Logs/Exp Past Papers Unit 3 Outcome 3 Multiple Choice Questions Each correct answer in this section is worth two marks. 1. Solve logb x − logb 7 = logb 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 log5 2 + log5 50 − log5 4.
3
[SQA]
3. Given x = log5 3 + log5 4, find algebraically the value of x .
4
[SQA]
4. Find x if 4 log x 6 − 2 logx 4 = 1.
3
5. Find the x -coordinate of the point where the graph of the curve with equation y = log3 (x − 2) + 1 intersects the x -axis.
3
[SQA]
6.
[SQA]
frag replacements O x y replacements O x y
hsn.uk.net
Page 1
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
PSfrag replacements O x y
Higher Mathematics
7.
[SQA]
frag replacements O x y
8.
[SQA]
frag replacements O x y
9.
[SQA]
frag replacements O x y
[SQA] 10. frag replacements
O x y
replacements O x y
hsn.uk.net
Page 2
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
PSfrag replacements O x y
Higher Mathematics
11.
[SQA]
frag replacements O x y
12.
[SQA]
frag replacements O x y
13.
[SQA]
frag replacements O x y
14.
[SQA]
frag replacements O x y
15. Before a forest fire was brought under control, the spread of the fire was described by a law of the form A = A0 ekt where A0 is the area covered by the fire when it was first detected and A is the area covered by the fire t hours later.
[SQA]
replacements
If it takes one and a half hours for the area of the forest fire to double, find the value of the constant k.
O x y
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
hsn.uk.net
Page 3
3
PSfrag replacements O x y
Higher Mathematics
[SQA] 16. frag replacements
O x y 17.
[SQA]
frag replacements O x y 18.
[SQA]
frag replacements O x y 19.
[SQA]
frag replacements replacements O x y
O x y
hsn.uk.net
Page 4
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
PSfrag replacements O x y
Higher Mathematics
20.
[SQA]
frag replacements O x y
21.
[SQA]
frag replacements O x y PSfrag replacements 22. The results of an experiment give rise to the graph shown. x y (a) Write down the equation of the line in terms of P and Q.
[SQA]
P 1·8 −3 O
Q
2
It is given that P = loge p and Q = loge q. (b) Show that p and q satisfy a relationship of the form p = aq b , stating the values of a and b .
replacements O x y
hsn.uk.net
Page 5
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
4
PSfrag replacements O x y
Higher Mathematics
23.
[SQA]
frag replacements O x y
24. The graph illustrates the law PSfrag y = kx nreplacements . log5 y If the straight line passes through B(0, 1) A(0·5, 0) and B(0, 1), find the values of x k and n. y
[SQA]
O
4
A(0·5, 0)
log5 x
25.
[SQA]
frag replacements O x y
replacements O x y
hsn.uk.net
Page 6
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
PSfrag replacements O x y
Higher Mathematics
26.
[SQA]
frag replacements O x y
frag replacements [SQA] 27. O x y
replacements O x y
hsn.uk.net
Page 7
c SQA Questions marked ‘[SQA]’ c All others Higher Still Notes
PSfrag replacements O x y
Higher Mathematics
28.
[SQA]
frag replacements O x y [END OF WRITTEN QUESTIONS]
replacements O x y
hsn.uk.net
Page 8
c SQA Questions marked ‘[SQA]’ c Higher Still Notes All others
