MCA Formula Review Packet

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MCA- Formula Review Packet

MCA Formula Review Packet

7 6 2 1 3 4 5

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MCA- Formula Review Packet 29 25 26 27 28 30 19 20 21 22 23 24 18 15 16 17 10 11 12 13 14 8 9

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A) Your parents ask you to water the lawn. It is a square plot that is 15 ft on each side and it has a square cement fountain in the center that is 3 ft on each side. What is the area of the lawn that you will water?

B) The figure below is made up of two squares with the areas shown. What is the length of x?

A) A field is 200 m by 260 m. A barn 22 m by 29 m is built in the field. How much area is left over?

B) The area of the parallelogram is _____.

A) ) Find the area (not drawn to scale): _B)_{Find the height of the triangle if the area is 10.26} (not drawn to scale).

8100 1600 x 6.7 cm 2.4 cm 7 cm

cm

2 2.7 cm 8 cm

1

2

3

(4)

(5)

A) Find the area. B) Find the area.

A) Given:

If AC = 18 and BD = 15, find the area of kite ABCD.

B) Find the area of this rhombus.

A) The area of the quadrilateral is _____.

B) A trapezoid has an area of 24 square units. The height is 3 units and the length of one of the bases is 5 units. Find the length of the other base.

AC

⊥

BD

4

5

5 33 cm

29 cm

55º

33.7 cm

43 cm

52º

50º

6

5

4

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A) A regular hexagon has an apothem of 2 and a side

length of . Its area is _____.

B) Find the length of each side of a regular polygon to the nearest foot if a ≈ 80 ft, n = 20, and A ≈ 20,000 sq ft.

A) Find the area of the circle. Use = 3.14.

B) The figure below represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Use

A) The circumference of a circle is Find the diameter and the radius of the circle.

B) The tires of an automobile have a diameter of 22 inches. If the wheels revolve ten times, how far does the automobile move? (Round the result to the nearest tenth of a foot.)

4 3

3 π

14 π

≈

314 . .

2.1 m 4.2 m

84 π

cm.

8

9

10

7

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A) For a circle of radius 9 feet, find the arc length subtended by a central angle of 12 .

B) For a circle of radius 8 feet, find the arc length of a central angle of 60 . Leave your answer in terms of .

A) Find the length of the arc of a circle if the central angle is 5π/6 and the radius is 1 inch.

B) Find the length of the arc of a circle if the central angle is 40 radians and the radius is 3 ft.

A) Find the area of a sector of a circle with a radius of 4 and a central angle of 90˚.

B) Find the area of a sector of a circle with a radius of 5 and a central angle of 60˚.

s

°

π

11

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A) Find the area of a sector of a circle with a radius of 4 and a central angle of π/2 radians.

B) Find the area of a sector of a circle with a radius of 5 and a central angle of π/3 radians.

A) Find the volume of the cylinder below. (Round the result to one decimal place.)

B) The volume of the right prism below is _____.

A) Calculate the volume of the cone. Use = 3.14

B) The base of the pyramid below is a nonregular heptagon with an area of 30.0 square yards. The height of the pyramid is 6.6 yards. Find the volume of the pyramid.

π

8 m 7 m

13

14

15

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A) How much air can be pumped into a basketball if its maximum diameter measures 20 cm?

B) Find the length of a radius of a sphere whose volume is 972π cm3.

A) Find the length of the leg of this right triangle. Give an approximation to 3 decimal places.

B) How long is a string reaching from the top of a 15 ft pole to a point 13 ft from the base of the pole?

A) Find the distance between the points (4, 3) and (2, –2). B) Find the length of each side of ▲ABC. Then tell whether ▲ABC is isosceles or scalene: A(-3, -3), B(1, -6), C(-2, -2)

a

23 30

16

17

18

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A)

Solve by the quadratic formula:

4x

2

+ 16x + 11 = 0

B) A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d = -16t2 - 2t + 445. How long after the rock is thrown is it 440 feet from the ground?

A) Write the variation and find the quantity indicated. x varies directly with y. If x is 128 when y is 160, find x when y is 180?

B) The weight, W, of a beam varies directly with its length, l. A 10 foot beam weighs 530 pounds. Write an equation relating W to l.

A) The variables x and y vary inversely. x = 7 when y = –4. Find an equation that relates the variables.

B) The price per person of renting a bus varies inversely with the number of people renting the bus. It costs $22 per person if 47 people rent the bus. How much will it cost per person if 74 people rent the bus?

19

20

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A) Write the expression represented by 9C6 . B) How many different 3-card hands can be drawn from a standard deck of 52 playing cards?

A) Write the expression represented by 5P1. B) Find the number of distinguishable permutations of the letters HONEST.

A)

Find the value of x and y.

B) Find the value of x and y.

22

23

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A) Find the value of x. B) Find the value of x and y.

A) Write sin A.

B) A ladder 18 feet long makes an angle of 61 with the ground as it leans against a barn. How far up the side of the barn does the ladder reach?

A) Write cos A.

B) Liola drives 12 km up a hill that is at a grade of What horizontal distance, to the nearest tenth of kilometer, has she covered?

A C B 24 7 25

°

A C B 15 8 17

12°.

26

27

25

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A) At a distance of 27.4 feet from a tree, the angle of elevation to the top of the tree is 40°. How tall is the tree?

B) Solve for x to the nearest degree.

A) If sin θ = 12/13 and cos θ = 5/13, then tan θ = _____. B) Find tan θ when cos θ = 4/5 and sin θ = -3/5.

A) Use sin2θ_{+ cos}2θ_{= 1 to derive an identity involving} tan2θ_{and sec}2θ_.

B) Verify the identity:

x x x x sin cos 1 cos 1 sin + = − 40 ° 27.4 ft

18

8 x°

28

29

30

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Formula Review Packet Answer Key

A B 1

_{216 ft}

2

_{130 units}

2

_{51,362 m}

2

680

3

_{8.04 cm}

2

_{7.6 cm}

4

_{392 cm}

2

_{571 cm}

2 5

_{135 sq. units}

₄₀

6

_{380 sq. units}

_{11 units}

7

₈

₃

_{sq. units}

_{25 ft.}

8

_153.86

_{41.5422 m}

2 9

_{84 cm; 42 cm}

_{57.6 ft}

10

_π

5

3 ft

π

3

8 ft

11

_{2.62 in}

_{120 ft}

12

_4π

_π

6

25 ft

13

_4π

_π

6

25 ft

14

_{89.7 π= 595.8 ft}

3

_{60 ft}

3 15

_{410.29 m}

3

_{66 yd}

₃

16

_π

3 4000

cm

3

9 cm

17

_19.261

₃₉₄

_ft

18

₂₉

AB=BC=5

AC= 2 , isos

19

2

5 4 ±

−

2

1 sec

20

_x

_{=ky; 144}

_W

_=53l

21

_y

₌

x

28 −

$13.97

22

(

9

6 )

!

6 !

!

9 ⋅

−

22,100

23

(

5

1 )

!

5 −

6!=720

24

x

=

7

3 y

= 14

x

= 10

y

=

10

3

25

_x

₌

2

5 x

=

7

2 y

= 7 +

7

3

26

25

7 15.74 ft

27

17

15 11.7 km

28

_{23 ft}

₆₆

sq. units

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MCA- Formula Review Packet 29

5

12

4

3 −

30

θ

2 2 2 2 2 2 2 2 2

sec

1 tan

cos

1 cos

cos

sin

1 cos

sin

=

+

=

+

=

+

x

sin

cos

1 sin

cos

1 sin

cos

1 sin

)

cos

1 (

sin

cos

1 cos

1 )

cos

1 (

sin

cos

1 cos

1 sin

sin

cos

1 cos

1 sin

2 2