Download Enter the appropriate value to answer the question or solve the

Name:
Class:
Date:
Algebra in Geometry Review!
Enter the appropriate value to answer the question or solve the problem.
1. This box is wrapped with two strips of ribbon as shown. What length of ribbon was needed to decorate the
box? ________________________ cm
2. How many 2-person conversations are possible at a party of 27 people?
Find the indicated measurement. Include units if necessary. Leave your answer in terms of if applicable.
Enter the appropriate word(s) to complete the statement.
3. An arc of a circle has a measure of 140° and a length of 33
cm. What is the diameter of the circle, rounded
to the nearest centimeter?
Indicate the answer choice that best completes the statement or answers the question.
4. r = 21 cm. The arc length of
, rounded to the nearest 0.01 cm, is ________________.
a. 296 cm
b. 40.32 cm
c. 42.32 cm
d. 131.95 cm
e. None of the above
Enter the appropriate value to answer the question or solve the problem.
5. The figure is a trapezoid. q = ___________________
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Algebra in Geometry Review!
Find the volume of each solid. All given measurements are in centimeters. Round your answers to the nearest
3
cm .
3
6. Volume = _________________ cm
2
7. Find the total surface area of the cone. Surface area = ____________ ft . (Round to the nearest 0.1.)
8. The function rule f(n) generates the sequence –20, –17, –14, –11, …
a. Find the nth term.
b. Find the 20th term.
Indicate the answer choice that best completes the statement or answers the question.
9. The ratio of the volumes of two spherical steel balls is 27:125. What is the ratio of their diameters?
a. 27:5
b. 3:5
c. 27:125
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Algebra in Geometry Review!
d. 9:25
e. None of these.
Enter the appropriate value to answer the question or solve the problem.
10. A guy wire from the top of a radio transmission tower is anchored to the ground 19.2 m from the base of the
tower. The wire makes a 57 angle with the ground. To the nearest tenth of a meter, what is the length of the
guy wire? _________________ m
11. Iris, a biologist, needs to find the height of a rare tree. She places a mirror on the ground 37 ft from the base
of the tree. She moves back, in line with the mirror and the tree, until she can see the reflection of the top of the
tree in the mirror. If she is 5 ft from the mirror and her eyes are 5 ft 2 in. from the ground, how tall is the tree, to
the nearest 0.1 ft? ___________________ ft
2
12. Surface area = _________ cm
13. Two sports cars leave the same city at 8 A.M. One heads south at 52 mi/h, while the other travels east at 39
mi/h. If the cars continue to travel at the same speed, how far apart are they at noon? ___________ mi
14. sin Q = __________________
cos Q = __________________
tan Q = __________________
Enter the appropriate value to answer the question or solve the problem.
15. Mr. James wants to coat the ceiling, walls, and floor of a rectangular storeroom with a flame-retardant
material that costs $39.95 per gallon. The dimensions of the room are 7.5 m by 7 m by 3.5 m. If one gallon
2
covers 110 m , how much will Mr. James need to spend to protect the storeroom? $_________
16. Ranger Jill’s station is 18.3 miles due east of Ranger Will’s station. A fire is burning in the distance.
Looking northwest from her station, Jill estimates that the angle between a road running east-west and the fire is
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Page 3
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Algebra in Geometry Review!
21°. Looking northeast from his station, Will estimates that the angle between the road and the fire is 48°. How
far is Jill from the fire? Round to the nearest tenth of a mile. __________________ mi
Round decimal answers to the nearest 0.1.
17. Surface area = 430 in
2
x = ________________ in.
2
18. A square with a diagonal of length 23 cm has area ____________ cm .
2
19. A triangle has an area of 28.5 cm . If the length of one side of the triangle is 6 cm, then the length of the
altitude to that side must be __________ cm.
20. If a 31-foot tree casts a 33-foot shadow at the same time a nearby building casts a 80-foot shadow, how tall
is the building, to the nearest foot? _________________ ft
21. Find the perimeter of the larger pentagon if the two pentagons are similar. _________________ ft
22. Area = ___________ in
2
23. If the diameter of the moon is 3475 km and an orbiting lunar station is circling 22 km above the lunar
surface, find the distance traveled by the lunar station in one orbit. Give your answer to the nearest kilometer.
__________________ km
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Algebra in Geometry Review!
24. Two cubes have edges in the ratio
. What is the ratio of their surface areas?
Enter the appropriate value to answer the question or solve the problem.
25. Find the perimeter of a regular octagon ROADSIGN, in centimeters, if the apothem measures 20 cm and the area is
320 square cm.
26. This solid is a right pyramid with a rectangular base. All measurements are in centimeters. Find exact values
for f, g, and h.
Enter the appropriate value to answer the question or solve the problem.
3
27. A square pyramid has volume 162 cm . If the height of the pyramid is 6 cm, what is the length of each side
of the square base? _________________ cm
28. Find the volume and the surface area of the hemisphere (including the base). The radius is in centimeters.
Enter the appropriate value to answer the question or solve the problem.
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Algebra in Geometry Review!
2
29. Area of shaded region _________ cm . (Roumd to the nearest cm.)
Find each measure to the nearest tenth of a unit. All lengths are in centimeters.
30. m = ___________ cm
31. r = ___________ m
Round your answers to the nearest unit.
32. Area of
2
ABC = __________________ mm
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Page 6
Answer Key
1. 98
2. 351
3. 85 cm
85cm
85 centimeters
85centimeters
4. b
5. 10
6. 7125
7. 82.5
8. a. 3n – 23, b. 37
9. b
10. 35.3
11. 38.2
12. 384
13. 260
14.
15. 75.00
16. 14.6
17. 5
18. 264.5
19. 9.5
20. 75
21. 130.5
22. 120
23. 11055
24.
25. 32
26. f = 8 cm, g =
cm, h =
cm
27. 9
28. 2250
29. 79
30. 8.7
31. 78
32. 483
3
cm
3
7069 cm ; 675
2
cm
2
2121 cm
Geometry Algebra Mastery #1 a.) 1.) Solve the equation, and explain your reasoning. € 1
(2x − 4) + x = x − 5 2
Steps Reasoning 2.) Draw a diagram to represent the following. Then find the value of x. Given line l and line m, l // m . Draw in a transversal line n. For a set of corresponding angles one of the angles measure of 83° and the °
other corresponding angle measures (x +10) Diagram: €
€
Work to find the value of x: €
Geometry Mastery #1 b.) 1.) Solve the equation, and explain your reasoning. €
1
4 − 3(x +1) = x − 5 2
Steps Reasoning 2.) Draw a diagram to represent the following. Then find m∠ABC . Given ∠ABC , draw the angle bisector, BD . m∠ABD = (x + 4)°
°
€
m∠DBC = (2x − 38)
€ Diagram: €
€
Work to find m∠ABC : Summative Assessment Geometry Mastery #1 c.) €
€
1.) Solve the equation, and explain your reasoning. 2(x −1) + 3 = 3x + 7 Steps Reasoning 2.) Draw a diagram to represent the following. Then find the value of x. ∠1 and ∠2 are vertical angles. m∠1 = (2x + 4)°
m∠2 =128
€
€
°
€ Diagram: Work to find the value of x: 3.) Prove that the following lines are parallel. Line 1: 2x + y = 6 Line 2: €
Parent Function 2
4.) Given the parent function f (x) = x , describe the transformations and 2
sketch a graph of f (x) = −(x + 3) − 4 . Transformations: €
€
Graph Geometry Mastery #2 a) 1.) Sketch a graph of the quadratic function, following information. f (x) = −(x −1)2 + 4 . Label the €
Transformations: Vertex: y-­‐intercept: x-­‐intercept: Domain: Range: 2.) Sketch a diagram that represents the following and then find all three angles of the isosceles triangles. °
In an isosceles triangle the base angles measure (2x − 6) and y° . The vertex angle is (2x + y − 2)° . €
Geometry Mastery #2 b) €
1.) Sketch a graph of the quadratic function, information. €
f (x) = x 2 − 25 . Label the following €
Transformations: Vertex: y-­‐intercept: x-­‐intercept: Domain: Range: 2.) Sketch a diagram that represents the following and then find the values of x and y. Draw vertical angles. One of the vertical angles measures (2x −18)° and the other vertical angle measures (x − 4)° . An angle next to the vertical angles measures (2 y + 20)° . Geometry Mastery #2 c) €
1.) Sketch a graph of the quadratic function, information. €
f (x) = €
(x + 2)2 − 9 . Label the following €
Transformations: Vertex: y-­‐intercept: x-­‐intercept: Domain: Range: 2.) Sketch a diagram that represents the following, then find the values of x and y. °
Given two parallel lines a // b , the measures of a set of corresponding angles are (x + 4) and y° . A vertical angle to the angle that measures y° measures (3x)° .
€
€
€
€
€
Geometry Mastery #3 a) 1.) Plot point A and point B on the Cartesian Plane below. Then find the distance between point A and point B. Explain in a complete sentence how you found the distance between the points. A (-­‐1, 5) B( 2, 0) Distance between A and B: Explanation: 2.) Plot points A, B, and C on the Cartesian Plane below. Use slopes to determine whether this is a right triangle. Explain how you knew if this was a right triangle in a complete sentence. A(4, 5) B( -­‐4, 3) C( 1, 0) Slopes: Is this a right triangle? Explanation: Geometry Mastery Semester 2 : 4 a) 1.) The hypotenuse of a right triangle is 108 . In her work, Zoe finds the hypotenuse to be 3 6 , but Lily finds the hypotenuse of the same triangle to be 6 3 . Which student has correctly simplified the hypotenuse? How do you know that she is correct? € What concept did the other student not understand? €
€ 2.) You leave your house and you travel due north and then you travel due east for the exact same distance that you traveled due north. You end up 8 miles from your house. How far did you travel due north? Simplify your solution and give the exact answer. Geometry Mastery Semester 2 : 4b) 1.) The hypotenuse of a right triangle is 320 . In his work Kyle finds the hypotenuse to be 4 20 , but Brian finds the hypotenuse of the same triangle to be 8 5 . Which student has correctly simplified the hypotenuse? Explain your reasoning of how you €
know she is correct. What concept did the other student not understand? €
€
2.) A train leaves the repair shop traveling due west for x miles and then travels due south for 2 more miles than the train traveled due west and arrives at another station. The station and the repair shop are 10 miles apart. How far did the train travel going due west? €
Geometry Mastery Semester 2 : 4c) 1.) The hypotenuse of a right triangle is 675 . In his work Kyle finds the hypotenuse to be 9 75 , but Brian finds the hypotenuse of the same triangle to be 15 3 . Which student has correctly simplified the hypotenuse? Explain your reasoning of how you €
know she is correct. What concept did the other student not understand? €
€
2.) A train leaves the repair shop traveling due east for x miles and then travels due north for 3 less miles than the train traveled due east and arrives at another station. The station and the repair shop are 17 miles apart. How far did the train travel going due north? €
Algebra Mastery 5a 1) Factor this quadratic equation and find both solutions for x. What do these solutions tell us about the graph of y =3 x2 +3 x – 18 ? 3x2 + 3x – 18 = 0 2) Solve the following formula for r. V = (1/3)πr2H