Use a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 )

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1 Use a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 ) A telescope is supported by a tower that casts a shadow 40 meters long. The distance from the top of the tower to the end of the shadow is 50 meters. How high is the tower? Use a calculator to find the missing sides of these right triangles. If a giraffe stands 576 cm tall, how long a shadow would it cast if it is compared to a man who is 180 cm tall casting a shadow 1 m long?

2 Robert sighted to the top of a tree along a stake that he knew to be 3 feet high. If he is standing 2 feet from the stake and 18 feet from the tree, how high is the tree? Line 1 is parallel to Line 2 and Line 3 is a transversal. Angle B has a measure of 25. What is the measure of Angle F and its relationship to Angle A? Line 1 is parallel to Line 2 and Line 3 is a transversal. Angle B has a measure of 25. The sides of a lot measure 120 feet, 80 feet, 110 feet and 200 feet. As a draftsman, you must prepare a drawing of this property for the owner. Use a ratio of similitude of 1 inch to 20 feet and show the scale drawing of the property. What are the measurements on your scale drawing? What is the measure of all of the angles in the figure?

3 In which figure are angles 1 and 2 supplementary? In the figure, m 1 = 30. Find m 2. A. B. C. D. Solve for x. Which figure appears to be congruent to? A. B. C. D. not given

4 Are all squares similar? Explain your answer. Given ABC = EBD, how long is DE? A. 3 B. 4 C. 5 D. cannot be determined GHI STU. Find x. A. x = 1 cm B. x = 2 cm C. x = 3 cm D. x = 4 cm Study the drawing and solve for x.

5 Which of the following is similar to the given rectangle? In the triangle, use the Pythagorean Theorem to find x. A. 2 B. 4 C. 5.8 D. 8 A. 6 6 B C. 3 D. 12 The lengths of the legs of a right triangle are 12 m and 16 m. Find the length of the hypotenuse. A. 20 m B. 12 m C. 14 m D. 16 m If the hypotenuse of a right triangle is 15 inches and one leg is 8 inches, find the length of the other leg.

6 Find b. A. 92 B. 76 C. 23 D. 16 Find a. A translation moves ABC 2 units to the right and 4 units down. The image is A B C. Write the coordinates of each vertex of A B C. If the figure is rotated about point A, the resulting figure could be: A. B. C. D.

7 The figure is a scale drawing of a bedroom. Find the length of the bedroom in meters if the scale is 1 cm : 1.5 m. A. 4.5 m B. 5 m C. 6 m D. 7 m In a house plan the actual height of 6 feet is represented by 2 inches. If the actual length of the house is 120 feet, what is the length the house in the drawing? 3 cm 4 cm If you had 20 feet of fencing, describe the shape you would use to give your pet the maximum amount of play room. Justify why it would be better than all other shapes. What are the coordinates of point C? A. (3, 5) B. ( 5, 3) C. (3, 0) D. (0, 3)

8 In the pattern, the volume of one small cube is one cubic unit. What would be the volume of the ninth figure? Use the formula V = lwh to find the height of a rectangular prism with volume = 96 m 3, width = 6 m, and length = 2 m. A. 84 m B. 12 m C. 8 m D m The area formula for a triangle is: A = 1 2 bh Find the area of a triangle with a base of 4 in and height of 2.5 in. Find the volume of a cone with a diameter of 1.5 inches and a height of 2 inches. A. 1.5 in 3 B in 2 C in 2 D in 3

9 Write as a ratio in lowest terms: 8 in to 4 ft. A. 1 to 6 B. 2 to 1 C. 1 to 5 D. 6 to 1 Write as a ratio in lowest terms: 6 months to 24 months. Find the ratio of (a) the perimeters and (b) the areas of a rectangle with sides 10 m and 8 m and another with sides of 15 m and 12 m. Solve: x 8 = A. {27} B. {48} C. {108} D. {432}

10 Describe how to use a calculator to solve = 12 d. Fran and Betty work together. If their earnings are in the ratio 4 to 3 respectively, how much does Fran earn when Betty earns $650? The sales tax on a new car costing $10,500 is $420. If the sales tax rate is the same, what is the sales tax on a new car costing $16,125? On a number line, if point M has coordinate 3 and point N has coordinate 4, how long is MN? A. 7 B. 7 C. 1 D. 1

11 Solve the following system of equations for x: x + y = 6 x y = 2 Solve the following system of equations algebraically and check: 3x + 2y = 6 5x 3y = 28 Solve the following system of equations algebraically and check: x 4y = 16 y = 1 x Solve the following system of equations graphically and check: 3x + y = 3 y = 2x 7

12 Solve graphically and check: 2x + y = 5 x 2y = 10 What is the solution of the system of equations 2x 5y = 11 and 2x + 3y = 9? A. ( 3, 1) B. ( 1, 3) C. (3, 1) D. (3, 1) Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $ Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza? The cost of three notebooks and four pencils is $8.50. The cost of five notebooks and eight pencils is $ Determine the cost of one notebook and the cost of one pencil. A. $1.50 B. $2.00 C. $3.00 D. $3.50

13 In the accompanying figure, what is one pair of alternate interior angles? Which pair of angles x and y are supplementary? A. m x = 113 m y = 67 C. m x = 140 m y = 190 B. m x = 76 m y = 14 D. m x = 180 m y = 180 A. 1 and 2 B. 4 and 5 C. 4 and 6 D. 6 and 8 Two congruent angles A and B are supplementary. Find the measure of angle A. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x + 10) and m CEB = 50, find x.

14 If two legs of a right triangle are 9 and 11, the hypotenuse is A. 20 B. 2 C. 40 D. 202 What is the length of the hypotenuse of a right triangle with legs of lengths 7 and 8? A. 9 B. 15 C. 15 D. 113 The length of the hypotenuse of a right triangle is 15 and the length of one leg is 12. Find the length of the other leg. In the accompanying diagram of ABC, a right angle is at C, AB = 8, and AC = 4. A. 12 B. 4 3 C. 4 5 D. 4

15 A wall is supported by a brace 10 feet long, as shown in the diagram. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach? The coordinates of the endpoints of the diameter of a circle are (3, 7) and ( 5, 3). Find the coordinates of the center of the circle. Point P has coordinates ( 12, 5). What is its distance from the origin? In the coordinates of A are ( 2, 3) and the coordinates of B are (7, 1), find, in radical form, the length of AB.

16 What is A expressed in simplest radical form? 2 B. 4 2 C. 8 D. 8 2 Which graph illustrates the relationship x varies directly as y? A. B. C. D. Which table is an example of y varying directly with x. A. x B. x y y A storage container in the shape of a right circular cylinder is shown in the accompanying diagram. C. x y D. x y What is the volume of this container, to the nearest hundredth? A in 3 B in 3 C in 3 D in 3

17 Which diagram represents the figure with the greatest volume? A. B. C. D.

18 Problem-Attic format version c EducAide Software Licensed for use by janet trubiano Terms of Use at untitled XXXX-XX-XX m 7.14 m, 5 m 21. C A(5, 0), B(5, 3), C(9, 3) m 27 feet 25 ; corresponding angles 155 A, D, E, H, 25 B, C, F, G B C circle; [answers will vary] [diagram]; 6 in., 4 in., 5.5 in., 10 in. B B [answers will vary] B C 3.75 cm C B A A C in C A to : 3, 4 : A 38. $ $ [answers will vary] A

19 Teacher s Key Page ( 2, 6) B D 43. x = 4, y = D 44. [graph] 65. A 45. x = 4, y = C 47. B 48. One notebook= $2.50 and one pencil= $0.25, and appropriate algebraic work is shown. 49. B 50. A D D B ( 1, 5) A