MPM1D Final Exam Review
Unit 2 – Powers and
Polynomials
1. Write as a power: 5 × 5 × 5 × 5 × 5 × 5
2. Write in expanded form: 83
7.
a) Consider the polynomial 4𝑦 − 5𝑧 2 . Classify
the polynomial by the number of terms and by
its degree.
b) Consider the polynomial 2𝑎2 𝑏 + 5𝑎𝑏 2 −
3𝑎2 𝑏 2 . Classify the polynomial by the number
of terms and by its degree.
8. Identify which of the following are like
3. Consider the power 9 . Express this power terms:
with a base of 3.
3𝑥, 4𝑥𝑦, 5𝑥𝑦 2 , 5𝑥 2 𝑦, −2𝑦𝑥 2
4
Vocabulary
4. Evaluate the expression: (7 −
1 3
5)4 (2)
9. Simplify: (3𝑥 + 4𝑦) + (2𝑥 − 5𝑦)
10. Simplify: (2𝑎 − 3𝑏) + (5𝑎 + 7𝑏) + (3𝑎 − 𝑏)
5. Evaluate the expression 𝑥 3 − 9𝑥 2 + 27𝑥 −
27 for 𝑥 = 3.
11. What is the opposite of −3𝑔 + 9ℎ?
12. Simplify: (𝑥 + 5𝑦) − (7𝑥 − 3𝑦).
6. Write as a single power then evaluate:
Correction Notes for Power and Polynomials Unit Test:
13. Simplify: (6𝑝 − 𝑞 + 3𝑟) − (5𝑝 + 7𝑞 − 2).
a) 32 × 3 × 35
b) 𝑏 4 × 𝑏 3 , when 𝑏 = 2
c)
𝑦7
𝑦5
, when 𝑦 = 9
d) (−22 )3
e) (𝑥𝑦 3 )4, when 𝑥 = 2 and 𝑦 = −1
14. Expand the following:
a) 3(5𝑦 − 2)
b) 7𝑎(𝑎2 + 2)
c) 3(2 + 5(4𝑝 − 3))
15. In a hockey tournament, teams are
18. Expand and Simplify.
awarded 4 points for a win and 2 points for an
overtime win.
a) 3(𝑥 2 + 2𝑥 − 5) + 4(𝑥 2 − 6𝑥 + 2)
20.
a) Determine an expression for the volume of a
cube with side length x.
a) Write an expression to determine the total
points for a team.
b) Suppose we doubled the side length of the
cube, determine a new expression for the
volume of the cube, in terms of x.
b) Use your expression to find the number of
points earned by a team that has five wins and
two overtime wins.
b) (4𝑚2 − 3𝑚𝑛 − 2𝑛2 ) − 5(𝑚2 + 𝑚𝑛 − 5𝑛2 )
c)
 20 x  24 y  6  25 x  20 y  15 


2
5


d)
3
2
(2x - 2) - (x +1)
5
3
c) How many times greater is the larger cube
than the smaller cube?
21. Determine a simplified expression for the
perimeter and area of the following figure
16. Simplify each of the following:
5 4
3 2
a) 𝑎 𝑏 × 𝑎 𝑏
b)
𝑑6 𝑑5
𝑑7
c)
(𝑦 6 )
3
(𝑦 5 )2
17. Simplify:
a) 2𝑥 2 − 6 + 𝑥 2 + 3
b) −5 + 𝑥 + 3 − 2𝑥
c) 3𝑤 2 + 2𝑤𝑦 − 𝑦 2 − 2𝑤 2 − 2𝑤𝑦 + 4𝑦 2
19. E. Coli is a type of bacteria that can cause
dangerous health problems. It doubles
every 20 minutes.
a) Write an expression that can help you
determine the number of bacteria after t
minutes.
d) 6𝑎3 − 4𝑎𝑏 + 5𝑏 2 − 3 + 5𝑎𝑏 2 − 3𝑎𝑏
b) Suppose you start with 1000 bacteria, use
your expression to determine the number
of bacteria after
i) 5 hours
ii) 8 hours
22. Determine the area of the shaded region.
Also determine an expression for ALL
edging (inside and outside). Note the frame
is an even width.