Mathematics II Formula Sheet

Transcription

1 Mathematics II Formula Sheet elow are the formulas you may find useful as you work the problems. However, some of the formulas may not be used. You may refer to this page as you take the test. Area Rectangle/Parallelogram A = bh Triangle A = ircle A = r 2 = d 3.4 Volume Rectangular Prism/ylinder V = h Pyramid/one V = Sphere 2 ircumference V 4 3 r 3 bh h 3 Surface Area Rectangular Prism SA = 2lw + 2wh + 2lh ylinder SA = 2 r rh Quadratic Formula b b ac x = ± 2a Population Standard eviation = 2 4 Standard Form ax 2 bx c y Vertex Form a x h 2 k y Mean Absolute eviation x x i= i the average of the absolute deviations from the mean for a set of data x x i= i 2 Sphere SA 4 r 2 Sample Standard eviation Trigonometric Relationships sin ( ) opp adj opp ; cos ( ) ; tan ( ) hyp hyp adj S x x i= i Triangle Special Right Triangles Triangle x 45 x 2 x 60 2x x 45 x

2 Accelerated Test #/ 2nd ine Weeks ame: ate:. A circular garden has a diameter of 2 feet. How many bags of topsoil must Linda buy to cover the garden if one bag covers an area of 3 square feet? A What is the volume of a rectangular solid with a length of 2, a width of 3, and a height of 4? A If the circumference of a circle is 0π inches, what is the area, in square inches, of the circle? A. 0π. 25π. 50π. 00π 6. Tamika has a hard rubber ball whose circumference measures 3 inches. She wants to box it for a gift but can only find cube-shaped boxes of sides 3 inches, 4 inches, 5 inches, or 6 inches. What is the smallest box that the ball will fit into with the top on? 3. What is the circumference of a circle whose area is 6π? A. 64π. 32π. 8π. 4π 7. The volume of a cube is 64 cubic inches. Its total surface area, in square inches, is 4. A right circular cylinder has a base whose area is 2π. If the height of the cylinder is 6, the volume of the cylinder is A A. 8π. 24π. 36π. 72π page

3 8. In the accompanying diagram, a rectangular container with the dimensions 0 inches by 5 inches by 20 inches is to be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches. What is the maximum number of full cups of water that can be placed into the container without the water overflowing the container? 0. As shown in the accompanying diagram, the length, width, and height of Richard s fish tank are 24 inches, 6 inches, and 8 inches, respectively. Richard is filling his fish tank with water from a hose at the rate of 500 cubic inches per minute. How long will it take, to the nearest minute, to fill the tank to a depth of 5 inches? 9. Which diagram represents the figure with the greatest volume?. A storage container in the shape of a right circular cylinder is shown in the accompanying diagram. A.... What is the volume of this container, to the nearest hundredth? A in in in in 3 page 2 Accelerated Test #/ 2nd ine Weeks

4 2. Tracey has two empty cube-shaped containers with sides of 5 inches and 7 inches, as shown in the accompanying diagram. She fills the smaller container completely with water and then pours all the water from the smaller container into the larger container. How deep, to the nearest tenth of an inch, will the water be in the larger container? 5. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 2 inches. What is the volume of the cone to the nearest cubic inch? A A block of wood is 5 inches long, 2 inches wide, and 3 inches high. What is the volume of this block of wood? A. 0 in in in in 3 6. A regular pyramid with a square base is shown in the diagram below. 4. The diagram below represents Joe s two fish tanks. Joe s larger tank is completely filled with water. He takes water from it to completely fill the small tank. etermine how many cubic inches of water will remain in the larger tank. A side, s, of the base of the pyramid is 2 meters, and the height, h, is 42 meters. What is the volume of the pyramid in cubic meters? page 3 Accelerated Test #/ 2nd ine Weeks

5 7. What is the volume, in cubic centimeters, of a cylinder that has a height of 5 cm and a diameter of 2 cm? 20. A sphere is inscribed inside a cube with edges of 6 cm. In cubic centimeters, what is the volume of the sphere, in terms of π? A. 80π. 540π A. 2π. 36π. 48π. 288π. 675π. 2,60π 2. The bases of a trapezoid have lengths 0 and 8. If the height of the trapezoid is 6, what is the area of the trapezoid? 8. A packing carton in the shape of a triangular prism is shown in the diagram below. 22. Keesha wants to tile the floor shown in the accompanying diagram. If each tile measures foot by foot and costs $2.99, what will be the total cost, including an 8% sales tax, for tiling the floor? What is the volume, in cubic inches, of this carton? A The diameter of a sphere is 5 inches. What is the volume of the sphere, to the nearest tenth of a cubic inch? A , Sean knows the length of the base, b, and the area, A, of a triangular window in his bedroom. Which formula could he use to find the height, h, of this window? A. h = 2A b. h = A 2b. h = (2A)(b). h = 2A b page 4 Accelerated Test #/ 2nd ine Weeks

6 Problem-Attic format version c EducAide Software Licensed for use by Markeita Irvin Terms of Use at Accelerated Test #/ 2nd ine Weeks 0/9/ inch box A , $ A