and radius?Write the equation of a circle given the centre and radius, and find the centre and radius from a general equation by completing the square8 min answer →
Differentiation
Module overview →- What is differentiation, and how do the power, chain, product and quotient rules let us find a derivative?Differentiate powers of x and use the power, chain, product and quotient rules to find derivatives9 min answer →
- How do we find the stationary points of a curve and decide whether each is a maximum or a minimum?Find stationary points by setting the derivative to zero and determine their nature using the second derivative or a sign test9 min answer →
- How do we find the equation of the tangent and the normal to a curve at a given point?Use the derivative to find the gradient of a curve at a point and write the equations of the tangent and normal there8 min answer →
Integration
Module overview →- How do we use a definite integral to find the area between a curve and the x-axis?Find the area of a region bounded by a curve and the x-axis using a definite integral, handling regions below the axis8 min answer →
- How do we evaluate a definite integral using limits, and what does the answer mean?Evaluate a definite integral by integrating and substituting the upper and lower limits8 min answer →
- What is integration, and how do we reverse the power rule to find an indefinite integral?Integrate powers of x by reversing the power rule, including the constant of integration, and integrate simple sums8 min answer →
Kinematics
Module overview →- How do we use differentiation to find velocity and acceleration from a displacement function?Differentiate a displacement function to find velocity, and differentiate velocity to find acceleration, and find when a particle is at rest8 min answer →
- What do displacement, velocity and acceleration mean, and how are they connected?Define displacement, velocity and acceleration for motion in a straight line and interpret their signs8 min answer →
- How do we use integration to recover velocity from acceleration, and displacement from velocity?Integrate acceleration to find velocity and integrate velocity to find displacement, using initial conditions to find the constant8 min answer →
Logarithmic and Exponential Functions
Module overview →- How do we solve equations where the unknown is in the exponent, or inside a logarithm?Solve exponential equations by taking logarithms, and solve logarithmic equations using the definition and laws of logarithms8 min answer →
- What do the graphs of exponential and logarithmic functions look like, and how are they related?Sketch graphs of exponential and logarithmic functions, identify their key features, and recognise them as reflections of each other8 min answer →
- What are logarithms, and how do the laws of logarithms let us combine and simplify log expressions?Define a logarithm as the inverse of a power, and use the product, quotient and power laws of logarithms to simplify expressions8 min answer →
Quadratic Functions and Equations
Module overview →- How do we turn a quadratic into completed-square form to read off its turning point and sketch its graph?Express a quadratic in completed-square form, identify the turning point and line of symmetry, and use these to sketch the parabola8 min answer →
- How do we solve a quadratic inequality and write the solution as a range of values of x?Solve quadratic inequalities by factorising and using a sketch or number line, and express the solution set correctly8 min answer →
- How does the discriminant tell us how many real roots a quadratic equation has, without solving it?Use the discriminant b squared minus 4ac to determine the nature of the roots of a quadratic equation and apply it to find unknown constants8 min answer →
Trigonometry and Identities
Module overview →- How do we solve a trigonometric equation and find all the angles in a given range?Solve simple trigonometric equations within a stated range using the basic angle and the quadrant rule8 min answer →
- What are the basic trigonometric identities, and how do we use them to simplify or prove expressions?Use the identities tan equals sin over cos and sin squared plus cos squared equals one to simplify expressions and prove simple results8 min answer →
- How do the sine, cosine and tangent ratios extend beyond right-angled triangles using the unit circle?Define sine, cosine and tangent for any angle using the unit circle, and find exact values and signs in each quadrant8 min answer →