MCA/GRAD Formula Review Packet

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 C) The perimeter of a square is 24 meters. Find its area. D) Find the area of a square inscribed in a circle with a radius 6 cm long. 2 A) Find the perimeter and area of a rectangle with length 250 ft and width 45 ft. B) 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? The MCA-II / BHS 2 Math Plan GRAD Page 3 of 16 Portions Copyright 2005 by Claude Paradis

C) The area of the parallelogram is. D) The area of the parallelogram is. 3 A) Find the area: B) Find the area: 5 ft 22 ft 9 cm 6. cm.8 cm 2.4 cm C) D) Find the height of the triangle if the area is 10.26 (not drawn to scale). cm 2 8 cm 2. cm The MCA-II / BHS 2 Math Plan GRAD Page 4 of 16 Portions Copyright 2005 by Claude Paradis

4 A) Find the area: B) Find the area: m 35 10m 3m 115 4m C) Find the area. D) Find the area. 29 cm 43 cm 50º 33 cm 55º 52º 33. cm 5 A) Find the area of the quadrilateral. (not drawn to scale) B) An expression for the area of kite ABCD is. 4 3 8 4 The MCA-II / BHS 2 Math Plan GRAD Page 5 of 16 Portions Copyright 2005 by Claude Paradis

C) Given: AC BD If AC = 18 and BD = 15, find the area of kite ABCD. D) 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 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. C) Find the area: 2 D) The area of a trapezoid is 198 in. If the height is 10 16 in. in. and the longer base is 31 in., what is the length of the shorter base? Round your answer to the nearest tenth. 8 in. 13 in. 24 in. The MCA-II / BHS 2 Math Plan GRAD Page 6 of 16 Portions Copyright 2005 by Claude Paradis

A) A regular hexagon has an apothem of 2 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 = 20, and A 20,000 sq ft. C) Find the area of a regular polygon with a 12 cm and p 81.6 cm. D) Find the perimeter of a regular polygon to the nearest tenth of a meter if a 9 m and A 259.2 m 2. A) Find the area of a circle with radius 2 cm. Use 3.14 for. π 8 B) Find the area of the circle. Use = 3.14. π 14 The MCA-II / BHS 2 Math Plan GRAD Page of 16 Portions Copyright 2005 by Claude Paradis

C) The figure below represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Use π 314.. D) Find the area of the circle with radius 15 cm. Use 3.14 for π. 2.1 m 4.2 m 9 A) Find the circumference of the circle. Use = 3.14. π B) Find the circumference of the circle. Use = 3.14. π 14 49 in. C) The circumference of a circle is 84π cm. Find the diameter and the radius of the circle. D) 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.) The MCA-II / BHS 2 Math Plan GRAD Page 8 of 16 Portions Copyright 2005 by Claude Paradis

10 s A) For a circle of radius 9 feet, find the arc length B) For a circle of radius 8 feet, find the arc length of a subtended by a central angle of 12. 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. 12 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 2 Math Plan GRAD Page 9 of 16 Portions Copyright 2005 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/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. 14 A) Find the volume of the rectangular prism. B) An aquarium in a restaurant is a rectangular prism and measures 3.5 feet by 4 feet by 4 feet. What is the volume of the aquarium? 1 m 3 m 2 m C) Find the volume of the cylinder below. (Round the result to one decimal place.) D) The volume of the right prism below is. The MCA-II / BHS 2 Math Plan GRAD Page 10 of 16 Portions Copyright 2005 by Claude Paradis

15 A) The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume. B) The volume of the pyramid below is. 8 ft 6 ft 2 ft C) Calculate the volume of the cone. Use = 3.14 π D) 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 m 16 A) Find the volume of a sphere 10 ft in diameter. Use π 314. and round your answer to the nearest tenth. B) How much air can be pumped into a basketball if its maximum diameter measures 20 cm? The MCA-II / BHS 2 Math Plan GRAD Page 11 of 16 Portions Copyright 2005 by Claude Paradis

C) Find the length of a radius of a sphere whose volume is 92π cm 3. D) Refer to the figure below. The volume of the sphere is about. 1 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 23 C) A set of Pythagorean triples is. [A] 1, 1, 2 [B] 3, 5, 9 [C] 6, 9, 12 [D] 5, 12, 13 D) A radio station is going to construct a 6-foot tower for a new antenna. The tower will be supported by three cables, each attached to the top of the tower and to points on the roof of the building that are 8 feet from the base of the tower. Find the total length of the three cables. The MCA-II / BHS 2 Math Plan GRAD Page 12 of 16 Portions Copyright 2005 by Claude Paradis

18 A) The distance between points A and B is. B) Find the distance between the points (4, 3) and (2, 2). y 6 A 6 6 x B 6 C) 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) D) Find the distance between the points (9, 5) and (6, 1). 19 A) Write sin A. B) Find sin P. B 25 A 24 C 25 24 P The MCA-II / BHS 2 Math Plan GRAD Page 13 of 16 Portions Copyright 2005 by Claude Paradis

C) 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? D) Evaluate x. Round the result to the nearest hundredth. x 25 44 20 A) Write cos A. B) Find cos P. B 1 8 25 A 15 C 24 P C) Liola drives 12 km up a hill that is at a grade of 12. What horizontal distance, to the nearest tenth of kilometer, has she covered? D) Find x to the nearest hundredth. 10 32 x The MCA-II / BHS 2 Math Plan GRAD Page 14 of 16 Portions Copyright 2005 by Claude Paradis

21 A) Find tan A and tan B. B) A photographer points a camera at a window in a nearby B building forming an angle of 42 with the camera platform. If the camera is 54 m from the building, how high above the c platform is the window, to the nearest hundredth? C 12 A x 42 54 m C) At a distance of 2.4 feet from a tree, the angle of elevation to the top of the tree is 40. How tall is the tree? D Solve for x to the nearest degree. 18 8 x 2.4 ft 40 Formula Review Packet Answer Key 1 2 3 4 5 A 216 ft 2 perimeter = 590 ft area = 11250 ft 2 2 55 ft 20.1 m 2 44 units 2 B 130 units 51, 362 m 2 8.04 cm 2 5.4 m 2 ( BD)( AC) 2 C 36 m 2 680 units 2 15 units 2 A 392 cm 2 135 units 2 D 2 cm 2 (14)(6)=84 units 2.6 cm A 51 cm 2 40 units 2 The MCA-II / BHS 2 Math Plan GRAD Page 15 of 16 Portions Copyright 2005 by Claude Paradis

6 8 9 10 A 380 sq. units 8 3 sq. units 2289.06 cm 2 43.96 units 3 s = feet 5 π B 11 units 25 ft. Area: 153.86 30.2 in. C 160 in. 2 489.6 cm 2 2 415422. m 84 cm; 42 cm D 8.6 in. P = 5.6 m 06.5 cm 2 5.6 ft 8 3 π feet 11 12 13 14 15 A 2.62 in. 4π 4π 3 6 m 32 ft 3 B 120 ft. 25π/6 25π/6 56 cubic feet 126 ft 3 C 89.π = 595.8 ft 3 410.29 m 3 D 60 ft 3 66 yd 3 16 1 18 19 20 15 A 523.3 ft 3 19.261 85 25 1 4000π/3 cm 3 or B 4188.9 cm 3 394 ft 29 sin P = cos P = 24/25 25 AB = BC = 5 C 9 cm 5, 12, 13 15.4 ft 11. km AC = 2, isos D 434.9 ft 3 30 ft 5 x = 1. 3 8.48 21 tan A =, 12 A 12 tan B = B 48.62 m C 23 ft D 66 The MCA-II / BHS 2 Math Plan GRAD Page 16 of 16 Portions Copyright 2005 by Claude Paradis