Unit 2 Equivalent Expressions And Quadratic Functions 2013

Topics: Maxima and minima, Quadratic equation, Polynomial Pages: 16 (4164 words) Published: July 1, 2015
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 domain
b)
d)
26) Halla used her graphing calculator to graph three different polynomial functions on the same axes. The equations of the functions appeared to be different, but her calculator showed only two different graphs. She concluded that two of her functions were equivalent.

a) Is her conclusion correct? Explain.
b) How could she determine which, if any, of the functions were equivalent without using her graphing calculator?
27) a) Consider the linear functions
and
. Suppose that
. Show that the functions must be equivalent.
b) Consider the two quadratic functions
and
,
,
. Show that the functions must be equivalent.
28) Is the equation

, and
. Suppose that

true for all, some, or no real numbers? Explain.

29) a) If
has two terms and
has three terms, how many terms will the product of
and
have
before like terms are collected?
b) In general, if two or more polynomials are to be multiplied, how can you determine how many terms the product will have before like terms are collected? Explain and illustrate with an example.

Solutions
3

2

2

2

2

2

2

13a) 25x + 15x – 20x 13b) 2x – 7x – 30 13c) 16x – 53 x + 33 13d) n – 13n + 72 13e) -68x – 52x – 2 13f) 5a – 26a – 37 3
3
2
3
2
3
2
3
2
14a) 4x – 100x 14b) -2a – 16a – 32a 14c) x – 5x – 4x + 20 14d) -6x + 31x – 23x – 20 14e) 729a – 1215a + 675a – 125 2
2
2
2
14f) a – 2ad – b + 2bc – c + d
4
3
2
2
3
6
4
3
2
2
15a) x + 4x + 2x – 4x + 1 15b) 8 – 12a + 6a – a 15c) x – x – 2x – 3x – 2x – 1 15d) -16x + 43x – 13 16a) (x -7)(x + 2) 16b) (x +5y)(x - y) 16c) 6(m -6)(m – 9) 16d) (2y +7)(y – 1)
16e) (4a – 7b)(2a + 3b) 16f) 2(2x + 5)(4x + 9)
4
2
17a) (x -3)(x + 3) 17b) (2n -7)(2n + 7) 17c) (x + 1)(x + 1)(x – 1)(x + 1) 17d)...
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