Edexcel IAL Mathematics P1.1.11 graphs of functions

Graph questions often pair a sketch with algebra: label intercepts or asymptotes, solve curve intersections and give exact coordinates in surd form.

Exam points

Sketch reciprocal, cubic or transformed curves with intercepts and asymptotes labelled.
Equate two function rules and solve exactly to find intersection coordinates.
Use graph shape and algebra to decide when a line meets a curve once or twice.

[Maximum number: 2]

Sketch the curve with equation

y=-\frac{k}{x} \quad k>0 \quad x \neq 0

M1 Negative reciprocal shape (top left/bottom right sections) in any position on a set of axes with no clear vertical or horizontal 'overlaps'.

A1 Correct sketch appearing in quadrants 2 and 4 only. Condone slips of the pen at the ends as long as the graph does not curve back on itself. Ignore any scaling on the axes.

Figure for Answer to Question P1.1.11 - Graphs of functions question 1 — Edexcel A-Level Mathematics AS

This scores M1A1. We condone these as they are not clear turning points and are regarded as slips of the pen.
(b) Note on EPEN it is M1B1A1. We are marking this B1ftB1B1

B1ft For attempting to translate their graph from part (a) up (or a correct graph if (a) is incorrect)

B1 For a correct intercept stated (or allow $1, \frac{k}{k}$ or (1,0) marked on the correct axis with the curve passing through this) OR y=k stated. Do not allow just k to be marked on the line of the asymptote.

B1 For a correct intercept stated (or allow $1, \frac{k}{k}$ or (1,0) marked on the correct axis with the curve passing through this) AND y=k stated. Do not allow just k to be marked on the line of the asymptote.

Note if they have a contradiction between what is stated and what is written on the graph then the graph takes precedence.

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P1.1.11 - Graphs of functions question 1