Question 1 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2015
Session	November
Marks	2
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Curve Sketching
Type	Sketch rational function from transformation
Difficulty	Easy -1.2 This is a straightforward transformation of the exponential function y = e^(ax), requiring only a vertical translation downward by 1 unit. Students need to identify the y-intercept (0,0), horizontal asymptote (y = -1), and general exponential shape—all routine skills with minimal problem-solving required.
Spec	1.06a Exponential function: a^x and e^x graphs and properties

1 Sketch the graph of \(y = \mathrm { e } ^ { a x } - 1\) where \(a\) is a positive constant.

Answer	Marks	Guidance
Draw curve with increasing gradient existing for negative and positive values of \(x\)	M1
Draw correct curve passing through the origin	A1	[2]

Draw curve with increasing gradient existing for negative and positive values of $x$ | M1 |
Draw correct curve passing through the origin | A1 | [2]

1 Sketch the graph of $y = \mathrm { e } ^ { a x } - 1$ where $a$ is a positive constant.

\hfill \mbox{\textit{CAIE P3 2015 Q1 [2]}}