MPM1D Exam Review
1.
Write in expanded form, then evaluate.
b)  4
a) 35
2.
Chapter 3 – Polynomials & Exponents
4
d)  
5
c)  4
2
2
3
 2
e)   
 6
Evaluate.
a) 5 2

c)  2 1
b)  4 5    3
3
3

3 6
d)
 2
 22
 32
2
4
e)
33  37  3 5

 24
 15
2
3.
Evaluate the expression x 3  9x 2  27x  27 for x  3
4.
Write each as a single power, then evaluate.
65
4
4
a) 33  3  35 b) 3 c) 2xy 3  when x  2 and y  1
d) 525
6
Classify the following polynomials by the number of terms and state their degrees.
a) 4y  5z 2
b) 2a 2b  5ab 2  3a 2b 2
5.
6.
Identify the like terms in each of the following:
a) 3x ,3xy ,3xy 2 ,8xy 2 ,5x 2 y ,2yx 2
b) 2b 3 ,2b 2 ,2b ,2
7.
Simplify the following:
a) 3x  4y   2x  5y 
d)
8.
c) 2x
2a  3b   7b  5a   3a  b 
6p  q  3r   7q  2r  5p  e) 5x  3  6x  4 f) 4y  3  5y  2
Use the distributive property to expand and simplify:
a) 35y  2
b) 7a a 2  2 c) 32  54 p  3 d) 32x  4  e) 2x  4
g)  7 3x  4x  3
2
9.
b)
h) 82x  3x  5 i) 230 56x  3x  j)
2
2
4m
2
 5y   7x  3y 
f) 32x  4
 3mn  2n 2   mn  m 2  5n 2 
In a soccer league, teams are awarded 3 points for a win and 1 point for a tie.
a) Write an expression to determine a team’s total points.
b) Use your expression to find the number of points earned by a team that has 5 wins and 2 ties.
10. State the degree of each term or polynomial.
a) 5x 4 b) 7m 5 c) 2c a 3b d) 5x  4 e) 5m 2  3m  6 f) 6a 2b  5ab 2  4ab  3
11. Simplify by collecting like terms.
a) 5x  6  3x b) 3x  x  2 c) 2x 2  6  x 2  3 d) 5  x  3  2x e) x  4  6  5x
f) 3x 3  x  2x 3  3x g) 4x 2  3x  5  5x 2  2x  7 h) 3x  5y  4x  6y
i) 6a 3  4ab  5b 2  3  5a 3  3ab j) 3w 2  2wy  y 2  2w 2  2wy  4y 2 k) 5d  3m  4d  5m
12. Simplify each of the following.
a) a 5 b 4   a 3b 2  b)
d 6d
d7
5
c)
y 
y 
13. Expand and simplify.
a) 3x 2  2x  5  4x 2  6x  2
c) 42x  3y   53x  6y 
6
3
5
2
b) 5x 2  2x  6  32x 2  6x  2
d) 2a 3a a  4  a 2a  3
14. a) Determine an expression for the volume of a cube with side length x .
b) Suppose we doubled the side length of the cube. Determine a new expression for the volume of
the cube, in terms of x .
c) How many times greater is the larger cube than the smaller cube?
Determine how many times bigger the following cube is than the first:
d) If the sides were tripled.
e) If the sides were made four times longer.
15. Determine a simplified expression for the Perimeter and Area of the following:
2x
3x
2x
2x + 1
16. a) Determine a simplified expression for the area of the shaded region.
b) Determine an expression for the total edging (both inside and outside).
2x+7
2x
x-1
x
17. Matt is building a dock at his cottage. The length of the dock is 3 metres longer than twice the
width.
a) Draw a diagram of the dock and label the width and length with algebraic expressions.
b) Find simplified expressions for both the Area and Perimeter of the dock.
c) Find the Perimeter and Area of the dock if the width is 2 metres.
Chapter 3 Exam Review – Solutions
64
1
e)
2a) -40 b) 7 c) 64 d) 2 e) -8 3) 0 4a) 6561 b) 36 c) 256 d) 1953125
125
81
5a) binomial, degree 2 b) trinomial, degree 4 6a) 3xy2 and 8xy2, 5x2y and 2yx2 b) none 7a) 5x - y b) 10a + 3b
c) -5x + 8y d) p – 8q +5r e) 11x  1 f) y  1 8a) 15y – 6 b) 7a3 + 14a c) 60p – 39 d) 6x  12 e) 2x  8
1a) 243 b) 16 c) -16 d)
f) 6x  12 g) 21x 2  28x  21 h) 16x 2  24x  40 i) 12880x 2  690x j) 3m 2  4mn  3n 2 9a) P = 3W + 1T
b) P = 17 10a) 4 b) 5 c) 4 d) 1 e) 2 f) 3 11a) 8x  6 b) 2x  2 c) 3x 2  3 d) x  2 e) 4x  2 f) 5x 3  2x
g) x 2  x  2 h) 7x  11y i) 11a 3  7ab  5b 2  3 j) w 2  3y 2 k) d  2m 12a) a8b6 b) d4 c) y8
13a) 7x 2  18x  7 b) x 2  8x  24 c) 7x  42y d) 4a 3  22a 2  3a 14a) V  x 3 b) V  8x 3 c) 8 times
d) 27 times e) 64 times 15) Perimeter = 10x  2 Area = 4x 2  3x 16a) Area = 9x b) Edging = 12x  12
17a)
b) Area = 2x 2  3x Perimeter = 6x  6 c) Area = 14m2 Perimeter = 18m