Bell Ringers ACT based 2014-2015 - PowerPoint Presentation

Slide1

Bell Ringers

ACT based

2014-2015Slide2

Verbally expanded

4

x 10

-5

0.00004 (decimal, 4 zero’s, 4)

Bell RingerSlide3

Equivalent form of

(x)(x)(x)(x

3

)?X

6

Bell RingerSlide4

How many solutions are there to the equation x

2

- 7 = 0?

2

√7 & √-7

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There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?

Solution

If 1 green and 1 blue ball are taken from the box, then there are 7 green, 3 blue and 3 white balls, a total of 13 balls. If one ball is selected at random, the probability that it is blue is given by

3

/ 13

Bell RingerSlide6

The length of a rectangle is 3 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?

Solution

If the width is 5 in and the length is 3 times the width, then the length is 3 * 5 = 15 in; The area is given by

5 * 15 = 75 in2 .

5 in

3(w) in

Area Formula = L x W

Bell RingerSlide7

For all x >2,

(

2x

2 + 2x - 12) / (x - 2) simplifies to ?

Solution

1

st

) factor: 2x

2

+ 2x –

12

2

nd

) GCF: 2(x

2

+ x - 6)

3

rd

) factor:

(x

2

+ x - 6)

(don’t forget to carry 2 along)

2(x + 3)(x - 2)

4

th

) Simplify:

[ 2(x + 3)(x - 2) ] / (x - 2) =

2(x + 3) Slide8

If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

Solution

Let x be the length of second leg and apply Pythagoras theorem as follows:

102 = 5

2

+ x

2

Solve for x

x

= √(100 - 25) = √75 =

5 √3

in

Bell RingerSlide9

If 8y = 3x - 11, then x =

Solution:

Solve for x:

X = 8/3y + 11/3

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2(x -

8

)

equivalent?

solution

:

2x - 16

X ?

s

olution

:

set equal to zero: 2x - 16 = 0

2x = +16

X= 8

Bell RingerSlide11

What is the slope of the line

4x = -3y + 8

Solution:

Solve for y:

Y = - 4/3 x + 8/3

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When graphed in the (

x,y

) coordinate plane, at what point do the lines 2x + 3y = 5 and x = -2 intersect?

Solution

To find the point of intersection of two lines, we need to solve the system of equations made up of the equations of the lines. We need to solve the following system of equations. 2x + 3y = 5 and x = - 2 Substitute x by -2 in the equation 2x + 3y = 5 and solve for y.

2(-2) + 3y = 5

3y = 9

y = 3

The two lines intersect at (-2 , 3).

Bell RingerSlide13

If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?

Solution

We first convert the speed into miles per minute.

66 / 60 = 1.2 miles per minute We now use the speed and the time to find the distance.

1.2 (miles/minute) * 99 minutes = 108.9 miles

D=

rt

Bell RingerSlide14

What is the smallest value of x that satisfies the equation

x(x + 4) = -3

Solution: -3

What if it is an inequality?

x(x + 4) > -3

Solution: any # greater than -3; to the right of -3 but NOT including -3

Bell RingerSlide15

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Describe the procedure used to solve an equation for a variable.Slide16

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What is one important difference, with respect to the answer, between solving equations and solving inequalities?

One answer ; Range of answers

**more on flash but must be checked**Slide17

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Graph: │x │> 3Slide18

NOT

CHECKEDIf

x + 4y = 5 and 5x + 6y = 7, then 3x + 5y = ?Slide19

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What important information about a line can you get from a linear equation ?

y

= mx + bSlide20

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What is usually the first step in factoring a quadratic trinomial that is not a perfect square and whose terms have no common factor greater than 1?

Find two integers that have product

ac

and sum b

.

a

x ±

bx

± c = 0

2Slide21

Bell Ringer

Factor the following:

x

- x – 6x + 2x – 3

2

2

(x – 3) (x + 2)

(x + 3) (x – 1)Slide22

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Factor completely

x

+ 2x – 15

2

(x + 5) (x – 3)Slide23

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Factor completely

3x + 2x – 5

2

(3x + 5) (x – 1)Slide24

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Completely factor this polynomial

9m - 12m + 4

2

(3m – 2)(3m – 2)Slide25

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Factor

y

+ 12y + 36

2

(y + 6)(y + 6)Slide26

Bell Ringer

Factor

9y + 12 y + 4

2

(3y + 2)(3y + 2)

See a pattern with perfect squares?Slide27

Bell Ringer

Completely factor this polynomial

m

- 12m +36

2

(m – 6)(m – 6)Slide28

Bell Ringer

An accounting firm must regulate the office temperature to protect its computers. The equation │½T – 40 │ = 3, gives the range of acceptable air temperatures for the office in degrees Fahrenheit. What is the range of temperature?

E

quation: │1/2T – 40 │ = 3

S

olve using rules for Absolute value

1/2T – 40 = 3

1/2T – 40 = -3

74



86Slide29

Bell Ringer

What is the sum of the solutions to the equation

│5M – 30 │= 10

12Slide30

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What is the solution set of this equation

│3y – 4│ + 1 = 6

{3,-1/3 }Slide31

Bell Ringer

What is the product of the solutions to the equation

│2x – 1│ = 3

-2

2X – 1 = 3

2X = 4

X = 2

2X – 1 = -3

2X = -2

X = -1Slide32

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Graph the solution of the absolute value equation

2│x – 1│+3 = 11

-3

5

0Slide33

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Solve the inequality

│2c – 10│ > 16

C > 13 C < - 3

ORSlide34

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Graph the solution to this inequality

│X + 4│

< 12

-16

8

0Slide35

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Factor…not factorable? Is this polynomial PRIME ?

m

- 18m + 30

b

- 4ac

2

2

(-18) – 4(1)(30) = 14.3

2

P R I M ESlide36

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Completely factor

x

+2x - 4

b - 4ac

2

2

(2) - 4(1)(-4)

2Slide37

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Factor

x

+ 3x + 18

2

b

- 4ac

2

P R I M ESlide38

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What is the possible base and height for the area of this rectangle?

A = x + x - 6

2

(x + 3)(x – 2)Slide39

Bell Ringer

The area of a rectangle id given by

A = 6x y + 4y x and the width of the rectangle is w = 2xy. What is the length,

l, of the rectangle if l =

A W

2

2

L = 3x + 2ySlide40

Bell Ringer

What is the area of the below rectangle ?

4x

3x + 5y

12x + 20xy

2Slide41

Bell Ringer

What is the area of the triangle below ?

A =

bh

2

2x + 7

3x - 9

6x + 3x – 63

2

2Slide42

Bell Ringer

A volleyball court is shaped like a rectangle. It has a width of x meters and a length of 2x meters.

What is the area of this court?

What is the perimeter of this court?

2x

2

6xSlide43

Bell Ringer

A rectangle has the length (x+3) and a width of (x – 1).

What is the perimeter?

What is the area?

4x + 4

x

+2x - 3

2Slide44

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Find the greatest common factor:

36x y + 108x + 54xy

3

2

2Slide45

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What is the area of the circle below ?

3

Hint: look at the formula sheet for formula

2.25∏Slide46

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When Robert was born, his grandfather invested $1,000 for his college education. At an interest rate of 4.5%, compounded annually, how much would Robert have at age 18 ?

A = P (1 + r)

t

2208Slide47

Bell Ringer

Evaluate the following algebraic expression:

(8xy + 6x y + 17y ) – (3x y – 6y + 3y )

2

2

2

2

2Slide48

Bell Ringer

Which of the following linear equations when graphed on a coordinate grid has the steepest slope? You will need to support your answer.

Y = 1/3x – 2

Y = 5/2x – 1Y = 3x + 1/4

Y = 4x + 3/5Slide49

Bell Ringer

Conner went to visit his friend in Houston. He drove at a constant rate of 55 miles per hour, and it took 3 hours to arrive. What was the total distance

Conner drove?