MCA Formula Review Packet

MCA Formula Review Packet 1 3 4 5 6 7 The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis

8 9 10 1 11 13 14 15 16 17 18 19 0 1 3 4 5 6 7 30 8 9 The MCA-II / BHS Math Plan Page of 15 Copyright 005 by Claude Paradis

1 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? 8100 1600 x A) A field is 00 m by 60 m. A barn m by 9 m is built in the field. How much area is left over? B) The area of the parallelogram is. 3 A) ) Find the area (not drawn to scale): B) Find the height of the triangle if the area is 10.6 (not drawn to scale). cm 7 cm 6.7 cm 8 cm.4 cm.7 cm The MCA-II / BHS Math Plan Page 3 of 15 Copyright 005 by Claude Paradis

The MCA-II / BHS Math Plan Page 4 of 15 Copyright 005 by Claude Paradis

4 MCA- Formula Review Packet A) Find the area. B) Find the area. 9 cm 43 cm 50º 33 cm 55º 5º 33.7 cm 5 AC BD A) Given: If AC = 18 and BD = 15, find the area of kite ABCD. B) Find the area of this rhombus. 4 5 5 4 6 A) The area of the quadrilateral is. B) A trapezoid has an area of 4 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. The MCA-II / BHS Math Plan Page 5 of 15 Copyright 005 by Claude Paradis

7 MCA- Formula Review Packet A) A regular hexagon has an apothem of and a side length of 4 3 3. Its area is. B) Find the length of each side of a regular polygon to the nearest foot if a 80 ft, n = 0, and A 0,000 sq ft. 8 π 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 π 314.. 14.1 m 4. m 9 A) The circumference of a circle is Find the diameter and the radius of the circle. 84π cm. B) The tires of an automobile have a diameter of inches. If the wheels revolve ten times, how far does the automobile move? (Round the result to the nearest tenth of a foot.) 10 The MCA-II / BHS Math Plan Page 6 of 15 Copyright 005 by Claude Paradis

A) For a circle of radius 9 feet, find the arc length subtended by a central angle of 1. s B) For a circle of radius 8 feet, find the arc length of a central angle of 60. Leave your answer in terms of. π 11 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. 1 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. The MCA-II / BHS Math Plan Page 7 of 15 Copyright 005 by Claude Paradis

13 A) Find the area of a sector of a circle with a radius of 4 and a central angle of π/ radians. B) Find the area of a sector of a circle with a radius of 5 and a central angle of π/3 radians. 14 A) Find the volume of the cylinder below. (Round the result to one decimal place.) B) The volume of the right prism below is. 15 A) Calculate the volume of the cone. Use = 3.14 π 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. 8 m 7 m The MCA-II / BHS Math Plan Page 8 of 15 Copyright 005 by Claude Paradis

16 A) How much air can be pumped into a basketball if its maximum diameter measures 0 cm? B) Find the length of a radius of a sphere whose volume is 97π cm 3. 17 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? 30 a 3 18 A) Find the distance between the points (4, 3) and (, ). B) Find the length of each side of ABC. Then tell whether ABC is isosceles or scalene: A(-3, -3), B(1, -6), C(-, -) The MCA-II / BHS Math Plan Page 9 of 15 Copyright 005 by Claude Paradis

19 A) Solve by the quadratic formula: 4x + 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 -16t - t 445. How long after the rock is thrown is it 440 feet from the ground? 0 A) Write the variation and find the quantity indicated. x varies directly with y. If x is 18 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. 1 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 $ per person if 47 people rent the bus. How much will it cost per person if 74 people rent the bus? The MCA-II / BHS Math Plan Page 10 of 15 Copyright 005 by Claude Paradis

A) Write the expression represented by 9 C 6. B) How many different 3-card hands can be drawn from a standard deck of 5 playing cards? 3 A) Write the expression represented by 5 P 1. B) Find the number of distinguishable permutations of the letters HONEST. 4 A) Find the value of x and y. B) Find the value of x and y. The MCA-II / BHS Math Plan Page 11 of 15 Copyright 005 by Claude Paradis

5 A) Find the value of x. B) Find the value of x and y. 6 A) Write sin A. B) A ladder 18 feet long makes an angle of 61 with the B ground as it leans against a barn. How far up the side of the barn does the ladder reach? 5 7 A 4 C 7 A) Write cos A. B) Liola drives 1 km up a hill that is at a grade of B What horizontal distance, to the nearest tenth of kilometer, has she covered? 17 8 1. A 15 C The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis

8 A) At a distance of 7.4 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. 18 8 x 7.4 ft 40 9 A) If sin θ = 1/13 and cos θ = 5/13, then tan θ =. B) Find tan θ when cos θ = 4/5 and sin θ = -3/5. 30 A) Use sin θ + cos θ = 1 to derive an identity involving tan θ and sec θ. B) Verify the identity: sin x 1+ cos x = 1 cos x sin x The MCA-II / BHS Math Plan Page 13 of 15 Copyright 005 by Claude Paradis

Formula Review Packet Answer Key A B 1 16 ft 130 units 51,36 m 680 3 8.04 cm 7.6 cm 4 39 cm 571 cm 5 135 sq. units 40 6 380 sq. units 11 units 7 8 3 sq. units 5 ft. 8 153.86 41.54 m 9 84 cm; 4 cm 57.6 ft 10 3 8 π ft π ft 5 3 11.6 in 10 ft 5 1 4π π ft 6 5 13 4π π ft 6 14 89.7 π= 595.8 ft 3 60 ft 3 15 410.9 m 3 66 yd3 4000 16 π cm 3 3 9 cm 17 19.61 394 ft 18 9 AB=BC=5 AC=, isos 19 4 ± 5 1 sec 0 x=ky; 144 W=53l 1 8 y= x $13.97 3 4 9! ( 9 6 )! 6! 5! ( 5 1)! x = 7 3 y = 14 sq. units,100 6!=70 x = 10 y = 10 3 5 5 x = 7 x = y = 7 + 7 3 6 7 5 15.74 ft 7 15 17 11.7 km 8 3 ft 66 The MCA-II / BHS Math Plan Page 14 of 15 Copyright 005 by Claude Paradis

9 30 1 5 sin θ + cos sin θ cos + cos θ cos θ = 1 tan θ + 1 = sec θ θ 1 = θ cos θ 3 4 sin x 1+ cos x = 1 cos x sin x sin x 1+ cos x 1+ cos x = 1 cos x 1+ cos x sin x sin x(1 + cos x) 1+ cos x = 1 cos x sin x sin x(1 + cos x) 1+ cos x = sin x sin x 1+ cos x 1+ cos x = sin x sin x The MCA-II / BHS Math Plan Page 15 of 15 Copyright 005 by Claude Paradis