A. x = and x = C. x = B. x = D. x = ____ 41. Solve this equation: A. x = 144 B. x = 12 C. x = 7 D. x = 3 ____ 42. Solve this equation: A. x = B. x = 25 C. x = 5 D. x = 10 ____ 43. Solve this equation: A. x = 4 B. x = 8 C. x = D. x = 16 ____ 44. Solve this equation: A. x = –3 B. x = 9 C. x = 3 D. x = –9 ____ 45. Factor: A. (x – 3)(x – 4) C. (x + 3)(x + 4) B. (x – 3)(x + 4) D. (x + 3)(x – 4) ____ 46. Factor this polynomial: A. ()() C. ()() B. ()() D. ()() ____ 47. Factor this polynomial expression: A. C. B. D. ____ 48. Factor this polynomial expression: A. C. B. D. ____ 49. Factor: A. C. B. D. ____ 50. Solve this equation: A. or C. or B. or D. or ____ 51. Solve: A. x = or x = C. x = or x = B. x = or x = D. x = or x = ____ 52. Solve by factoring: A. or C. B. D. or ____ 53. Solve by factoring: A. C. B. D. ____ 54. Solve by factoring: A. C. B. D.
4. Determine whether the given value of x is a root of this equation. Justify your answer. ; 5. Consider the polynomial . Determine a value for k so that is a factor of the polynomial. Explain your strategy. 6. The perimeter, P, of a rectangular concrete slab is 46 m and its area, A, is 90 m2. Use the formula . Determine the dimensions of the slab. Show your work. 7. A ball is thrown in the air. The approximate height of the ball, h metres, after t seconds can be modelled by the equation . Will the ball ever reach a height of 15 m? Explain your answer. 8. a) Solve this quadratic equation by expanding, simplifying, then applying the quadratic formula: b) Solve the equation in part a using the quadratic formula without expanding. 9. Determine the values of k for which the equation has no real roots, then write a possible equation. 10. Use graphing technology to solve this equation: Explain your strategy. 11. Determine the measures of A and B to the nearest tenth of a degree. Explain your strategy. 12. A guy wire helps to support a tower as shown. Determine the height of the tower to the nearest tenth of a metre. What assumptions about the ground are you making? Explain your work. 13. Guy wires are attached to buildings as shown. A student says the angles of inclination of the wires are the same. Is the student correct? Justify your answer. 14. Point P(9, –4) is a terminal point of an angle  in standard position. Determine  to the nearest degree, then sketch the angle. Show your work. 15. In ABC, AB = 6 cm and . Complete the chart below for your own values of BC. Length of BC (cm) Value of How does compare with sin A? Description of possible triangles No triangles are possible. 1 isosceles triangle 1 scalene triangle 2 scalene triangles 16. Two divers are 50 m apart. Each diver sees a treasure chest on the sea floor. The treasure chest is vertically below the line between the divers. From the divers, the angles of depression to the treasure chest are 35° and 51°. To the nearest metre, how far is the treasure chest from each diver? Consider possible cases and show your work.
13. ANS: Label the right triangles ABC and DEF. In ABC, B represents the angle of inclination of the guy wire attached to the shorter building. In ABC, The angle of inclination of the guy wire attached to the shorter building is approximately 48.1°. In DEF, E represents the angle of inclination of the guy wire attached to the taller building. In DEF, The angle of inclination of the guy wire attached to the taller building is approximately 43.0°. The student is not correct. The angles of inclination are different. PTS: 0 DIF: Difficult REF: 6.1 Angles in Standard Position in Quadrant 1 LOC: 11.T2 TOP: Trigonometry KEY: Communication | Problem-Solving Skills 14. ANS: Determine the distance r from the origin to P. , Use: The reference angle, to the nearest degree, is: Since x is positive and y is negative, the terminal arm is in Quadrant 4, and  is approximately . PTS: 0 DIF: Moderate REF: 6.2 Angles in Standard Position in All Quadrants LOC: 11.T2 TOP: Trigonometry KEY: Procedural Knowledge | Communication 15. ANS: Possible solution: Length of BC (cm) Value of How does compare with sin A? Description of possible triangles 5 0.8333... No triangles are possible. 6 1 1 isosceles triangle 7 1.1666... 1 scalene triangle 5.9 0.9833... 2 scalene triangles PTS: 0 DIF: Moderate REF: 6.3 Constructing Triangles LOC: 11.T3 TOP: Trigonometry KEY: Conceptual Understanding | Problem-Solving Skills 16. ANS: The treasure chest could be between the two divers or on one side of both divers. Case 1: The treasure chest C is between the two divers, A and B.