Pure Math 30
Module 2 Test (A)
Multiple Choice Questions
Each question is worth one mark. Please put your answers on page 5.
1. Solve for x: log 5 ( 2x + 1 ) + log 5 x = log 5 10
A. x = - 2.5 and 2
B. x = 2
C. x = 3
D. x = 2 and 3.
2. log is equal to
A. 2 log m – 3 log x – log y
B. 2 log m – log x – log y
C. 2 log m – log x + log y
D. 2 log m –log x – log y
3. Expressed as a single logarithm, 2 log 3 a – log 3 d + is
A. log 3
B. log 3
C. log 3
D. log 3
4. A student wishes to graph y = log 3 x on a calculator, but her calculator can only graph logarithmic functions if the equations are expressed in common logarithms (base 10). She could obtain the graph of y = log 3 x by graphing
A. y =
B. y =
C. y = log ( x – 3 )
D. y = log
5. Given: f(x) = log a x , where x > 0 and a 1 .
The domain of the function f( x + 2 ) is
A. x > – 2
B. x < – 2
C. x > 2
D. x < 2
6. The number of E. coli bacteria at time, t in hours, is given by
N t = N 0 (8) t , where N 0 is the initial number of bacteria at t = 0. If the initial number of bacteria is 4 000, then the expected number of bacteria l hour and 15 minutes later is
A. 4600
B. 5000
C. 43 713
D. 53 817
7. The expression , where b>0 and c>0, is equal to
A.
B.
C.
D.
8. Written as a single logarithm, is:
A.
B.
C.
D.
9. If , then x is:
A. 2
B. 4
C. 6
D. 12
10. The equations y=5x and y=log5x are symmetric with respect to
A. the origin
B. the x-axis
C. the y-axis
D. y=x
11. Approximately how many years would it take for $75 to increase to $160 at 7.4%
compounded annually?
A. 10
B. 11
C. 12
D. 16
Numeric Response.
Fill in the boxes below, starting in the left hand box and proceeding to the right. (1 mark )
1. Nicole invests $2 500 in an account which pays 8.8%/a compounded quarterly. How many years will it take her investment to double? Express your answer to the nearest tenth of a year. ______.
Long Answer: Show all work
1. Given , solve for x. (2 marks)
2. Solve for x. (2 marks)
3. Change each of the following from exponential form to logarithmic form. (4 marks)
a. y = 3(2)x
b.
4. Write the following expression as a single logarithm. (2 marks)
log B + log D – 5log E – log A2 + ½ log A
5. Solve for the variable in each equation. Verify. (4 marks)
a. log 9 x + log 9 3 = 1
b. log 2 3a + log 2 2 + log 2 8 – log 2 4
Pure Math 30 Formula Sheet
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