Unit 2 Equivalent Expressions And Quadratic Functions 2013
MCR3U0: Unit 2 – Equivalent Expressions and
Quadratic Functions
Radical Expressions
1) Express as a mixed radical in simplest form.
a)
c)
b)
e)
d)
f)
2) Simplify.
a)
b)
d)
e)
c)
f)
3) Simplify.
a)
b)
c)
d)
e)
f)
4) Simplify.
a)
d)
b)
e)
f)
c)
For questions 5 to 9, calculate the exact values and express your answers in simplest radical form.
5) Calculate the length of the diagonal of a square with side length 4 cm.
6) A square has an area of 450 cm2. Calculate the side length.
7) Determine the length of the diagonal of a rectangle with dimensions 3 cm
9 cm.
8) Determine the length of the line segment from A(-2, 7) to B(4, 1).
9) Calculate the perimeter and area of the triangle to the right.
10) If
and
, which is greatest,
or
?
11) Express each radical in simplest form.
a)
c)
b)
d)
12) Simplify
FMSS 2013
.
Page 1 of 16
Solutions
1a)
2a)
3a)
4a)
4e)
8)
11a)
1b)
1c)
1d)
2c) 32
2b)
3b)
3c)
4b)
1e)
2d)
3d)
9) Perimeter =
11b)
3e)
4c)
5)
4f)
1f)
2e)
cm
2f) -140
3f)
4d)
6)
units, Area = 12 square units 10)
11c)
11d) –
cm
7)
cm
12)
Polynomial Expressions
13) Expand and Simplify
a)
b)
c)
d)
e)
f)
14) Expand and Simplify
a)
b)
c)
d)
e)
f)
15) Expand and Simplify
a)
b)
d)
e)
16) Factor
a)
b)
c)
d)
e)
f)
17) Factor
a)
b)
c)
d)
e)
f)
18) Factor
a)
b)
c)
d)
e)
f)
19) Show that
and
are equivalent.
20) Show that
and
are not equivalent.
FMSS 2013
Page 2 of 16
21) a) Is equivalent to
? Justify your decision.
b) Write a simplified expression that is equivalent to
.
22) Show that the expressions
and
are not equivalent.
23) Determine whether the functions in each given pair are equivalent.
a)
and
b)
and
c)
and
e)
and
f)
and
g)
and
h)
and
24) The two equal sides of an isosceles triangle each have a length of
. Determine the length of the third side.
. The perimeter of the triangle is
25) For each pair of functions, label the pairs as equivalent, non-equivalent, or cannot be determined.
a)
c)
e)
for all values of in the
Quadratic Functions
Radical Expressions
1) Express as a mixed radical in simplest form.
a)
c)
b)
e)
d)
f)
2) Simplify.
a)
b)
d)
e)
c)
f)
3) Simplify.
a)
b)
c)
d)
e)
f)
4) Simplify.
a)
d)
b)
e)
f)
c)
For questions 5 to 9, calculate the exact values and express your answers in simplest radical form.
5) Calculate the length of the diagonal of a square with side length 4 cm.
6) A square has an area of 450 cm2. Calculate the side length.
7) Determine the length of the diagonal of a rectangle with dimensions 3 cm
9 cm.
8) Determine the length of the line segment from A(-2, 7) to B(4, 1).
9) Calculate the perimeter and area of the triangle to the right.
10) If
and
, which is greatest,
or
?
11) Express each radical in simplest form.
a)
c)
b)
d)
12) Simplify
FMSS 2013
.
Page 1 of 16
Solutions
1a)
2a)
3a)
4a)
4e)
8)
11a)
1b)
1c)
1d)
2c) 32
2b)
3b)
3c)
4b)
1e)
2d)
3d)
9) Perimeter =
11b)
3e)
4c)
5)
4f)
1f)
2e)
cm
2f) -140
3f)
4d)
6)
units, Area = 12 square units 10)
11c)
11d) –
cm
7)
cm
12)
Polynomial Expressions
13) Expand and Simplify
a)
b)
c)
d)
e)
f)
14) Expand and Simplify
a)
b)
c)
d)
e)
f)
15) Expand and Simplify
a)
b)
d)
e)
16) Factor
a)
b)
c)
d)
e)
f)
17) Factor
a)
b)
c)
d)
e)
f)
18) Factor
a)
b)
c)
d)
e)
f)
19) Show that
and
are equivalent.
20) Show that
and
are not equivalent.
FMSS 2013
Page 2 of 16
21) a) Is equivalent to
? Justify your decision.
b) Write a simplified expression that is equivalent to
.
22) Show that the expressions
and
are not equivalent.
23) Determine whether the functions in each given pair are equivalent.
a)
and
b)
and
c)
and
e)
and
f)
and
g)
and
h)
and
24) The two equal sides of an isosceles triangle each have a length of
. Determine the length of the third side.
. The perimeter of the triangle is
25) For each pair of functions, label the pairs as equivalent, non-equivalent, or cannot be determined.
a)
c)
e)
for all values of in the