100+ Free Wales L2 Additional Maths Practice Questions

Unit 1 Algebra (mandatory, non-calculator)

Surds and index laws (including fractional and negative indices), algebraic proof with ≡ notation, solving quadratics by factorising or completing the square (leading coefficient ≤ 1 for CTS), applications, linear–quadratic simultaneous equations, discriminant and root conditions, quadratic graphs, arithmetic and geometric sequences and series (sum to n terms; sum to infinity not required).

Unit 2 Calculus (mandatory, calculator allowed)

Differentiation of polynomials for integer powers, second derivatives, locating and classifying stationary points (max/min; points of inflection not required), tangent equations, reverse of differentiation, definite integrals of polynomials, and area between a curve and the x-axis where the curve does not cross the axis in the interval.

Unit 3 Geometry and Trigonometry

Straight-line equations, parallel and perpendicular conditions, midpoint, Pythagoras and circle equation (x − a)² + (y − b)² = r², circle touch conditions, trig graphs and identities tan θ ≡ sin θ/cos θ and sin²θ + cos²θ ≡ 1, solving simple trig equations in a given interval, sine rule, cosine rule, and area (1/2)ab sin C including the ambiguous case.

Unit 4 Statistics

Addition law for mutually exclusive events, multiplication law for independent events, Venn diagrams and the general addition law, mean/median/mode, range, IQR, variance and standard deviation (listed, frequency and grouped data), box plots, cumulative frequency, histograms, skewness, scatter and regression interpretation (coefficients not calculated), and discrete random variables (mean and variance).

Unit 5 Mechanics

Scalar versus vector quantities, contact and non-contact forces including weight, free-body diagrams, resultant and equilibrium forces in one dimension, Newton’s three laws and F = ma, constant-acceleration suvat equations, vertical motion under g = 9.8 m/s², and interpretation of displacement–time and velocity–time graphs.

Unit 6 Discrete and Decision Mathematics

Graph/network vocabulary (degree, path, cycle, tree, MST, etc.), Eulerian and semi-Eulerian graphs, algorithms and flow charts, bubble sort and quick sort, Kruskal’s and Prim’s algorithms for MSTs, Dijkstra’s algorithm for shortest paths, activity-on-arc critical path analysis (early/late times, float; dummies may appear but constructing dummies is limited), and two-variable linear programming with graphical or vertex methods (integer solutions where required).