geometry spring semester exam review 2015-2016 … exam... · geometry spring semester . exam...

Geometry Spring Semester

Exam Review 2015-2016

Name: ______________________

Chapter 12 - Due: __________ Chapter 11 - Due: __________ Chapter 10 - Due: __________ Chapter 8 - Due: __________ Chapter 7 - Due: __________ Chapter 6 - Due: __________

Name _________________________________ Date ______________________ Geometry – Spring Semester Review (15-16)

SEMESTER REVIEW: Chapter 12 SHOW ALL WORK!! Don’t forget your units! Leave answers in terms of π

1. Write the formulas for the following:

________________________area of a triangle ________________________area of a rectangle

________________________area of a circle ________________________area of a regular polygon

________________________area of a trapezoid ________________________circumference of a circle

2. Name the following using the polyhedron at the right.

Name 2 edges: ____________ _________________

Name a lateral face:_______________________

Name the bases:____________&____________

Name the vertices:_______________________

3. Draw an example of a pyramid 4. Draw an example of a prism

5. Name two differences between pyramids and prisms.

____________________________________________________________________________________________________________________________________________________________________________________________

6. Using the views of a slid figure below, draw the back view of the figure.

7. The base of a prism is a regular hexagon that measures 5 cm on each side. The prism has a height of 12 cm. What is its lateral area?

8. Find the surface area of a cylindrical water tank that is 5 meters tall and has a diameter of 8 meters.

9. Find the lateral area, surface area and volume of the cylinder below.

Lateral______________________

Total________________________

Volume______________________

10. Find the surface area of a square pyramid if the side lengths of the base is 13 cm and the slant height is 8cm.

11. Draw the net of each solid. Then name the solid.

12. Calculate the slant height, lateral area, total surface area, and volume of the right cone below.

L=_______________________

Lateral = __________________

Total = ___________________

Volume=__________________

13. Calculate the lateral area, total area and volume of the cylinder.

Lateral = __________________

Total = ___________________

Volume=__________________

14. If a spherical ballon has a great circle with a circumference of 16π inches, how much air is needed to fill it?

15. The volume of the larger prism is 128cm cubed. If the prisms are similar, What is the volume of the smaller prism?

16. Find the volume of the hexagonal prism below. Remember to find the are of hexagon first!

17. Two cones are similar. If the ratio of their radii is 3:4, then

a) What is the ratio of their surface areas?

b) What is the ration of their volumes?

18. Name the following:

I. Two lines containing point N___________________

II. A segment containing point Q __________________

III. A triangle_______________

IV. How many great circles are shown? ____________

20. Compare Plane Eucliedean and Spherical Geometries.

Euclidean Spherical

Line

Triangle


SEMESTER REVIEW: Chapter 11 For # 1-6, write the Area formula for the following polygons: 1. __________________Triangle 2. _________________ Parallelogram 3. _________________Trapezoid 4. _________________ Rhombus 5. _________________ Kite 6. _________________ Regular Polygon For # 7 – 12, find the area of each polygon. Round answers to the nearest tenth.

13. If two figures are similar and the ratio of sides lengths is a:b, then the ratio of perimeters is _________ and the ratio of areas is ______. 14. The ratio of areas of two similar figures is 144:49. Write the ratio of the lengths of the corresponding sides. 15. Two triangles are similar. The smaller triangle has a side length of 4, while the larger has a side length of 10. If the area of the larger triangle has an area of 200, what is the area of the smaller triangle.

16. You have a great photo that is 3” by 5”. You want to enlarge the area of the picture using a scale factor of 3. (11.3)

A) What is the area of the larger picture? B) Will it fit on your 9 x 12 scrapbook page?

17. Find the exact and approximate circumference of a circle with a diameter of 50 inches. Exact = ________________ Approximate:_______________ Formulas for Circles:

Area = 2rπ Circumference = 2 rπ or dπ Length of an arc = 2360N rπ• Area of a Sector = 2

360N rπ•

For # 18 & 19, find the indicated measure.

20. Find the length of arc CD with an arc measure of 108 ° and a radius of 17 cm. For # 21 & 22, find the indicated measure.

23. Find the area of a sector with an arc measure of 114 ° and a radius of 10 in.

18. 19.

21. 22.


SEMESTER REVIEW: Chapter 10 Solve for x: 1. 2. 3. x = ____ x = ____ x = ____ 4. 5. 6. x = ____ x = ____ x = ____ For # 7 – 16, write the segment, ray, or line (using proper notation) that best describes the given part of the circle.

17. If the measure of an arc is less than 180° , then the arc is a _____________ arc. 18. If the measure of an arc is greater than 180° , then the arc is a _______________ arc. 19. If the measure of an arc is equal to 180° , then the arc is a _________________. 20. The opposite angles in an inscribed quadrilateral are ______________________.

21. The circle is circumscribed by the pentagon as shown. If AB = 10, BC = 5, AI = 14, GF = 6, and GE = 12. Find the following measures:

22. Find the value of x. x = ____ 23. Find the radius of the circle. r = ____ 24. Find the measure of arc AC. arc AC = ____ 25. Find the m < 1.

26. Find the m < ABC. m < ABC = ____ 27. Find the measure of arc ABC. arc ABC = ____ 28. Find the m < 2. m < 2 = ____ 29. Find the measure of arc AC and the measure of arc CD. arc AC = ____ arc CD = ____

m < 1 = ____

In # 30-32, find the value of x. 30. 32. 33. x = ________ x = ________ x = ________ 33. How many common tangents do the two circles share? Common Tangents: _________ 34. Find the value of x and y. 35. Find the value of x and y. 36. Find KD. 37. Given: O , AC = 24. Find BD. 38. Write the equation of a circle with center (5, -2) and diameter is 3. Graph it. Equation: _________________________


SEMESTER REVIEW: Chapter 8 1. What is the Pythagorean Formula? ______________________ 2. Find the unknown side length of the right triangle. Write your answer in simplest radical form and decimal rounded to the nearest hundredth.

(A) ______ = ______ (B) ______ = ______ (C) ______ = ______ 3. Determine if the given measures are measures of the sides of a right triangle. _______ 15, 36, 39 _______ 21, 72, 75 _______ 24, 46, 51 4. Find the geometric mean of 40 and 10. _______ 5. Find the geometric mean of 6 and 9. _______ 6. Find the value of x. Round your answers to the nearest hundredth.

(A) ___________ (B) ___________ (C) _____________ 7. Find the missing measures. Write your answers in simplest radical form. a. b. . c. a=______ b=________ x=_____ y=______ x=_____ y=______

8. Can the following measures be the sides of a triangle? If so, classify the triangles formed by the side lengths as acute, right, or obtuse.

(A) 6, 8, 9 ___________________

(B) 10, 2 2 , 6 3 ___________________ (C) 15, 20, 5 ___________________ (D) 13, 18, 24 ___________________

Matching: 9-11) Match the following ratios: (3 pts each)

______ sin A a) oppositeadjacent

______ cos A b) opposite

hypotenuse

______ tan A c) adjacent

hypotenuse

12. Find the indicated ratio. Put answers in simplest form. (3 pts each)

Q sin N = _______ sin Q = _______

cos N = _______ cos Q = _______

tan N = _______ tan Q = _______

For #13-16, use sine, cosine and tangent of angles to find the indicated lengths or angles. Round all lengths to the nearest hundredth and all angles to the nearest degree. You must show work! 13. 14. 15. 16.

N

13 5

12

17. Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground? Draw figure. Round the answer to the nearest degree. 18. A kite’s string is 200 meters long. Find the altitude (height off the ground) at which the kite is flying if the string makes an angle of 30 degrees with the ground. Draw a figure. Round the answer to the nearest hundredth. 19. A 16-foot ladder leaning against a building has an angle of depression of 68° . How far is the base of the ladder from the base of the building? Round the answer to the nearest hundredth.


SEMESTER REVIEW: Chapter 7

1. Refer to the similar triangles. Given: ∆ABC ∼ ∆XYZ.

a. Write all pairs of congruent angles. __________ ___________ ___________

b. Write the ratios of proportional sides.

________ = ________ = ________ c. What is the scale factor of ∆ABC to ∆XYZ?

S. F. = ImageOriginal

= _______

d. Write a proportion to solve for the values of x and y. Then, find x and y. x = ________ y = ________ 2. Given: ∆RST ∼ ∆RUV.

3. Alyssa wants to measure the height of the flagpole school. She places a mirror on the ground 54 feet from the flagpole, then walks backward until she is able to see the top of the flagpole in the mirror. Her eyes are 5.9 feet above the ground, and she is 14 feet from the mirror. What is the height of the flagpole to the nearest tenth of a foot? 4. Segments a, b, and c are parallel. Find the value of x. x = ________ 5. Given: ∆ABC ∼ ∆ADE (not drawn to scale). AC = 8, and AE = 12. If the perimeter of triangle ABC = 20, what is the perimeter of triangle ADE answer ____________

Write a proportion to solve for the values of x and y. Then, find x and y. x = ________ y = ________

6. Given: DABC ~ DEDC (not drawn to scale). AB = 1.5, BC = 2, and DE = 4.5. a. What is the perimeter of triangle DEC? answer _____________

A 10 B

C x 7

X Y

Z

y

18 14

R

S

U

T

V

18

6

21

x 12

y

a

b

c

x

20

27

23

12 8

A

D

E

B

C

A

D

E

B C

4.5

2

1.5


SEMESTER REVIEW: Chapter 6 1. Give the names for each polygon with the given number of sides: 3 sides __________________ 7 sides __________________ 4 sides __________________ 8 sides __________________ 5 sides __________________ 9 sides __________________ 6 sides __________________ 10 sides__________________ 2. Find the following for a regular hexagon: _________(A) The interior angle sum _________(B) The measure of each interior angle

_________(C) The exterior angles sum _________(D) The measure of each exterior angle

3. Find the following for a regular 19-gon: ________ (A) The interior angles sum ________ (B) The measure of each interior angle ________ (C) The exterior angles sum ________ (D) The measure of each exterior angle

4. Put an X in the box if the shape always has the given property.

Property Parallelogram Rectangle Rhombus Square Kite Trapezoid All sides are congruent Both pairs of opposite sides are congruent Both pairs of opposite sides are parallel Exactly one pair of opposite sides are parallel All angles are congruent Exactly one pair of opposite angles are congruent Diagonals are perpendicular Diagonals are congruent Diagonals bisect each other

5. Given the following combinations of calculations, which figures can you identify?

Parallelogram Rectangle Rhombus Square Kite Trapezoid Distance formula only Slope formula only Either distance or slope Both distance and slope are required

geometry spring semester exam review 2015-2016 … exam... · geometry spring semester . exam...

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