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Edexcel A-Level Mathematics AS P2.5 Exponentials and Logarithms Questions

Practise exponential graphs, logarithm laws and log-based equation solving, from sketch features to exact and decimal answers.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • sketch exponential curves, showing intercepts and horizontal asymptotes
  • use log laws to turn logarithmic equations into algebraic equations
  • take logarithms to solve exponential models and interpret constants in context

Covered syllabus points

P2.5.1 - y = ax and its graphP2.5.2 - Laws of logarithmsP2.5.3 - Solving equations using logarithms

Question 1

[Maximum number: 3]

Sketch the curve with equation

y=a−x+4y=a^{-x}+4

where a is a constant and a>1
On your sketch show
- the coordinates of the point of intersection of the curve with the y-axis
- the equation of the asymptote to the curve.

Question 2

[Maximum number: 6]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

Question (a)

(a)

Using the laws of logarithms, solve

2log⁡2(2−x)=4+log⁡2(x+10)2 \log _{2}(2-x)=4+\log _{2}(x+10)
[ 5 ]

Question (b)

(b)

Find the value of

log⁡aa6\log _{\sqrt{a}} a^{6}

where a is a positive constant greater than 1

[ 1 ]

Question 3

[Maximum number: 2]
Figure 1

Figure 1

\section*{In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.}

Figure 1 shows a sketch of the curve with equation y=3×2−xy=3 \times 2^{-x}
The point P(k, 300000) lies on the curve.

Use logarithms to find the value of k to 2 decimal places.

Table for Question 3 — Edexcel A-Level Mathematics AS

The table shows corresponding values of x and y for y=3×2−xy=3 \times 2^{-x}
The values of y are given to 3 decimal places where appropriate.

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