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AS Unit 1 Pure Mathematics A

9 dot points across 9 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we manipulate surds, indices, quadratics, polynomials and inequalities, and transform graphs?

Surds and indices, quadratic functions and the discriminant, simultaneous equations, inequalities, polynomial division and the factor theorem, and graph transformations.
A focused answer to WJEC AS Unit 1 algebra and functions, covering surds and indices, quadratics and the discriminant, simultaneous equations and inequalities, polynomials and the factor theorem, and graph transformations.
13 min answer →

How do we describe straight lines and circles algebraically and find where they meet?

Equations of straight lines, parallel and perpendicular gradients, the equation of a circle, tangents and chords, and intersections of lines and curves.
A focused answer to WJEC AS Unit 1 coordinate geometry, covering the equation of a straight line, parallel and perpendicular gradients, the equation of a circle, tangents and chords, and finding intersections.
12 min answer →

How do we find the gradient of a curve at a point, and use it to locate tangents and turning points?

Differentiation from first principles, differentiating powers of $x$ , gradients, tangents and normals, increasing and decreasing functions, and stationary points.
A focused answer to WJEC AS Unit 1 differentiation, covering differentiation from first principles, the power rule, tangents and normals, increasing and decreasing functions, and finding and classifying stationary points.
13 min answer →

How do exponential and logarithmic functions behave, and how do we use logs to solve equations and model growth?

The exponential function and $\mathrm{e}^x$ , logarithms and their laws, solving equations with logs, and fitting exponential models with a log-linear graph.
A focused answer to WJEC AS Unit 1 exponentials and logarithms, covering the exponential function $\mathrm{e}^x$ , the laws of logarithms, solving exponential equations, and using log-linear graphs to fit exponential models.
12 min answer →

How do we reverse differentiation, and use the definite integral to find the area under a curve?

Integration as the reverse of differentiation, indefinite integrals with a constant, definite integrals and the limits, and the area under a curve.
A focused answer to WJEC AS Unit 1 integration, covering integration as the reverse of differentiation, indefinite integrals and the constant of integration, definite integrals with limits, and finding the area between a curve and the axis.
12 min answer →

How do we prove a mathematical statement rigorously, and how do we show one is false?

Proof by deduction, proof by exhaustion, and disproof by counterexample, with the language and structure WJEC rewards.
A focused answer to WJEC AS Unit 1 proof, covering proof by deduction, proof by exhaustion, disproof by counterexample, and the precise logical language examiners expect in a structured argument.
11 min answer →

How do we expand a bracket raised to a positive integer power without multiplying it out term by term?

The binomial expansion of $(a+b)^n$ for positive integer $n$ , binomial coefficients and Pascal's triangle, and finding a specified term.
A focused answer to WJEC AS Unit 1 sequences and series, covering the binomial expansion of $(a+b)^n$ for positive integer $n$ , binomial coefficients and Pascal's triangle, and finding a specified term of an expansion.
11 min answer →

How do we work with trig graphs, identities and equations, and solve triangles that are not right-angled?

Graphs of sine, cosine and tangent, the identities $\sin^2\theta+\cos^2\theta=1$ and $\tan\theta=\sin\theta/\cos\theta$ , solving trig equations, and the sine and cosine rules.
A focused answer to WJEC AS Unit 1 trigonometry, covering the sine, cosine and tangent graphs, the Pythagorean and quotient identities, solving trigonometric equations, and the sine and cosine rules with the area formula.
13 min answer →

How do we represent and combine vectors in two dimensions, and use position vectors in geometry?

Vectors in two dimensions, magnitude and direction, addition and scalar multiplication, position vectors, and dividing a line segment in a given ratio.
A focused answer to WJEC AS Unit 1 vectors, covering two-dimensional vectors, magnitude and direction, vector addition and scalar multiplication, position vectors, and dividing a line segment in a given ratio.
11 min answer →