Bell Ringers
ACT based
2014-2015
Bell Ringer
Verbally expanded
4 x 10-5
0.00004 (decimal, 4 zero’s, 4)
Bell Ringer
Equivalent form of (x)(x)(x)(x3)?
X
6
Bell Ringer
How many solutions are there to the equation x2 - 7 = 0?
2
√7 & √-7
Bell Ringer
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 Ringer
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? Area Formula = L x W
3(w) in
5 in
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 .
For all x >2,
(2x2 + 2x - 12) / (x - 2)
simplifies to ?
Solution
1st) factor: 2x2 + 2x – 12
2nd) GCF: 2(x2 + x - 6)
3rd) factor: (x2
+ x - 6) (don’t forget to carry 2 along)
2(x + 3)(x - 2)
4th) Simplify:
[ 2(x + 3)(x - 2) ] / (x - 2) =
2(x + 3)
Bell Ringer
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 = 52 + x2
Solve for x
x = √(100 - 25) = √75 =
5 √3 in
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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?
solution:
set equal to zero: 2x - 16 = 0
2x = +16
X= 8
Bell Ringer
What is the slope of the line
4x = -3y + 8
Solution:
Solve for y:
Y=
- 4/3 x + 8/3
Bell Ringer
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 Ringer
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 Ringer
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 Ringer
Describe the procedure used
to solve an equation for a
variable.
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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**
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Graph: │x │> 3
NOT CHECKEDIf x + 4y = 5 and
5x + 6y = 7, then 3x + 5y = ?
Bell Ringer
O What important information
about a line can you get from
a linear equation ?
y = mx + b
Bell Ringer
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.
ax2 ± bx ± c = 0
Bell Ringer
Factor the following:
2
x -x–6
(x – 3) (x + 2)
2
x + 2x – 3
(x + 3) (x – 1)
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Factor completely
2
x + 2x – 15
(x + 5) (x – 3)
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Factor completely
2
3x + 2x – 5
(3x + 5) (x – 1)
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Completely factor this polynomial
2
9m - 12m + 4
(3m – 2)(3m – 2)
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Factor
2
y + 12y + 36
(y + 6)(y + 6)
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Factor
See a pattern
with perfect
squares?
2
9y + 12 y + 4
(3y + 2)(3y + 2)
Bell Ringer
Completely factor this polynomial
2
m - 12m +36
(m – 6)(m – 6)
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?
Equation:
│1/2T – 40 │ = 3
Solve using rules for Absolute value
1/2T – 40 = 3
74  86
1/2T – 40 = -3
Bell Ringer
What is the sum of the solutions to the equation
│5M – 30 │= 10
12
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What is the solution set of this equation
│3y – 4│ + 1 = 6
{3,-1/3 }
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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 = -1
Bell Ringer
Graph the solution of the absolute value equation
2│x – 1│+3 = 11
-3
5
0
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Solve the inequality
│2c – 10│ > 16
C > 13
OR
C<-3
Bell Ringer
Graph the solution to this inequality
│X + 4│ < 12
8
-16
0
Bell Ringer
Factor…not factorable? Is this polynomial PRIME ?
2
m - 18m + 30
2
(-18) – 4(1)(30) = 14.3
2
b - 4ac
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Completely factor
2
x +2x - 4
2
(2) - 4(1)(-4)
b - 4ac
2
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Factor
2
x + 3x + 18
b - 4ac
2
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What is the possible base and height
for the area of this rectangle?
(x + 3)(x – 2)
2
A=x +x-6
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The area of a rectangle id given by
2
2
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
L = 3x + 2y
Bell Ringer
What is the area of the below
rectangle ?
3x + 5y
4x
2
12x + 20xy
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What is the area of the triangle below ?
2x + 7
A = bh
2
3x - 9
2
6x + 3x – 63
2
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?
2x
2
What is the perimeter of this court?
6x
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Bell Ringer
A rectangle has the length (x+3)
and a width of (x – 1).
What is the perimeter?
4x + 4
What is the area?
2
x +2x - 3
Find the greatest common
factor:
2
36x y + 108x + 54xy
3
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2
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What is the area of the circle below ?
3
2.25∏
Hint: look at the formula sheet for formula
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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
2208
Bell Ringer
Evaluate the following algebraic
expression:
2
2
2
2
2
(8xy + 6x y + 17y ) – (3x y – 6y + 3y )
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.
a) Y = 1/3x – 2
b) Y = 5/2x – 1
c) Y = 3x + 1/4
d) Y = 4x + 3/5
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?