Wales · WJECQ&A
MathsQ&A by dot point
A short Q&A bank for every Wales Maths 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.
AS Unit 1 Pure Mathematics A
- Surds and indices, quadratic functions and the discriminant, simultaneous equations, inequalities, polynomial division and the factor theorem, and graph transformations.4Q&A pairs
- Equations of straight lines, parallel and perpendicular gradients, the equation of a circle, tangents and chords, and intersections of lines and curves.4Q&A pairs
- Differentiation from first principles, differentiating powers of , gradients, tangents and normals, increasing and decreasing functions, and stationary points.3Q&A pairs
- The exponential function and , logarithms and their laws, solving equations with logs, and fitting exponential models with a log-linear graph.5Q&A pairs
- Integration as the reverse of differentiation, indefinite integrals with a constant, definite integrals and the limits, and the area under a curve.4Q&A pairs
- Proof by deduction, proof by exhaustion, and disproof by counterexample, with the language and structure WJEC rewards.4Q&A pairs
- The binomial expansion of for positive integer , binomial coefficients and Pascal's triangle, and finding a specified term.3Q&A pairs
- Graphs of sine, cosine and tangent, the identities and , solving trig equations, and the sine and cosine rules.5Q&A pairs
- Vectors in two dimensions, magnitude and direction, addition and scalar multiplication, position vectors, and dividing a line segment in a given ratio.5Q&A pairs
AS Unit 2 Applied Mathematics A
- Newton's three laws, force diagrams, weight, normal reaction, tension, friction, and connected particles over a pulley.6Q&A pairs
- Quantities and units in mechanics, displacement, velocity and acceleration, motion graphs, and the constant-acceleration (suvat) equations including vertical motion under gravity.6Q&A pairs
- Probability of events, Venn diagrams and set notation, the addition rule, mutually exclusive and independent events, and tree diagrams.4Q&A pairs
- Discrete random variables and probability distributions, the binomial distribution and its conditions, and calculating binomial probabilities.4Q&A pairs
- Null and alternative hypotheses, one-tailed and two-tailed tests, the significance level, critical regions, and the binomial hypothesis test.3Q&A pairs
- Populations and samples, random and non-random sampling methods, and presenting and interpreting data with measures of location, spread, histograms and box plots.4Q&A pairs
A2 Unit 3 Pure Mathematics B
- The modulus function and its graphs and equations, composite and inverse functions, and resolving rational expressions into partial fractions.7Q&A pairs
- The chain, product and quotient rules, implicit differentiation, derivatives of exponential, logarithmic and trigonometric functions, and the second derivative and concavity.3Q&A pairs
- Integrating standard functions, integration by substitution, integration by parts, integration using partial fractions, and definite integrals for areas.5Q&A pairs
- Locating roots by change of sign, iterative methods, the Newton-Raphson method, and the trapezium rule for numerical integration.6Q&A pairs
- Parametric equations of curves, converting between parametric and Cartesian forms, and differentiating parametrically to find gradients and tangents.4Q&A pairs
- Proof by contradiction, the structure of the method, and the classic results proved this way (the irrationality of root 2, the infinitude of primes).4Q&A pairs
- Arithmetic and geometric sequences and series, sigma notation, the sum to infinity of a convergent geometric series, and the binomial expansion for any rational index.5Q&A pairs
- Radian measure, the reciprocal functions secant, cosecant and cotangent, the compound and double-angle formulae, and the harmonic form R sin(theta + alpha).5Q&A pairs
A2 Unit 4 Applied Mathematics B
- Conditional probability, the conditional probability formula, the multiplication rule, independence, and probability from two-way tables and tree diagrams.4Q&A pairs
- Forming differential equations from a rate of change, solving first-order equations by separating the variables, and applying them to growth, decay and mechanics.3Q&A pairs
- Resolving forces on inclined planes, the friction model and the coefficient of friction, connected particles, and moments and the equilibrium of rigid bodies.6Q&A pairs
- Hypothesis testing for a correlation coefficient, and hypothesis testing for the mean of a Normal distribution using the distribution of the sample mean.5Q&A pairs
- Kinematics with calculus for variable acceleration, vectors in kinematics, and projectile motion resolved into horizontal and vertical components.6Q&A pairs
- Continuous random variables and the Normal distribution, standardising to the standard Normal, finding probabilities, and the Normal approximation to the binomial.3Q&A pairs