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Honors Trigonometry - Summer Assignment

**You will be given a Quiz based on the contents of this packet at the beginning of your Honors Trig course. You must score an 80% or better.**

Algebra Review

A. Evaluate using order of operations :

1. when x = -3, y = -2 2. when x = -1

B. Solve equations:

3. 4.

C. Linear Equations - Sketch graphs, write linear equations using slope and intercept:

5. In which quadrant is (5, -4)?

Sketch the graph of the following linear equations:

6. 7.

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8. 9.

10. Find the slope of (-15, 11) and (8, -4)

11. Find the intercepts of x-intercept:

y-intercept:

12. Rewrite in slope-intercept form:

slope:

y-intercept:

13. Write an equation of the line containing (1, 1) and (2, -2).

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14. Write an equation of the line passing through (7, 2) and having a slope of 0.

15. Write an equation of the line having an undefined slope (no slope) and passing through the point (-2, 5).

D. Add, Subtract and Multiply Polynomials:

16. 17.

18. 19.

20. 21.

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E. Factoring - Greatest Common Factor, Trinomials, Difference of Squares:

22. x2 – 49 23. x2 + 4x – 21

24. 25.

26. 2x2 – 5x – 12 27. x3 + 5x2 – 9x – 45

28. 29.

F. Simplify Using Exponent Rules:

30. 31.

32. 33.

34. 35.

36. 37.

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G. Quadratic Equations

38. Solve .

In #39-40, solve using quadratic formula and simplify :

39. x2 + 4x – 3 = 0 40. 3x2 + 2x – 2 = 0

In #41-42, factor to find all real solutions:

41. x2 – 5x = 0 42.

H. Complex (Imaginary) Numbers:

Simplify the following :

43. √−9 44. √−7 45. −√−4 46. −√−15

47. (3i)2 48. (2i)2 49. 3i2 50.

Solve the equation :

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51. x2 = 9 52. x2 = -7

Perform the indicated operation:

53. (9 + 3i) + ( 7 – i) 54. (1 – 6i) – (8 + i)

55. 2i(5 + 3i) 56. (5 + 4i)(2 + i)

I. Radicals and Rational Exponents:

57. Write in radical form and simplify:

58. Write in rational exponent form: a.) b)

59. Simplify, then add like radicals:

Simplify:

60. 61.

Solve (check for extraneous solutions):

62. 63.

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64. 65.

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Geometry Review:

Solve for x in each of the below problems:

1. 2. 3.

X = ________ X = ________ X = ________

4. Find the geometric mean and arithmetic mean between 3 and 9. GM = ______ AM = ______

5. The sides of a polygon are 6, 7, 11, and 16. Find the perimeter of a similar polygon whose longest side is 20 cm.

6. The sides of a polygon are 3, 5, 8, 7, and 9. The shortest side of a similar polygon is 12 in. Find the longest side.

7. Sam is 5 feet 4 inches tall and casts a shadow of 4 feet. Find the height of a nearby flagpole that casts a shadow of 30 feet.

8. A man travels 5 miles north, 2 miles east, 1 mile north, and then 4 miles east. How far is he from his starting point?

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18. Find: AB = _____

BC = _____

AE = _____

EB = _____

CE = _____

19. Using ∆RST, answer the following. In parts b-d, round segment lengths to the nearest tenth and angle measures to the nearest degree.

a) RT = 5, TS = 8, RS = _____

b) RT = 7, RS = 8, mÐS » _____

c) mÐR = 75˚, RT = 4, TS » _____

d) mÐS = 24˚, TS = 2, RS » _____

20. From the top of a cliff 50 meters high, a camper sees a deer. The angle of depression is 62˚. How far is the deer from the base of the cliff? (Round answer to the nearest tenth.)

21. a) Find the perimeter of the trapezoid.b) Find the area of the trapezoid. c) Find the length of the median of the trapezoid.

22. In ABCD, mÐA= 5y˚ and mÐB = (2y + 19)˚. Find y.

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23. If both pairs of opposite sides of a quadrilateral are congruent and the diagonals are

congruent, then the quadrilateral is a __________________.

24. Find the sum of the measures of the angles of a heptagon.

25. Five angles of a convex hexagon are 90˚, 120˚, 120˚, 130˚, and 140˚. Find the measure of the 6th angle.

26. The interior angles of a pentagon are in the ratio of 4:5:5:5:8. Find the measure of the largest exterior angle.

27. Find the sum of the exterior angles of a regular 30-gon.

28. Name the polygon that contains 90 diagonals.

29. If the midpoints of the sides of a rhombus are connected in order, the figure formed is a

_____________________________________.

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30. Given: O, radii OD,OE ,tangent DF , secant BF ,m BC=60 ˚ ,m DC=100˚ ,m DE=80 ˚ ,m EA=40 ˚

Find: a) m AB = ______

b) mÐ1 = ______

c) mÐ2 =______

d) mÐBXC = ______

e) mÐ3 = ______

f) mÐBDF = ______

g) If BE = 21 and EF = 4, then DF = ______

h) If BD = 22, BX = 10, and AX = 6, then CX = ______

31. In a circle of radius 10, a chord of length 16 is drawn. Find the distance from the center of the circle to the chord.

32. RACK is inscribed in O. If RC = 3x + 7 and KA = 12x + 12, find the radius of the circle.

33. If point E is the centroid of ∆ABC, BD = 12, EF = 7, and AG = 15, find EB.

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34. The vertices of ∆EFG are E = (2, 4), F = (10, -6), and G = (-4, -6). Find the coordinates of the orthocenter of ∆EFG.

35. Name the shortest and longest segments in the diagram.

36. Find the exact circumference and area of a circle that passes through (7, 5) and whose center is (4, -3).

37. Find the length of a side of a square that has a diagonal of 16.

38. Find the area of a trapezoid with sides 10, 12, 10, and 28.

39. Given: Equilateral Triangle Find: the area and perimeter of the shaded region

40. Find the area of a regular hexagon with a side length of 10.

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41. Find the area of a triangle with sides 8, 11, and 15. Is this triangle acute, right, or obtuse?

42. Find the area of JACK.

43. Find the area of an equilateral triangle whose apothem is 4.

44. Find the perimeter and area of a rhombus with diagonals of length 8 and 15.

45. Find the area of an 80˚ sector of a circle with a radius of 6.

46. Find the length of a 45˚ arc in a circle with a diameter of 24.

47. Woody Woodpecker pecked at a 17m wooden pole until it cracked and the upper part fell, with the top hitting the ground 10 m from the foot of the pole. Since the upper part had not completely broken off, Woody pecked away where the pole had cracked. How far was Woody above the ground?

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48. Given: YW bisects AX , ÐA≅ÐX, Ð5≅Ð6Prove: ZW ≅ YW(Use a two column proof)

49. Given: ∆ABC is not isosceles, BD is an altitude of ∆ABCProve: BD does not bisect AC(Use an indirect proof)

B

DA C

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