Unit 3 Test Review

Write the numbers 1 – 20 on a piece of paper

Instructions

There are 20 multiple choice questions.

Do not copy out the questions just do them.

The questions and answers are available on classnet.

Try to do the questions before you look at the possible answers.

There will be no multiple choice questions on the real test but these questions represent many of the types of questions that could appear on the test.

1) Determine the number of zeros.

a)

b)

c)

d)

e)

4)3(2)( 2 xxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

2) Determine the number of zeros.

a)

b)

c)

d)

e)

2)1(2)( xxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

3) Determine the number of zeros.

a)

b)

c)

d)

e)

)2)(2(2)( xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

4) Determine the number of zeros.

a)

b)

c)

d)

e)

342)( 2 xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

5) Determine the number of zeros.

a)

b)

c)

d)

e)

22)( 2 xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

6) Determine the number of zeros.

a)

b)

c)

d)

e)

44)( 2 xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

7) Select the correct statement about the equations corresponding to the graphs below.

a)

b)

c)

d)

e)

A and B would each have 2 real roots.

A and B would each have 2 imaginary roots.

A and B would each have 1 real root.

A would have 2 real roots while B would have no roots.

A would have 2 real roots while B would have 2 imaginary roots.

GRAPH A GRAPH B

8)Determine the vertex.

a)

b)

c)

d)

e)

142)( 2 xxxf

(-1, -1)

(2, 25)

(0, 1)

(-4, 17)

(1, 7)

9)Determine the vertex.

a)

b)

c)

d)

e)

1)4(2)( 2 xxf

(4, -1)

(2, 4)

(-4, 1)

(4, 1)

(-4,-1)

10) Determine the vertex.

a)

b)

c)

d)

e)

)14)(23()( xxxf

(2/3, -1/4)

(5/12, -2)

(5/24 , -121/48)

(-13/8, 13/6)

(2/3, 1/4)

11) Determine the vertex.

a)

b)

c)

d)

e)

xxxxf 2)3)(1(2)(

(1, 1)

(1, -2)

(-1/2 ,-13/2)

(1/2,-9.5)

(-1, -6)

12)One root of an equation is 2 + 3i. Determine the other root.

a)

b)

c)

d)

e)

-2 – 3i

2 – 3i

2 + 3i

5i

-2 + 3i

13)Determine the roots.

a)

b)

c)

d)

e)

1/2 and -3/2

-1 and -3

6 and -2

-6 and 2

-1/2 and 3/2

0344 2 xx

14)Determine the roots.

a)

b)

c)

d)

e)

2

2 and -2

+2i and -2i

no roots

-4

082 2 x

15)Determine the roots.

a)

b)

c)

d)

e)

0744 2 xx

i62

1

2

1

no roots

22

1

62

1

2

1

i22

1

16)Determine the roots.

a)

b)

c)

d)

e)

08)1(2 2 x

i4153 and

no roots

i2131 and

17)Determine the revenue function if

and x represents number of items sold.

a)

b)

c)

d)

e)

52)( xxp

52)( xxR

xxR 7)( 23 52)( xxxR xxxR 52)( 2

3)( xR

18)Determine the profit function if

a)

b)

c)

d)

e)

132)(6)( 2 xxCandxxxR

134)( 2 xxxP

)132)(6()( 2 xxxxP

134)( 2 xxxP

138)( 2 xxxP

134)( 2 xxxP

19) The cost to feed a cow is $1 per day. The cow currently weighs 100kg and is gaining 0.5kg per day. The price per kg of beef is $2 and falling by 5 cents per day. The profit function is:

a)

b)

c)

d)

e)

xxxxP 1)05.02)(5.0100()(

xxxxP 1)205.0)(1005.0()(

)05.02)(5.0100()( xxxP

xxxxP 1)52)(5.0100()(

)5.02)(05.0100()( xxxP

20) Determine the value of k if the function has 2 real roots.

a)

b)

c)

d)

e)

2/1k

0842 xkx

2/1k

2k

2k2/1k

Unit 2 Test ReviewANSWERS

1) Determine the number of zeros.

a)

b)

c)

d)

e)

4)3(2)( 2 xxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

2) Determine the number of zeros.

a)

b)

c)

d)

e)

2)1(2)( xxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

3) Determine the number of zeros.

a)

b)

c)

d)

e)

)2)(2(2)( xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

4) Determine the number of zeros.

a)

b)

c)

d)

e)

342)( 2 xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

acb 42

40

)3)(2(442

5) Determine the number of zeros.

a)

b)

c)

d)

e)

22)( 2 xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

acb 42

4

)2)(1(422

6) Determine the number of zeros.

a)

b)

c)

d)

e)

44)( 2 xxxf

0 zeros

1 zero

2 zeros

3 zeros

Cannot be determined.

acb 42

0

)4)(1(4)4( 2

7) Select the correct statement about the equations corresponding to the graphs below.

a)

b)

c)

d)

e)

A and B would each have 2 real roots.

A and B would each have 2 imaginary roots.

A and B would each have 1 real root.

A would have 2 real roots while B would have no roots.

A would have 2 real roots while B would have 2 imaginary roots.

GRAPH A GRAPH BGraph A has 2 x-intercepts therefore 2 real roots,

Graph B has no x-intercepts therefore 2 imaginary roots.

8)Determine the vertex.

a)

b)

c)

d)

e)

142)( 2 xxxf

(-1, -1)

(2, 25)

(0, 1)

(-4, 17)

(1, 7)

a

b

2

14

4

)1(f 1

9)Determine the vertex.

a)

b)

c)

d)

e)

1)4(2)( 2 xxf

(4, -1)

(2, 4)

(-4, 1)

(4, 1)

(-4,-1)

vertex form parabola.

10) Determine the vertex.

a)

b)

c)

d)

e)

)14)(23()( xxxf

(2/3, -1/4)

(5/12, -2)

(5/24 , -121/48)

(-13/8, 13/6)

(2/3, 1/4)

x-ints: 2/3 and -1/4

axis: (2/3 + -1/4) / 2

=5/24

OV: f(5/24)

=-121/48

11) Determine the vertex.

a)

b)

c)

d)

e)

xxxxf 2)3)(1(2)(

(1, 1)

(1, -2)

(-1/2 ,-13/2)

(1/2,-9.5)

(-1, -6)

xxxxf 2)32(2)( 2 622)( 2 xxxf

a

b

2

2/1

4/2

)2/1(f 2/13

12)One root of an equation is 2 + 3i. Determine the other root.

a)

b)

c)

d)

e)

-2 – 3i

2 – 3i

2 + 3i

5i

-2 + 3i

The other root is known as the complex conjugate. Switch the sign of the imaginary part of the number.

13)Determine the roots.

a)

b)

c)

d)

e)

1/2 and -3/2

-1 and -3

6 and -2

-6 and 2

-1/2 and 3/2

0344 2 xx

1226

426

03264 2 xxx

0)32(1)32(2 xxx

0)32)(12( xx

14)Determine the roots.

a)

b)

c)

d)

e)

2

2 and -2

+2i and -2i

no roots

-4

082 2 x

82 2 x

42 x

4x

ix 2

15)Determine the roots.

a)

b)

c)

d)

e)

0744 2 xx

i62

1

2

1

no roots

22

1

62

1

2

1

i22

1

)4(2

)7)(4(4)4(4 2 x

8

964 x

8

16164 x

8

64

8

4 ix

ix 62

1

2

1

16)Determine the roots.

a)

b)

c)

d)

e)

08)1(2 2 x

i4153 and

no roots

i2131 and

8)1(2 2 x

4)1( 2 x

ix 21

ix 21

17)Determine the revenue function if

and x represents number of items sold.

a)

b)

c)

d)

e)

52)( xxp

52)( xxR

xxR 7)( 23 52)( xxxR xxxR 52)( 2

3)( xR

p(x) is the price. Multiply the price by the number of items sold to get revenue.

18)Determine the profit function if

a)

b)

c)

d)

e)

132)(6)( 2 xxCandxxxR

134)( 2 xxxP

)132)(6()( 2 xxxxP

134)( 2 xxxP

138)( 2 xxxP

134)( 2 xxxP

)()()( xCxRxP

)132(6)( 2 xxxxP

19) The cost to feed a cow is $1 per day. The cow currently weighs 100kg and is gaining 0.5kg per day. The price per kg of beef is $2 and falling by 5 cents per day. The profit function is:

a)

b)

c)

d)

e)

xxxxP 1)05.02)(5.0100()(

xxxxP 1)205.0)(1005.0()(

)05.02)(5.0100()( xxxP

xxxxP 1)52)(5.0100()(

)5.02)(05.0100()( xxxP

20) Determine the value of k if the function has 2 real roots.

a)

b)

c)

d)

e)

2/1k

0842 xkx

2/1k

2k

2k2/1k

042 acb

0)8)((4)4( 2 k

03216 k

1632 k

2/1k

Tomorrow we will review mostly problem solving questions.

Begin working on the assigned textbook review.

These questions are on CLASSNET if you want to try them again.