A-Level Maths Specification

OCR B (MEI) H640

Section 4: Graphs

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#4.1

Understand and use graphs of functions.

Graphs of functions

#4.2

Understand how to find intersection points of a curve with coordinate axes.

Including relating this to the solution of an equation.

Graphs of functions

#4.3

Understand and be able to use the method of completing the square to find the line of symmetry and turning point of the graph of a quadratic function and to sketch a quadratic curve (parabola).

The curve y = a(x + p)2 + q has
• a minimum at \((-p, q)\) for \(a > 0\) or a maximum at \((-p, q)\) for \(a < 0\)
• a line of symmetry \(x = -p\).

Quadratic functions and graphs Completing the square

#4.4

Be able to sketch and interpret the graphs of simple functions including polynomials.

Including cases of repeated roots for polynomials.

Graphs of functions

#4.5

Be able to use stationary points when curve sketching.

Including distinguishing between maximum and minimum turning points.

Graphs of functions

#4.6

Be able to sketch and interpret the graphs of \(y = \dfrac{a}{x}\) and \(y = \dfrac{a}{x^2}\).

Including their vertical and horizontal asymptotes and recognising them as graphs of proportional relationships.

Graphs of functions

#4.7

Be able to sketch curves of the forms \(y = af(x)\), \(y = f(x) + a\), \(y = f(x + a)\) and \(y = f(ax)\), given the curve of \(y = f(x)\) and describe the associated transformations.
Be able to form the equation of a graph following a single transformation.

Including working with sketches of graphs where functions are not defined algebraically.

Notation: Map(s) onto. Translation, stretch, reflection.

Transformations of graphs

#4.8

Understand the effect of combined transformations on a graph and be able to form the equation of the new graph and to sketch it. Be able to recognise the transformations that have been applied to a graph from the graph or its equation.

Notation: Vector notation may be used for a translation.
\(\begin{pmatrix} a \\ b \end{pmatrix}\), \(a\bold{i} + b\bold{j}\)

Transformations of graphs

#4.9

Be able to use stationary points of inflection when curve sketching.

Graphs of functions