MHF4U Test #3: Chapters 6-7
Name: ______________________________________
Date:
Part A – Multiple Choice [K/U – 15 marks]
1. The function
passes through the point
b. (1, –4)
a. (–1, 4)
2. The x-intercept of the function
a. 1
b. 6
c. (–1, –4)
d. (1, 4)
c. 0
d. does not exist
is
3. The exponential function for the following data set is
a.
b.
4. Another way of writing
c.
x
2
3
4
5
d.
is
a.
b.
5. Another way of writing
c.
d.
is
a.
b.
c.
d.
b. 1
c. 2
d. 3
7. The equation of the vertical asymptote for the function
a. x = –4
b. x = 3
is
c. x = 4
d. x = 0
8. The x-intercept of the function
a. 4
b. –5
c. 5
d.6
6. Evaluate
a. 0
9. Express
a.
10. Express
a.
.
is
as a power with a base of 2.
b.
c.
d.
as a power with a base of 2.
b.
c.
d.
y
9
27
81
243
11. Solve the equation
a.
.
b.
c.
d.
12. A sample of plutonium decays to 25% of its original mass in 30 h. Find the half-life of this sample.
a. 15 h
b. 75 h
c.60 h
d. 45 h
13. Write as a single logarithm.
a.
b.
c.
d.
14. The restrictions on the variable in the expression
a. x > 3
15. Solve the equation
a. x = 0
is
c. x < –3
b. x < 3
d. A and C
.
c. x = –10
b. x = 8
d. B and C
Part B – Thinking and Investigation [TI – 15 marks]
1. Show that
2. Solve the equation
.✓✓✓✓
. Leave your answer in exact form ✓✓✓
3. Write as the sum or difference of logarithms. Simplify, if possible. ✓✓✓✓
4. Solve the equation
. Round answers to two decimal places. ✓✓✓✓
Part C – Communication [COMM – 10 marks]
1. Match each graph with its function. ✓✓✓✓
2. List the steps and explain the effect of each transformation to graph the function
.✓✓✓
.✓
a) State the domain and range ✓
3. Sketch a graph the function
b) State the x- and y-intercepts✓
Part D – Application [APP – 15 marks]
1. A person needs $15 000 for a down payment on a car. If the person invests $10 000 at 9% interest, compounded
monthly, how many years will it take before she can make the down payment? ✓✓✓
2. Fog can greatly reduce the intensity of oncoming headlights. The distance, d, in metres, of an oncoming car
𝐼
whose headlights have an intensity of light, I, in lumens (lm), is given by 𝑑 = −167log⁡(125).
a. How far away is a car whose headlight intensity is 50lm? ✓
b. If an oncoming car is 30m away, what is the intensity of its headlights? ✓✓
c. If the headlight intensity doubles, does this mean the car is half as far away? Explain. ✓✓✓
3. The sound level of a moving power lawn mover is 109 dB. The noise level in front of the amplifiers at a concert is
about 118 dB. How many times louder is the noise at the front of the amplifier than the noise of the moving power
lawn mower? ✓✓✓
4. The value of a rookie hockey card is modelled by the function
, where x is the number of
years since the year 2008. How much will that card be worth in the year 2020? ✓✓✓
Test Summary
Knowledge &
Understanding
Thinking & Invest.
/15
/15
Communication
Application
/10
/15