Transcript Monkey Sheet PowerPoint File

CAPT Practice
Jan 2013
Pythagorean Theorem
Holding an electronic measurement tool 5.5 feet
above the ground, the rock climber measures her
horizontal distance from the cliff to be 32.25 feet
and the distance to the top of the cliff
to be 54.5 feet.
How high, in feet, is the cliff
from the ground?
Pythagorean Theorem
Horizontal distance from the cliff: 32.25 ft
Distance to the top of the cliff: 54.5 ft.
How high, in feet, is the cliff
from the ground?
Pythagorean Theorem
How high, in feet, is the cliff
from the ground?
Pythagorean Theorem:
a2+b2 = c2
where c = hypotenuse.
32.252+b2 = 54.52
1040.1+b2 = 2970.25
b2 = 1930.15
b = 43.93
43.93
Pythagorean Theorem
How high, in feet, is the cliff
from the ground?
b = 43.93 is the side of the triangle
Height of cliff is 43.93
+ 5.5
49.43ft
Starts 5.5 ft above
the ground
43.93
Pythagorean Theorem
How high, in feet, is the cliff
from the ground?
Height of cliff is 43.93
+ 5.5
49.43ft
49 43
Transformation
Nailah’s graphics software allows her to draw
and rotate images by a specified angle.
Nailah begins by drawing hexagon E
and sqaure D.
She plans to rotate square D
to produce square F.
By how many degrees
must Nailah instruct the software to rotate
square D to produce square F?
Transformation
By how many degrees must Nailah instruct
the software to rotate square D to produce
square F?
A Regular Hexagon has 60-degree
Rotational Symmetry.
So Rotating 120-degrees will move
square D to square F.
60◦
60◦
Data/Statistics
• Lorna swam 30 laps per day for the first 6 days of
swim practice.
• She swam 40 laps per day for the next 4 days of
practice.
• What was the mean number of laps that Lorna
swam per day for these 10 days?
6(30) + 4(40) = 180 + 160 = 340 total laps
Average = 340 / 10 = 34 laps per day
Number Properties
On the real number line between what two
consecutive integers is 7 ?
22 = 4
32 = 9 so, it is between 2 and 3.
7
Prom Candles
Chloe is responsible for making
32 centerpieces for the tables
at this years’ school prom.
She will place 8-inch tall candles
into prism vases of the same
height. Then she will fill the
vases with blue sand.
Prom Candles
Sand is sold in 240 cubic inch
Bags at $4.79 per bag.
How much will Chloe spend on
sand to create 32 centerpieces?
Prom Candles
Plan:
1. Find volume of the Prism.
2. Find volume of Cylinder.
3. Find the difference in volumes.
4. Divide by 2 (only half filled).
5. Times 32 Centerpieces
6. Determine number of bags.
7. Find Cost of sand.
Prom Candles
1. Find volume of the Prism.
V = lwh
V=5x5x8
V = 200 in3
2. Find volume of Cylinder.
V= Πr2h
r = 4.5/2 = 2.25
V = 3.14(2.25)2(8)
V = 127.17in3
Prom Candles
1. Find volume of the Prism.
V = lwh = 200 in3
2. Find volume of Cylinder.
V= Πr2h = 127.17in3
3. Find the difference in volumes.
200 in3 - 127.17in3 = 72.83
4. Divide by 2 (only half filled).
72.83 / 2 = 36.415in3
5. Times 32 Centerpieces
32(36.415) = 1165.28in3
Prom Candles
How much will Chloe spend on
sand to create 32 centerpieces?
She needs 1165.28in3 of sand
Sand is sold in 240 cubic inch
Bags at $4.79 per bag.
6. Determine number of bags.
1165.28 / 240 = 4.86bags
7. Find Cost of sand.
5 bags x 4.79 = $23.95
Prom Candles
How much will Chloe spend on
sand to create 32 centerpieces?
Chloe will spend $23.95
on sand for the centerpieces.
Data Displays
A car manufacturer is testing a new car on a test track.
The graph below represents the relationship between
The number of miles driven and amount of gas left.
Data Displays
Write an equation that relates
gas in the tank (y)
to miles driven (x).
Equation of a line can be written
in slope intercept form
y = mx + b
Where m is the slope
And b is the y-intercept
Data Displays
Write an equation that relates
gas in the tank (y)
to miles driven (x).
y = mx + b
m is the slope = rise
run
slope = -2/75
And b is the y-intercept
The y-intercept = 12
Rise = -2
Run = 75
Data Displays
Write an equation that relates
gas in the tank (y)
to miles driven (x).
Rise = -2
y = mx + b
slope = -2/75
The y-intercept = 12
2
y   x  12
75
Run = 75
Percents
Martin correctly answered 90% of the questions
on a math test that contained exactly 40
questions. How many of the questions did he
answer incorrectly?
90% correct means 10% incorrect
10% of 40 = 4
Martin answered
4 questions incorrectly.
p
is

100 of
10
x

100 40
100x = 400
X=4
Percent
The graph shows a
family’s annual expenses.
If the family’s annual
income is $40,000,
what is the family’s annual
expense for housing?
30% of $40,000
30
x
100x = 1,200,000

X = 12,000
100 40000
Probability
To win a game, Yepa must get
a sum of 8 on her next two
spins.
All the sections of the
spinner are of equal size.
What is the probability that
the results of Yepa’s next two
spins will have a sum of 8?
Probability
What is the probability that
the results of Yepa’s next two
spins will have a sum of 8?
Spin
1
2
3
4
5
1
2
3
4
5
6
2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
Probability of getting a sum of 8 is 3/25
3/25 is 0.12 or 12%
Pythagorean Theorem
What is the length, in units,
of line segment AC?
Pythagorean Theorem:
a2+b2 = c2
where c = hypotenuse.
32 + 42 = c2
9 + 16 = c2
25 = c2
C=5
C
4
3
Area
• What is the area, in square units, of triangle
ABC?
A = ½bh
A = ½(3)(4)
A = ½(12) = 6units 4
3
Area
• Draw a rectangle that has the same area in
square units as triangle ABC.
A = 6units
Dimensions: 3 by 2
(same base by
½ the height)
4
2
3
Martin needs to estimate the cost of a lunch for
himself and 12 of his friends at a Mystic restaurant.
•
•
•
•
•
•
The highest priced menu item is $8.85
The lowest priced menu item is $4.35
Drinks are $0.90 each with free refills
Everyone will have a $1.75 dessert
A 6% sales tax will be added to the bill
He will leave the serer a 15% tip based on the bill
after the tax
• He will pay the bill in cash
• What is a reasonable estimate for the price of
the lunch?