← Maths syllabus

Northern IrelandMaths

AS 1 Pure Mathematics

8 dot points across 8 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do indices, surds, quadratics and polynomials let us manipulate and solve algebraic expressions?

The laws of indices and surds, completing the square and the quadratic formula, the discriminant, simultaneous equations, inequalities, and polynomial manipulation including the factor and remainder theorems.
A CCEA A-Level Mathematics answer on the laws of indices and surds, solving quadratics by factorising, completing the square and the formula, the discriminant, simultaneous and quadratic inequalities, and polynomial division with the factor and remainder theorems.
13 min answer →

How do equations describe straight lines, circles and the shapes of common graphs?

The equation of a straight line and conditions for parallel and perpendicular lines, the equation of a circle and its key properties, and sketching and transforming standard curves.
A CCEA A-Level Mathematics answer on the equation of a straight line, gradients of parallel and perpendicular lines, the equation of a circle and its tangent and chord properties, and sketching and transforming standard curves.
13 min answer →

How does differentiation measure the gradient of a curve and locate its turning points?

Differentiation from first principles, differentiating powers of $x$ , the gradient of a curve, tangents and normals, increasing and decreasing functions, and locating and classifying stationary points.
A CCEA A-Level Mathematics answer on differentiation from first principles, differentiating powers of x, finding the gradient of a curve, equations of tangents and normals, increasing and decreasing functions, and locating and classifying stationary points with the second derivative.
13 min answer →

How do exponential functions and logarithms describe growth and let us solve equations with the variable in the power?

Exponential functions and the number $e$ , the laws of logarithms and the relationship between exponentials and logarithms, solving equations of the form $a^x = b$ , and using logarithms to linearise data.
A CCEA A-Level Mathematics answer on exponential functions and the number e, the laws of logarithms, the inverse relationship between exponentials and logarithms, solving equations of the form a to the x equals b, and using logarithms to linearise exponential and power data.
13 min answer →

How does integration reverse differentiation and let us find areas under curves?

Integration as the reverse of differentiation, indefinite integrals with a constant of integration, the definite integral and its evaluation, and finding the area under a curve.
A CCEA A-Level Mathematics answer on integration as the reverse of differentiation, indefinite integrals of powers of x with the constant of integration, evaluating definite integrals, and finding the area between a curve and the x-axis including regions below the axis.
12 min answer →

How does the binomial theorem expand powers of a bracket, and how are series described and summed?

The binomial expansion of $(a + b)^n$ for positive integer $n$ using binomial coefficients, and sequences and series described by sigma notation and recurrence.
A CCEA A-Level Mathematics answer on the binomial expansion of bracket powers for positive integer n, binomial coefficients and Pascal's triangle, finding a specific term, and describing sequences and series with sigma notation and recurrence relations.
12 min answer →

How do trigonometric ratios, identities and graphs let us model and solve angle problems?

The trigonometric ratios and their graphs, the sine and cosine rules and the area of a triangle, the identities $\sin^2\theta + \cos^2\theta = 1$ and $\tan\theta = \sin\theta/\cos\theta$ , and solving trigonometric equations.
A CCEA A-Level Mathematics answer on the trigonometric ratios and their graphs, the sine and cosine rules and the area of a triangle, the Pythagorean identity, and solving trigonometric equations over a given interval.
13 min answer →

How do vectors represent quantities with magnitude and direction in two dimensions?

Two-dimensional vectors in component and unit-vector form, the magnitude and direction of a vector, addition and scalar multiplication, position vectors, and using vectors in geometric problems.
A CCEA A-Level Mathematics answer on two-dimensional vectors in component and unit-vector form, finding magnitude and direction, vector addition and scalar multiplication, position vectors and displacement, and applying vectors to geometric problems.
12 min answer →