Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.

Transcription

1 Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right triangle measures 8.4 meters. One leg measures 6 meters. To the nearest tenth of a meter, what is the length of the other leg? 2. The measures of the side lengths of a triangle are 15, 32, and 34. Classify the triangle as acute, right, or obtuse Find the unknown side length Find the missing side. Are they a Pythagorean Triple? 8. Draw a triangle with the relationship of the side lengths. 9. Draw a triangle with the relationship of the side lengths. 10. The hypotenuse of an isosceles right triangle is 54 units. To the nearest tenth, what is the length of one of the legs? 11. The longest side of a triangle measures 8. What is the length of the longer leg? Leave your answer in simplest radical form. 12. Use a special right triangle to write sin 60⁰ as a fraction. 13. Use your calculator to find the trigonometric ratios sin(79 ), cos(47 ), tan(77 ). Round to the nearest tenth. 14. Use your calculator to find the angle measures sin -1 (0.7), cos -1 (0.3), tan -1 (38.4). Round to the nearest tenth. 15. Find the values of x and y in simplest radical form. 16. Find the value of x in simplest radical form. 17. Write the trigonometric ratios as a fraction and as a decimal rounded to the nearest hundredth. sin A = cos B = tan A = 18. Find the length of x and y. Round to the nearest hundredth.

2 19. Find the length of x for each triangle. Round to the nearest hundredth for side lengths and nearest degree for angles. Angles of Elevation and Depression 20. Ryan was skiing at Snow Bowl, Arizona last winter. He was at the top of Sunset Peak. He measured the angle of depression to the bottom of the run to be 14. He read that the actual length of the run is 2675 feet. What is the change in altitude to the bottom of the run? 21. A ship is sighted from a lighthouse at Port Richey at an angle of depression of 15. How far from Port Richey is the ship if the lighthouse is 52 meters high? 22. From the top of a 35 meter cliff, Lori spots a hiker at an angle of depression of 62. How far away is Lori from the hiker? 23. Find the angle of depression. Then, find the horizontal distance between the ship and the airplane. Chapter 12: Circles 24. Find the area of circle E in terms of pi. 25. Identify the chords, tangent, radii, secant, and diameter in the circle below. 26. Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at that point.

3 27. Segments LM and NM are tangent to circle K. Find LM. 28. Find each measure. a) b) Segment QR is tangent to circle P. QR = 18 and PS = 11. a) Find m PRQ b) Find SR. Round your answer to the nearest tenths place. 32. Find NP. 33. Find the area of the shaded sector. Give your answer in 34. Find the area of the shaded segment terms of pi and rounded to the nearest hundredths place. to the nearest hundredth. 35. Find the area of a segment of a circle, if the central angle is 60 and the radius is 8 cm. Round your answer to the nearest hundredths place. 36. Find the arc length of an arc with measure 44 degrees in a circle with diameter 10 in. Give your answer in terms of pi and rounded to the nearest hundredth.

4 37. Find each measure. a. b. c. d. Chapter 15: Quadratic Functions For each function: - state what form the function is in - convert to the other two forms - determine whether the graph opens upward or downward - find the vertex - find the axis of symmetry - find the minimum or maximum - find the y-intercept - find the x-intercept(s) - find the domain and range - increasing and decreasing interval - graph the function on a piece of graph paper 38. f(x) = -x 2 + 2x h(x) = -3(x - 6) f(x) = (x + 4)(x 3) 41. g(x) = 2x 2 8x 42. h(x) = x x t(x) = 2x 2-16x j(x) = x 2 6x g(x) = (x + 3) f(x) = -3(x + 5)(x + 1) 47. Name the following polynomials by their name and their degree. (a) 4x 5 + 7x 2 (b) -3x 3 + 5x (c) 15 (d) 0.5x + 4x A soccer ball bounces straight up into the air off of the head of a soccer player at a height of 4 feet with an initial velocity of 36 feet per second. The height of the ball can be represented by: h(t) = -16t t + 4 Graph the function using your graphing calculator. When does the soccer ball hit the ground? At what time does the soccer ball reach its highest point? What is the maximum height of the soccer ball?

5 Chapter 14: Factoring 49. Factor x 2 + 8x Factor 6x 2-11x Factor x 2-13x Factor -3x x Factor x Factor 5x x 2-100x 55. Determine if the trinomial is a perfect square. If so, factor it. If not, explain why. 9x x Determine if the trinomial is a perfect square. If so, factor it. If not, explain why. 25x x Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why. x Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why x The area of a rectangle is 12x 2 8x 15. The width is (2x 3). What is the length of the rectangle? Chapter 16: Solving Quadratic Functions 60. Find the zeros of f(x) = x 2 + 2x 3 by graphing. 61. Find the zeros of f(x) = x 2-8x + 12 by factoring. 62. Find the zeros of g(x) = 3x x by factoring. 63. A toy rocket is launched from ground level with an initial vertical velocity of 80 ft/s. When will the rocket hit the ground? 64. Another toy rocket is launched. However, this time the toy rocket is launched from the roof of a building that is 20 feet tall. The toy rocket s initial velocity is 76 ft/s. When will is hit the ground? 65. Write a quadratic function in standard form with zeros 4 and Write a quadratic function in standard form with zeros 3 and Find the roots of 16x 2 = 1 by factoring. 68. Find the roots of 40x = 8x by factoring. 69. Solve x 2 10x + 25 = 27 by square roots. 70. Solve 2x = -31 by square roots. 71. Solve x 2-2 = 9x by completing the square. 72. Solve x 2 16x = -48 by completing the square. 73. Solve g(x) = x 2 + 7x + 15 by quadratic formula. 74. Solve g(x) = 2x 2-10x + 18 by quadratic formula. 75. Find the number and type of solutions for 2x = 2x. 76. Find the number and type of solutions for 4x 2 28x = -49.

6 77. One leg of a right triangle is 6 inches longer than the other leg. The hypotenuse of the triangle is 25 inches. What is the length of each leg to the nearest inch? 78. A pebble is tossed from the top of a cliff. The pebble s height is given by y(t) = 16t , where t is the time in seconds. Its horizontal distance in feet from the base of the cliff is given by d(t) = 7t. How far will the pebble be from the base of the cliff when it hits the ground? Chapter 13: Complex Numbers 79. Express 6 12 number in terms of i. 80. Solve for x: 2x = Solve for x: x 2 + 2x = Write the complex conjugate of i. 83. Write the complex conjugate of 15 - i. 84. Find the values of x and y that make the equation true. -2x + 6i = -14 (24y)i 85. Subtract (4 - i) - (5 + 8i). Write in the form a + bi. 86. Add (6-2i) + (-6 + 2i). Write in the form a + bi. 87. Find the absolute value of -9 + i 88. Find the absolute value of -4i 89. Multiply 2i(3-5i). Write the result in the form a + bi. 90. Multiply (5-6i)(4-3i). Write the result in the form a + bi. 91. Divide 6+i. Write the result in the form a + bi. 4 i 92. Divide 10+22i. Write the result in the form a + bi. 2+3i 93. Simplify -4i Simplify i Simplify 6i i Sketch a graph of the complex plane. Label your axes. Then, plot the following points. A. 3i B. -5i C. 4 + i D. 2 6i E i F. -6 3i 97. Find the sum of the following complex numbers by graphing: (5 + 4i) + (-1 + 2i)