Geometry Semester 2 Final Exam Review

1. Five coins are flipped at the same time. a) What is the total number of outcomes? b) What is the probability of getting any single combination? c) If those same coins are flipped, what is the probability that they will show up as either all heads or all tails? 2. A bag contains 5 red, 3 white, and 2 blue marbles. If the marbles ARE replaced after each pick, find the following probabilities: a. P(red, red, blue) b. P(red, red, red) c. P(red, white, blue) d. P(white, white, blue) e. P(blue, blue, blue) 3. A bag contains 5 red, 3 white, and 2 blue marbles. If the marbles ARE NOT replaced after each pick, find the following probabilities: a. P(red, red, blue) b. P(red, red, red) c. P(blue, blue, blue) d. P(red, white, blue) e. P(white, white, blue) 4. You throw a dart at the board below. Your dart is equally likely to hit any point inside the square board. a) What is the area of the square? b) What is the area of the 2 in circle? c) What is the area of the 5 in circle? d) What is the probability that your dart does not land in one of the two circles? 5. If the two triangles below are similar, find the missing side and their scale factor, given :∆𝐾𝐿𝐽~∆𝑄𝑅𝑃 6. If the two triangles below are similar, solve for x and their scale factor, given :∆𝐴𝐵𝐶~∆𝐹𝐸𝐷 7. A tree is standing next to a 100 ft. high building. The tree casts a 30 ft. shadow and the building casts a 50 ft. shadow. How tall is the tree? 8. A school flagpole casts a shadow that is 45 feet long. At the same time, a boy who is five feet eight inches’ tall casts a shadow that is 51 inches long. How tall is the flagpole to the nearest foot? 9. 10. 15. In the triangle below, find Sin C, Cos C and tan C as a ratio. a. b. 16. Use the triangle to answer the questions, 11. 12. Given the polygons, identify as not a triangle, acute triangle, obtuse triangle or right triangle. a) Side lengths of: 15, 10, and 8. b) Side lengths of: 14, 10 and 24. c) d) a. Which trigonometric ratios are equivalent to 3/5? b. Which trigonometric ratios are equivalent to 4/5? c. Which trigonometric ratios are equivalent to 4/3? 17. The triangles below are similar. Triangle RTU has side lengths RT=39, RU=36 and TU=15 respectively. Select the angles whose cosine equals 12/13. 13. A fence with dimensions as shown is being constructed in the shape of a right triangle, how long must the other side be? 18. In the triangle below, solve for x. 14. 19. If an acute angle of a right triangle has a Sine ratio of 40/41 and a Cosine ratio of 9/41, what would be its Tangent Ratio? 20. If an acute angle of a right triangle has a Sine ratio of 9/41 and a Cosine ratio of 40/41, what would be its Tangent Ratio? 24. The image below is a parallelogram, solve for x, TS and RU. 21. A tree stands 100ft. tall. It casts a shadow of 50ft. upon the ground. What is the angle of elevation from the tip of the shadow to the top of the tree? 22. You are measuring the height of a tree. Your angle measuring device is 3.5 feet tall. You stand 40 feet from the base of the tree. The angle of elevation to the top of the tree is 65o. Find the height of the tree to the nearest foot. 25. The image below is a parallelogram, solve for x and find the measure of all angles. 26. The image below is a parallelogram, solve for x and find the measure of all angles. 27. The image below is an isosceles trapezoid, find the measure of the indicated angle and all other angles. 23. In the following problems, find the missing side length. a. b. c. d. 28. Write if the statements below are sometimes, always or never true. a. All rectangles are squares. b. All quadrilaterals are parallelograms. c. All parallelograms are rectangles. d. All parallelograms are quadrilaterals. e. The diagonals of an isosceles trapezoid bisect each other. f. The diagonals or a rhombus are perpendicular. g. The diagonals of a kite are congruent. h. The diagonals of a rectangle are congruent. i. The diagonals of a parallelogram are perpendicular. 29. Find the circumference of a circle in terms of 𝜋 and to the nearest tenth with a diameter of 36cm. 36. Find the areas of the following triangles a. b. 30. Find the area of a circle in terms of 𝜋 and to the nearest tenth with a diameter of 36cm. 31. Find the area of a circle in terms of 𝜋, with a circumference of 36𝜋. 37. Calculate the area of the shaded regions below. a. b. 32. In the following image, find the length of the arc and the area of the sector. 38. Use the figure below, 33. In the following image, find the length of the arc and the area of the sector. a. Calculate the height of the triangle. b. Calculate the area of the triangle. 34. In the following image, find the length of the arc and the area of the sector. 39. Use the figure below, 35. a. Calculate the height of the parallelogram b. Calculate the area of the parallelogram. 40. Use the figure below, d. e. a. Calculate the height of the parallelogram. b. Calculate the area of the parallelogram. f. 41. In the following problems, find the area of the shaded region. g. a. b. c. d. Find the area of the square. Find the area of the circle Find the area of the shaded region. What is the probability that a dart lands on the shaded region? h. 42. In the following problems, find the surface area and volume of the solid. a. b. a. b. c. d. e. f. c. g. Tips to study for final: Show all your work on a separate paper. No Notes allowed. Equation sheet will be provided. Make a study group and practice the problems suggested. Check your answers with the back of the book. Your electronic devices will not be allowed. Get a good night sleep the night before and eat a healthy breakfast. If caught cheating the district policy will apply – receive a zero score and parent contact will be made. Geometry Final Exam Equation Sheet Probability: &'()*+ -. ./0-+/)1* -'23-(*4 • Theoretical Probability: !(#) = 5-2/1 6'()*+ -. -'23-(*4 &'()*+ -. 4'33*44*4 • Experimental Probability: !(#) = • Independent Events: ! # 89: ; = !(#) ∙ !(;) • Dependent Events: ! # 89: ; = !(#) ∙ !(; 8=>?@ #) &'()*+ -. 2+7/14 D A F Similar Polygons: C E • If ∆#;B ∼ ∆DEF, B o Corresponding Angles are congruent ∠# ≅ ∠D, ∠; ≅ ∠E, ∠B ≅ ∠F JK KN NJ o Corresponding side lengths are proportional = = = P, where k is the scale factor. LM MO OL Triangle Inequality: For any triangle ∆#;B, #; + ;B > #B, #B + ;B > #;, and #; + #B > ;B Pythagorean Theorem: • For any right triangle, 8S + T S = U S , where c is the hypotenuse of the triangle • If 8S + T S = U S , then ∆#;B triangle is a right triangle. • If 8S + T S > U S , then ∆#;B is acute. • If 8S + T S < U S , then ∆#;B is obtuse. Trigonometric Ratios (SohCahToa): for right triangles ^__^`abc de_^bcfg`c lWmlncfb jkZ ] = de_^bcfg`c ^__^`abc z{\ ] = lWmlncfb opposite Z[\ ] = θ adjacent Circles: W = XY Y= W ^__^`abc ) de_^bcfg`c 8:s8U?9> ] = cos hr ( ) ℎuvw>?9xy? wvvwy>? ] = tanhr ( ) 8:s8U?9> ] = Z[\hi ( X Area Formulas: Circle Parallelogram/ Rectangle 2 A = bh A =πr Trapezoid A= Surface Area and Volume: Prism Cylinder SA = PH + 2 B SA = 2π rH + 2π r 2 V = BH V = π r2H 1 h ( b1 + b2 ) 2 Rhombus/Kite Triangle 1 d1d 2 2 1 A = bh 2 A= Pyramid Pl SA = +B 2 BH V= 3 P= Perimeter of base B=area of base H=height of solid Cone SA = π rl + π r 2 π r2H V= 3 Regular Polygon (i.e. Hexagon) 1 A = aP 2 Sphere SA = 4π r 2 4 V = π r3 3