CAPT Practice

Jan 2013

Pythagorean TheoremHolding an electronic measurement tool 5.5 feet above the ground, the rock climber measures herhorizontal 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

How high, in feet, is the cliff from the ground?

Horizontal distance from the cliff: 32.25 ft

Distance to the top of the cliff: 54.5 ft.

Pythagorean TheoremHow high, in feet, is the cliff from the ground?

Pythagorean Theorem:

a2+b2 = c2

where c = hypotenuse.

Hypote

nuse

:

32.252+b2 = 54.52

1040.1+b2 = 2970.25b2 = 1930.15b = 43.93

43.93

Pythagorean TheoremHow high, in feet, is the cliff from the ground?

Hypote

nuse

:

b = 43.93 is the side of the triangle

43.93

Starts 5.5 ft above the ground

Height of cliff is 43.93 + 5.5 49.43ft

Pythagorean TheoremHow high, in feet, is the cliff from the ground?

Height of cliff is 43.93 + 5.5 49.43ft

4 9 4 3

TransformationNailah’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?

TransformationBy how many degrees must Nailah instruct the software to rotate square D to produce square F?

60◦

60◦A Regular Hexagon has 60-degreeRotational Symmetry.

So Rotating 120-degrees will movesquare D to square F.

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 ?

22= 4 32 = 9 so, it is between 2 and 3.

7

7

Prom Candles

Chloe is responsible for making 32 centerpieces for the tables at this years’ school prom.

She will place 8-inch tall candlesinto prism vases of the same height. Then she will fill the vases with blue sand.

Prom Candles

Sand is sold in 240 cubic inchBags at $4.79 per bag.

How much will Chloe spend onsand 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 Centerpieces6. Determine number of bags.7. Find Cost of sand.

Prom Candles1. Find volume of the Prism.V = lwh

2. Find volume of Cylinder.V= Πr2h

V = 5 x 5 x 8V = 200 in3

r = 4.5/2 = 2.25V = 3.14(2.25)2(8)V = 127.17in3

Prom Candles1. Find volume of the Prism.V = lwh = 200 in3 2. Find volume of Cylinder.V= Πr2h = 127.17in3 3. Find the difference in volumes.

4. Divide by 2 (only half filled).

5. Times 32 Centerpieces

200 in3 - 127.17in3 = 72.83

72.83 / 2 = 36.415in3

32(36.415) = 1165.28in3

Prom Candles

How much will Chloe spend onsand to create 32 centerpieces?

She needs 1165.28in3 of sandSand is sold in 240 cubic inchBags at $4.79 per bag.6. Determine number of bags.

7. Find Cost of sand.1165.28 / 240 = 4.86bags

5 bags x 4.79 = $23.95

Prom Candles

How much will Chloe spend onsand to create 32 centerpieces?

Chloe will spend $23.95on sand for the centerpieces.

Data DisplaysA car manufacturer is testing a new car on a test track.The graph below represents the relationship betweenThe number of miles driven and amount of gas left.

Data DisplaysWrite 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 + bWhere m is the slopeAnd b is the y-intercept

Data DisplaysWrite an equation that relates gas in the tank (y)to miles driven (x).

y = mx + bm is the slope =

And b is the y-intercept

run

rise

Rise = -2

Run = 75

slope = -2/75

The y-intercept = 12

Data DisplaysWrite an equation that relates gas in the tank (y)to miles driven (x).

y = mx + b

Rise = -2

Run = 75slope = -2/75The y-intercept = 12

1275

2 xy

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 =40100

10 x

of

isp

100100x = 400 X = 4

4

Martin answered 4 questions incorrectly.

PercentThe 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

40000100

30 x 100x = 1,200,000

X = 12,000

ProbabilityTo 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?

ProbabilityWhat 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 3/253/25 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

4

3

9 + 16 = c2

25 = c2

C = 5

C

Area

• What is the area, in square units, of triangle ABC?

4

3

A = ½bh A = ½(3)(4)A = ½(12) = 6units

Area

• Draw a rectangle that has the same area in square units as triangle ABC.

4

3

A = 6units

2

Dimensions: 3 by 2(same base by ½ the height)

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?