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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
- Apply the laws of indices to simplify expressions involving positive, negative, zero and fractional powers and to solve simple exponential equations5Q&A pairs
- Use the remainder theorem to find the remainder on division by a linear factor and the factor theorem to identify and extract factors of a polynomial9Q&A pairs
- Solve cubic and higher polynomial equations by factorising fully and applying the zero-product principle to find all real roots5Q&A pairs
- Simplify surds, perform the four operations on surds, and rationalise denominators including those of the form a plus root b4Q&A pairs
Binomial Theorem and Partial Fractions
- Expand expressions of the form a plus b to the power n for a positive integer n using the binomial theorem and binomial coefficients7Q&A pairs
- Use the general term of a binomial expansion to find a specified term, the coefficient of a given power, or the term independent of x8Q&A pairs
- Express a proper rational fraction with distinct linear factors in the denominator as a sum of partial fractions7Q&A pairs
- Express proper fractions with repeated linear factors or an irreducible quadratic factor as partial fractions, choosing the correct numerator forms6Q&A pairs
Coordinate Geometry and Circles
- Find the area of a triangle or polygon from the coordinates of its vertices using the shoelace determinant method7Q&A pairs
- Find the gradient, length and midpoint of a line segment, write the equation of a line, and use the conditions for parallel and perpendicular lines9Q&A pairs
- Write the equation of a circle in standard and general form and find the centre and radius by completing the square6Q&A pairs
- Find the intersection of a line and a circle, determine tangency using the discriminant or perpendicular radius, and find tangent equations7Q&A pairs
Differentiation and Its Applications
- Interpret the derivative as a gradient and rate of change, and differentiate powers of x and the standard exponential, logarithmic and trigonometric functions5Q&A pairs
- Apply the product, quotient and chain rules, individually and in combination, to differentiate products, quotients and composite functions7Q&A pairs
- Use the chain rule to relate connected rates of change, finding one rate from another for two quantities linked by an equation7Q&A pairs
- Find stationary points by setting the first derivative to zero and determine their nature using the first or second derivative test7Q&A pairs
- Use the derivative as the gradient to find the equations of the tangent and the normal to a curve at a given point9Q&A pairs
Integration and Its Applications
- Find the area enclosed between two curves, or a curve and a line, by integrating the difference of the upper and lower functions between their intersection points8Q&A pairs
- Evaluate definite integrals using limits and use them to find the area of a region bounded by a curve and the x-axis11Q&A pairs
- Integrate powers of x and standard functions as the reverse of differentiation, including the constant of integration, and integrate linear composites8Q&A pairs
- Integrate the exponential, reciprocal and trigonometric functions and their linear composites as the reverse of the corresponding derivatives6Q&A pairs
Kinematics
- Solve kinematics problems involving maximum or minimum displacement and velocity, total distance travelled, and changes of direction4Q&A pairs
- Define displacement, velocity and acceleration for motion in a straight line and interpret their signs and the graphs that connect them4Q&A pairs
- Differentiate to pass from displacement to velocity to acceleration, and integrate to reverse the process, fixing constants from initial conditions7Q&A pairs
Logarithmic and Exponential Functions
- Solve exponential equations by taking logarithms and logarithmic equations by converting to index form, rejecting invalid solutions5Q&A pairs
- Sketch the graphs of exponential and logarithmic functions, identify their key features, and recognise them as reflections of each other6Q&A pairs
- State and apply the product, quotient and power laws of logarithms and the change-of-base relationship to simplify and evaluate expressions9Q&A pairs
- Transform a non-linear relationship into the form Y equals mX plus c and use the gradient and intercept of the straight-line graph to find unknown constants6Q&A pairs
Quadratic Functions and Equations
- Use the discriminant b squared minus 4ac to determine whether a quadratic has two, one or no real roots and to solve related problems5Q&A pairs
- Solve equations reducible to quadratic form by a suitable substitution, including equations in powers, surds and exponentials7Q&A pairs
- Express a quadratic in completed-square form and use it to find the vertex, the maximum or minimum value, and the line of symmetry8Q&A pairs
- Solve quadratic inequalities by factorising and reasoning about the sign of the quadratic between and beyond its roots4Q&A pairs
Trigonometry and Identities
- Apply the addition formulae for sine, cosine and tangent and the double angle formulae to expand, simplify and evaluate trigonometric expressions7Q&A pairs
- Express a sine plus cosine as a single R sine or R cosine function and use it to find maximum and minimum values and to solve equations6Q&A pairs
- Solve trigonometric equations within a stated interval, finding the basic angle and using symmetry to obtain every solution7Q&A pairs
- State and use the Pythagorean, reciprocal and quotient identities to simplify expressions and prove trigonometric identities6Q&A pairs
- Define sine, cosine and tangent for any angle using the unit circle, determine signs by quadrant, and use reference angles and special angles6Q&A pairs