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: FINAL MARKS:

Instructions:

� Put your name and student ID on your exam paper.

� Answer all questions and submit your answers as an editable file (for example,

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.

Eton Academy 1 North York, Canada

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

(

7π

4

)

1 − tan

(

π

12

)

tan

(

7π

4

)

b) cos

(π

9

)

cos

(

19π

18

)

− sin

(π

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?

Eton Academy 2 North York, Canada