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Chapter 7 P R A C T I C E T E S T
For questions 1 to 4, select the best answer.
1. 8 is equivalent toA 4
B 22_3
C 23_2
D (22)3
2. What is the solution to 2x 1 4x?
A 1
B 2
C 4
D 1
3. Which is the product law of logarithms?
A log a log b log (ab)
B log a log b log (ab)
C log a log b log (ab)
D log a log b log (ab)
4. The expression log2
5 log2
10 log2
25 is
equal to
A log 2
B 0
C 1
D 2
5. Write as a single logarithm, and then evaluate.
log3
6 log3
4 log3(8_3)
6. Solve.
a) 8x 2 42x 1
b) 3x 81x 4
c) log 2 log (x 5) 1
d) log 8 log (x 2) 1
7. Use Technology Check your answers to
question 6 using graphing technology.
8. Consider the graphing calculator screens shown.
a) What equation is being solved?
b) What is the solution? Explain how you know.
c) Verify this solution using algebraic reasoning.
9. A technician places 50 mg of a certain
radioactive substance into a laboratory chamber.After 10 min,
there are 41 mg remaining.
a) Determine the half-life of the substance.
b) How long will it take for the material to
decay to 1% of its initial amount?
10. The carbon fusion cycle is one way that a
star is fuelled. Through a series of processes,
carbon atoms combine with hydrogen to form
other elements such as nitrogen and oxygen,
before returning back to carbon. Throughout
this cycle, energy is released. In one step of
the carbon fusion cycle, nitrogen-13spontaneously decays into
carbon-13. Suppose
that in a laboratory simulation, a sample of
nitrogen-13 is measured to be 10% of its
initial amount after approximately 33 min.
Determine the half-life of nitrogen-13.
410 MHR Advanced Functions Chapter 7
8/9/2019 Section 7 Pactice Test
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11. a) Solve 2 log (x 1) log (x 1) and
identify any extraneous roots.
b) Check your answer using graphingtechnology.
12. Examine the scatter plot shown.
a) Could a quadratic curve of best fit be
drawn through these points? Explain why
or why not.
b) Could an exponential curve of best fit be
drawn through these points? Explain why
or why not.
c) Describe a scenario that these data might fit,
in which the better model is
i) exponentialii) quadratic
Justify your answers in each case.
13. Use Technology A cup of tea is placed on a
counter and allowed to cool. The table shows
the temperature of the tea over time.
a) Create a scatter plot of temperature versus
time.
b) Create a quadratic model to fit the data.
c) Create an exponential model to fit the data.
d) Which model is better, and why?
e) Use the better model to
i) predict the temperature of the tea after
15 min
ii) predict how long will it take for the tea
to reach 38C
f) Describe any assumptions you must make.
Time (min) Temperature (C)
0 98
2 88
4 79
6 72
8 66
10 62
12 58
y
x0
Chapter 7 Practice Test MHR 411
