Logs/Exp Past Papers Unit 3 Outcome 3 - Mathsrevision.com

Higher Mathematics
PSfrag replacements
O
x
y
Logs/Exp Past Papers Unit 3 Outcome 3
Multiple Choice Questions
Each correct answer in this section is worth two marks.
1. Solve log b
x − log b
7 = log b
3 for
x > 0.
A. x = 21
B. x = 10
C. x = 7 3
D. x = 3 7
[END OF MULTIPLE CHOICE QUESTIONS]
Written Questions
[SQA] 2. Evaluate log 5
2 + log 5
50 − log 5
4. 3
[SQA] 3. Given x = log 5
3 + log 5
4, find algebraically the value of x. 4
[SQA] 4. Find x if 4 log x
6 − 2 log x
4 = 1. 3
[SQA]
5.
Find the x-coordinate of the point where the graph of the curve with equation
y = log 3
(x − 2) + 1 intersects the x-axis. 3
[SQA]
6.
rag replacements
O
x
y
replacements
O
x
y hsn.uk.net
Page 1
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
7.
rag replacements
O
x
y
[SQA]
8.
rag replacements
O
x
y
[SQA]
9.
rag replacements
O
x
y
[SQA] 10.
rag replacements
O
x
y
replacements
O
x
y hsn.uk.net
Page 2
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
11.
rag replacements
O
x
y
[SQA]
12.
rag replacements
O
x
y
[SQA]
13.
rag replacements
O
x
y
[SQA]
14.
rag replacements
O
x
y
[SQA]
replacements
15.
Before a forest fire was brought under control, the spread of the fire was described
by a law of the form A = A 0 e kt where A 0 is the area covered by the fire when it
was first detected and A is the area covered by the fire t hours later.
If it takes one and a half hours for the area of the forest fire to double, find the
value of the constant k. 3
O
x
y hsn.uk.net
Page 3
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA] 16.
rag replacements
O
x
y
[SQA]
17.
rag replacements
O
x
y
[SQA]
18.
rag replacements
O
x
y
[SQA]
19.
rag replacements
O
replacements x
y
O
x
y hsn.uk.net
Page 4
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
20.
rag replacements
O
x
y
[SQA]
21.
rag replacements
O
x
y
[SQA]
22.
PSfrag replacements
The results of an experiment give rise to the graph shown.
x
y
(a) Write down the equation of the line in
1·8
terms of P and Q. 2
−3 O
Q
P
It is given that P = log e
p and Q = log e
q.
(b) Show that p and q satisfy a relationship of the form p = aq b , stating the
values of a and b. 4
replacements
O
x
y hsn.uk.net
Page 5
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
23.
rag replacements
O
x
y
[SQA] 24. The graph illustrates the law
PSfrag
y = kx n replacements
.
log 5
y
If the straight line passes through
A(0·5, 0) and B(0, 1), find the values of B(0, 1)
k and n. 4
x
y
A(0·5, 0)
O
log 5
x
[SQA]
25.
rag replacements
O
x
y
replacements
O
x
y hsn.uk.net
Page 6
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
26.
rag replacements
O
x
y
rag replacements
[SQA] 27.
replacements
O
x
y
hsn.uk.net
O
x
y Page 7
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
28.
rag replacements
O
x
y
[END OF WRITTEN QUESTIONS]
replacements
O
x
y hsn.uk.net
Page 8
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes