The document consists of practice questions for logarithmic and exponential functions as part of the CIE IGCSE Additional Mathematics curriculum from 2016-2020. It includes various mathematical modeling problems, population growth calculations, and logarithmic expressions to simplify. The exercises focus on applications of logarithmic identities and the manipulation of exponential functions.

1. TOPIC 7:
LOGARITHMIC AND
EXPONENTIAL FUNCTIONS
CIE IGCSE ADDITIONAL MATHEMATICS
(0606)
TOPICAL PRACTICE QUESTIONS
Paper 1
Variants 1, 2 and 3
2016- 2020
Compiled from:
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2. © UCLES 2018
1 The population, P, of a certain bacterium t days after the start of an experiment is modelled by
P = 800ekt, where k is a constant.
(i) State what the figure 800 represents in this experiment. [1]
(ii) Given that the population is 20000 two days after the start of the experiment, calculate the value
of k. [3]
(iii) Calculate the population three days after the start of the experiment. [2]
Source: 0606/11/M/J/18 - Question No. 5 Page 1
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3. © UCLES 2018
2 (a) Write log log log
p q
2
2 3 3
+
^ ^
h h as a single logarithm to base 3. [3]
(b) Given that log log
5 4 5 3 0
a a
2 - + =
^ h , find the possible values of a. [3]
Source: 0606/11/M/J/18 - Question No. 6 Page 2
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4. © UCLES 2019
3 (a) Solve log log
x x 12
3 9
+ = . [3]
(b) Solve ( ) (
log log
y
3 10 2
2
1
4
2
4
- = )
y 1
- + . [5]
Source: 0606/11/M/J/19 - Question No. 7 Page 3
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5. © UCLES 2016
2 Given that
( )
p qr
p q r
p q r
a b c
5
3
2
3
1
2
1
2
3
=
-
-
, find the value of each of the integers a, b and c. [3]
4 By using the substitution log
y x
3
= , or otherwise, find the values of x for which
( )
log log log
x x
3 9 0
3
2
3
5
3
+ - = . [6]
Source: 0606/11/O/N/16 - Question No. 3 Page 4
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6. © UCLES 2018
5 (a) Express lg lg
x y
2 3
+ - as a single logarithm to base 10. [3]
(b) (i) Solve x
x
6 7
3
0
+ - = . [2]
(ii) Hence, given that log log a
6 3 7 3 0
a 3
+ - = , find the possible values of a. [4]
Source: 0606/11/O/N/18 - Question No. 7 Page 5
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7. © UCLES 2018
6 A population, B, of a particular bacterium, t hours after measurements began, is given by B 1000e
t
4
= .
(i) Find the value of B when t = 0. [1]
(ii) Find the time taken for B to double in size. [3]
(iii) Find the value of B when t = 8. [1]
Source: 0606/12/M/J/18 - Question No. 7 Page 6
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8. © UCLES 2018
7 (a) (i) Solve lgx 3
= . [1]
(ii) Write lg lg
a b
2 3
- + as a single logarithm. [3]
(b) (i) Solve x
x
5
6
0
- + = . [2]
(ii) Hence, showing all your working, find the values of a such that log log
a 5 6 4 0
a
4
- + = .
[3]
Source: 0606/12/M/J/18 - Question No. 9 Page 7
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9. © UCLES 2019
8 The number, B, of a certain type of bacteria at time t days can be described by B 200 800
e e
t t
2 2
= + -
.
(i) Find the value of B when t 0
= . [1]
Source: 0606/12/M/J/19 - Question No. 3 Page 8
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10. © UCLES 2018
9 The population, P, of a certain bacterium t days after the start of an experiment is modelled by
P = 800ekt, where k is a constant.
(i) State what the figure 800 represents in this experiment. [1]
(ii) Given that the population is 20000 two days after the start of the experiment, calculate the value
of k. [3]
(iii) Calculate the population three days after the start of the experiment. [2]
Source: 0606/13/M/J/18 - Question No. 5 Page 9
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11. © UCLES 2018
10 (a) Write log log log
p q
2
2 3 3
+
^ ^
h h as a single logarithm to base 3. [3]
(b) Given that log log
5 4 5 3 0
a a
2 - + =
^ h , find the possible values of a. [3]
Source: 0606/13/M/J/18 - Question No. 6 Page 10
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12. © UCLES 2020
11 (a) Given that log log
x y
2 8
2 4
+ = , find the value of xy. [3]
(b) Using the substitution y 2x
= , or otherwise, solve 2 2 2 1 0
x x x
2 1 1
- - + =
+ +
. [4]
Source: 0606/13/M/J/20 - Question No. 2 Page 11
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13. © UCLES 2016
12 (i) Given that log xy
2
5
9
= , show that log log
x y 5
3 3
+ = . [3]
(ii) Hence solve the equations
log xy
2
5
9
= ,
log log
x y 6
3 3
# =- . [5]
Source: 0606/13/O/N/16 - Question No. 5 Page 12
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14. © UCLES 2018
13 (i) Show that log log
4 2
9 3
= . [2]
(ii) Hence solve log log x
4 3
9 3
+ = . [3]
Source: 0606/13/O/N/18 - Question No. 5 Page 13
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15. © UCLES 2019
14 (a) Given that log x p
a
= and ,
log y q
a
= find, in terms of p and q,
(i) ,
log axy
a
2
[2]
(ii) log
ay
x
a
3
e o, [2]
(iii) .
log log
a a
x y
+ [1]
(b) Using the substitution ,
m 3x
= or otherwise, solve .
3 3 4 0
x x
1 2
- + =
+
[3]
Source: 0606/13/O/N/19 - Question No. 8 Page 14
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