Back to Singapore Additional Mathematics
Singapore · SEABQ&A
Additional MathematicsQ&A by dot point
A short Q&A bank for every Singapore Additional Mathematics syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Algebra: Surds, Indices and Polynomials
- State and apply the laws of indices, including zero, negative and fractional indices, to simplify expressions and solve simple index equations6Q&A pairs
- Apply the remainder theorem and the factor theorem to find remainders, test for factors, and factorise a cubic polynomial8Q&A pairs
- 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)9Q&A pairs
Binomial Theorem and Partial Fractions
- Find a specific term or coefficient in a binomial expansion using the general term formula7Q&A pairs
- Express a proper algebraic fraction with linear factors in the denominator as a sum of partial fractions6Q&A pairs
- Use the binomial theorem to expand (a plus b) to the power n for a positive integer n, using binomial coefficients6Q&A pairs
Coordinate Geometry and Circles
- Find the gradient, length and midpoint of a line segment, and find the equation of a straight line through given points8Q&A pairs
- Use the gradient conditions for parallel and perpendicular lines to find equations of lines and solve geometry problems8Q&A pairs
- Write the equation of a circle given the centre and radius, and find the centre and radius from a general equation by completing the square5Q&A pairs
Differentiation
- Differentiate powers of x and use the power, chain, product and quotient rules to find derivatives8Q&A pairs
- Find stationary points by setting the derivative to zero and determine their nature using the second derivative or a sign test5Q&A pairs
- Use the derivative to find the gradient of a curve at a point and write the equations of the tangent and normal there6Q&A pairs
Integration
- Find the area of a region bounded by a curve and the x-axis using a definite integral, handling regions below the axis6Q&A pairs
- Evaluate a definite integral by integrating and substituting the upper and lower limits5Q&A pairs
- Integrate powers of x by reversing the power rule, including the constant of integration, and integrate simple sums9Q&A pairs
Kinematics
- Differentiate a displacement function to find velocity, and differentiate velocity to find acceleration, and find when a particle is at rest6Q&A pairs
- Define displacement, velocity and acceleration for motion in a straight line and interpret their signs6Q&A pairs
- Integrate acceleration to find velocity and integrate velocity to find displacement, using initial conditions to find the constant8Q&A pairs
Logarithmic and Exponential Functions
- Solve exponential equations by taking logarithms, and solve logarithmic equations using the definition and laws of logarithms7Q&A pairs
- Sketch graphs of exponential and logarithmic functions, identify their key features, and recognise them as reflections of each other5Q&A pairs
- Define a logarithm as the inverse of a power, and use the product, quotient and power laws of logarithms to simplify expressions4Q&A pairs
Quadratic Functions and Equations
- Express a quadratic in completed-square form, identify the turning point and line of symmetry, and use these to sketch the parabola5Q&A pairs
- Solve quadratic inequalities by factorising and using a sketch or number line, and express the solution set correctly4Q&A pairs
- Use the discriminant b squared minus 4ac to determine the nature of the roots of a quadratic equation and apply it to find unknown constants3Q&A pairs
Trigonometry and Identities
- Solve simple trigonometric equations within a stated range using the basic angle and the quadrant rule5Q&A pairs
- Use the identities tan equals sin over cos and sin squared plus cos squared equals one to simplify expressions and prove simple results5Q&A pairs
- Define sine, cosine and tangent for any angle using the unit circle, and find exact values and signs in each quadrant8Q&A pairs