Additional Mathematics study guides

An N(A)-Level Additional Mathematics (4051) overview of the surds, indices and polynomials outcomes in the Algebra strand. How the laws of indices simplify powers and solve index equations, how to simplify and rationalise surds, and how the remainder and factor theorems find remainders and factorise a cubic, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of coordinate geometry and circles in the Geometry and Trigonometry strand. How to find the gradient, length, midpoint and equation of a line, the gradient conditions for parallel and perpendicular lines, and the equation of a circle with its centre and radius, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of differentiation in the Calculus strand. How the derivative as a gradient leads to the power, chain, product and quotient rules, then to tangents and normals, and to stationary points and deciding their nature, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of integration in the Calculus strand. How integration reverses the power rule, why the constant of integration matters, how to evaluate a definite integral by substituting limits, and how to find the area under a curve including regions below the axis, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of kinematics in the Calculus strand. The meanings and signs of displacement, velocity and acceleration in straight-line motion, how differentiation steps down from displacement to velocity to acceleration, and how integration steps back up using initial conditions, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of logarithmic and exponential functions in the Algebra strand. The definition of a logarithm as the inverse of a power, the product, quotient and power laws, the shapes and symmetry of the graphs, and how to solve exponential and logarithmic equations, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of quadratic functions and equations in the Algebra strand. How completing the square reveals the turning point and lets you sketch the parabola, how the discriminant decides the nature of the roots, and how to solve quadratic inequalities, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of the binomial theorem and partial fractions in the Algebra strand. How to expand a power of a bracket using binomial coefficients, how the general term picks out a specific term or coefficient, and how to split a proper algebraic fraction with linear factors, with links to every dot point.

An N(A)-Level Additional Mathematics (4051) overview of trigonometry and identities in the Geometry and Trigonometry strand. The unit-circle definitions of sine, cosine and tangent and their signs in each quadrant, the quotient and Pythagorean identities, and how to solve trigonometric equations within a stated range using the basic angle, with links to every dot point.