MCR3U0: Device 2 – Equivalent Expression and

Quadratic Functions

Significant Expressions

1) Express like a mixed revolutionary in most basic 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)

Intended for questions your five to 9, calculate the actual values and express your answers in simplest radical form. 5) Calculate the length of the diagonal of a rectangular with area length 5 cm. 6) A sq has an area of 450 cm2. Calculate the side length. 7) Determine the size of the oblicuo of a rectangular shape with measurements 3 centimeter

9 cm.

8) Decide the length of the line segment via A(-2, 7) to B(4, 1). 9) Calculate the perimeter and area of the triangle to the proper. 10) In the event

and

, which is greatest,

or

?

11) Express each major in easiest form.

a)

c)

b)

d)

12) Simplify

FMSS 2013

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Alternatives

1a)

2a)

3a)

4a)

4e)

8)

11a)

1b)

1c)

1d)

2c) 32

2b)

3b)

3c)

4b)

1e)

2d)

3d)

9) Perimeter sama dengan

11b)

3e)

4c)

5)

4f)

1f)

2e)

cm

2f) -140

3f)

4d)

6)

units, Area = 12 square units 10)

11c)

11d) –

cm

7)

centimeter

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

happen to be equivalent.

20) Show that

and

aren't equivalent.

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21) a) Is

equivalent to

? Justify your decision.

b) Write a made easier expression that is equivalent to

.

22) Show the expressions

and

are not equivalent.

23) Determine whether the features in every single given couple are comparative. a)

and

b)

and

c)

and

e)

and

f)

and

g)

and

h)

and

24) The 2 equal attributes of an isosceles triangle have a period of. Determine the length of the third area.

. The edge of the triangular is

25) For each couple of functions, ingredients label the pairs as equivalent, nonequivalent, or perhaps cannot be decided. a)

c)

e)

for all those values of in the domain

b)

d)

26) Halla used her graphing calculator to graph three several polynomial features on the same axes. The equations of the functions appeared to be several, but her calculator showed only two different graphs. She concluded that two of her functions had been equivalent.

a) Is her conclusion correct? Explain.

b) How could she determine which, if any, of the capabilities were comparable without using her graphing calculator?

27) a) Consider the linear features

and

. Suppose that

. Show the fact that functions should be equivalent.

b) Consider both quadratic capabilities

and

,

,

. Present that the features must be comparable.

28) Is definitely the equation

, and

. Suppose that

authentic for all, a few, or no genuine numbers? Explain.

29) a) If

features two terms and

has three conditions, how a large number of terms does the product of

and

include

before just like terms are collected?

b) In general, if perhaps two or more polynomials are to be increased, how can you determine how many terms the product will have before just like terms happen to be collected? Make clear and demonstrate with a good example.

Solutions

several

2

2

2

two

2

a couple of

13a) 25x + 15x – 20x 13b) 2x – 7x – 35 13c) 16x – 53 x + 33 13d) n – 13n & 72 13e) -68x – 52x – 2 13f) 5a – 26a – 37 several

3

a couple of

3

two

3

two

3

2

14a) 4x – 100x 14b) -2a – 16a – 32a 14c) by – 5x – 4x + 20 14d) -6x + 31x – 23x – 20 14e) 729a – 1215a + 675a – a hundred and twenty-five 2

two

2

two

14f) a – 2ad – n + 2bc – c + m

4

a few

2

two

3

six

4

several

2

two

15a) times + 4x + 2x – 4x + one particular 15b) almost 8 – 12a + 6a – a 15c) back button – back button – two times – 3x – two times – you 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)...