# math MHF4U: Midterm Exam Revision – January 15, 2022 MHF4U: MIDTERM EXAM Due: 11.59 P.M. February 13, 2022 Total grade: 100 marks NAME OF STUDENT: FINA

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MHF4U: Midterm Exam Revision – January 15, 2022

MHF4U: MIDTERM EXAM
Due: 11.59 P.M. February 13, 2022

NAME OF STUDENT: FINAL MARKS:

Instructions:

WORD).

� Feel free to discuss how to do these problems with your classmates, but all the work
you hand in should be your own. Copying other’s work and submitting it as your
own is an academic offence and will not be tolerated.

� Put enough (and only enough) details in your work, so the instructor is able to read
and understand your solutions. Both a solution of just a simply correct answer with
no detail, and a solution with too many pages of details are not satisfactory.

1. (10 marks) Identify the intervals of increase/decrease, the symmetry, and the domain
and range of each function.

a) f(x) = 3x

b) f(x) = x2 + 2

c) f(x) = 2x − 1

2. (10 marks) Estimate the instantaneous rate of change for each function at each given
point. Identify any point that is a maximum/minimum value.

a) h(p) = 2p2 + 3p; p = −1,−0.75 and 1

b) k(x) = −0.75×2 + 1.5x + 13; x = −2, 4, and 1

3. (10 marks) Sketch the graph of f(x) = (x − 3)(x + 2)(x + 5) using the zeros and end
behaviours.

4. (10 marks) Solve the following inequality using graphing technology:

x3 − 2×2 + x − 3 ≥ 2×3 + x2 − x + 1

5. (10 marks) The population of locusts in a Prairie a town over the last 50 years is
modelled by the function

f(x) =
75x

x2 + 3x + 2

The locusts population is given in hundreds of thousands. Describe the locust population
in the town over time, where x is time in years.

6. (10 marks) Select a strategy to solve each of the following.

MHF4U: Midterm Exam Revision – January 15, 2022

a)
−x
x − 1

=
−3
x + 7

b)
2

x + 5
>

3x

x + 10

7. (10 marks) The following graphs (f(x) and g(x)) are a sine curve and a cosine curve,
determine the equations of the graphs.

Figure 1: Figure for question 7

8. (10 marks) Prove following trigonometric identities.

a)
1 − sin2(x)

cot2(x)
= 1 − cos2(x)

b)
2 sec2(x) − 2 tan2(x)

csc(x)
= sin(2x) sec(x)

9. (10 marks) Evaluate each expression.

a)
tan

(
π
12

)
+ tan

(

4

)
1 − tan

(
π
12

)
tan

(

4

)
b) cos

9

)
cos

(
19π

18

)
− sin

9

)
sin

(
19π

18

)
10. (10 marks) A tower that is 65 m high makes an obtuse angle with the ground. The
vertical distance from the top of the tower to the ground is 59 m. What obtuse angle
does the tower make with ground, to the nearest hundredth of a radian?

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