GEOMETRY SUMMER 2016 PRACTICE FINAL EXAM

Transcription

1 GEOMETRY SUMMER 2016 PRACTICE FINAL EXAM Name: Instructions: 1. Show all work on the test itself for every problem. Partial credit is better than no credit. 2. Instructions have been provided for each type of problem. Make sure to read all instructions carefully. In some problems, you must use a specific method to solve each problem, i.e. quadratic formula versus factoring. If you choose not to follow these instructions, you will not be eligible to receive full credit for that problem. 3. Formulas have been provided on last sheet. This sheet may be detached for ease of use but must be reattached before submission. 4. Circle final answers. If you have not achieved a final answer, write how you would achieve it. This will help maximize your credit. 5. You may use a pencil and a graphing calculator ONLY. No pen. 6. Point values are listed after instructions for each problem or set of problems.

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3 Determine whether the following set of numbers can be the measures of the sides of a right triangle. If no, explain. 1) 12, 16, 20 2) 7, 15, 19 Find the third value, x, which makes the following set of numbers a Pythagorean Triple. 3) x, 24, 25 Find each missing side length, x. Write answers as a whole number or in radical form. Radical answers may or may not be reduced. 4) 5) 6) 7) Page 3

4 Using the right triangle provided, find the following trigonometric ratios: sin L, cos L, and tan L. Write each ratio as a reduced fraction. 8) l = 20, m = 21, n = 29 9) l = 15, m = 36, n = 39 Find AB. Round to nearest tenth. 10) 11) Find the measures of A and B using a graphing utility. Round to nearest tenth. 12) 13) Page 4

5 Find the values of x and/or y for each of the following. Use what you know regarding special right triangles to aid you in doing so. 14) 15) Find the area and perimeter of each parallelogram, triangle, trapezoid or rhombus/kite. Round to nearest tenth. 16) 17) 18) 19) Page 5

6 Find the area of each circle or shaded region. Round to nearest tenth. 20) 21) 22) Find the area of each regular polygon or composite figure. Round to nearest tenth. 23) 24) Page 6

7 Find the surface area for each of the following three dimensional solids. Round to nearest tenth. 25) 26) 27) 28) 29) 30) Page 7

8 Find the volume for each of the following three dimensional solids. Round to nearest tenth. 31) 32) 33) 34) Refer to the circle provided to complete the set of statements that corresponds. Be sure to use appropriate notation in order to do so. 35) [a] Name the circle. [b] Name a radius that is not part of a diameter. [c] Name a chord that is not a diameter. [d] Name a minor arc. [e] Name a major arc. [f] Name a semicircle. Page 8

9 Find the exact circumference of each circle. Round to nearest tenth wherever necessary. 36) 37) 12 ft 9 ft 6 cm Find the value of x or x in each circle. 38) 39) Find the indicated measure or measures for each circle. Drawings not to scale. 40) In P, the radius is 13 and RS = 24. Find RT. 41) In P, the radius is 10 and RS = 12. Find PT. Page 9

10 Find the indicated measure or measures for each circle. 42) In P, QR = 7x 20 and TS = 3x. What is x? 43) In Q, CD CB, GQ = x + 5 and EQ = 3x 6. What is x? Find the indicated measure or measures for each circle. 44) Find mac. 45) Find x. 46) Find m T. Page 10

11 FORMULAS YOU MAY NEED Pythagorean Theorem: c 2 = a 2 + b 2 Formulas for Areas of Triangles, Various Quadrilaterals, Circles, and Sectors Area of a Parallelogram Area of a Triangle Area of a Trapezoid A = b h A = 1 2 (b h) A = 1 2 (b 1 + b 2 ) h Area of a Rhombus or Kite Area of a Regular Polygon Area of a Circle A = 1 d 2 1d 2 A = 1 ap A = πr2 2 Formulas for Surface Areas and Volumes of Three Dimensional Solids Surface Area of a Prism Surface Area of a Cylinder Surface Area of a Pyramid SA = B + LA LA = Ph SA = 2πr 2 + 2πrh SA = B Pl Surface Area of a Cone Surface Area of a Sphere Volume of a Prism SA = πr 2 + πrs SA = 4πr 2 V = Bh Volume of a Cylinder Volume of a Pyramid/Cone Volume of a Sphere V = πr 2 h V = 1 3 Bh V = 4 3 πr3 Page 11