Download Second Semester Final REVIEW SHEET

Second Semester Final REVIEW SHEET
Name: __________________
Topics Covered on the Final
Unit 2: Similarity
 I can find and use scale factor
 I can set up and solve proportions
 I can find missing side lengths in similar figures using ratios/proportions
 I know the angle relationship between similar figures
 I can redraw and set up proportions for similar right triangles
Unit 3: Right Triangles and Trigonometry
 I can use the Pythagorean Theorem to find missing sides of right triangles
 I can classify a triangle as right, acute, or obtuse given its side lengths
 I can find missing sides in right triangles using Trig (SOH-CAH-TOA)
 I can draw a picture to help solve trig problems
 I can find missing angles in right triangles using Inverse Trig
Unit 4: Area and Volume
 I can find the area of a triangle, rectangle, parallelogram, kite, rhombus, and trapezoid
 I can find the area of regular polygons (pentagon, hexagon, etc.)
 I can find the volume of prisms, pyramids, cylinders, cone, and spheres and composite solids
 I can identify cross sections in 3-dimensional figures
 I can use similarity (and ratios/proportions) to find measurements of similar figures
Unit 5: Coordinate Geometry
 I can identify the center and radius of a circle if given the equation
 I can find the distance of a line segment
 I can find the midpoint between two points
 I can find the other endpoint if given the midpoint and one endpoint
 I can classify a shape if given the side lengths and slopes of sides
Unit 6: Circles
 I can find arc measures and central angles
 Find the measures of angles inside, outside and on a circle
 Find circumference and area of a circle
 Find the radius or diameter given the circumference or area
 Find arc length
Unit 2: Similarity
1. Determine whether the triangles are similar. If so, write a similarity statement and name the
postulate or theorem you used. If not, explain.
a.
b.
2. The polygons are similar. Find the value of each variable.
3. Find the value of x and y in the similar right triangles.
4. Find the values of the missing variable.
5. The measures of two complementary angles are in the ratio 7 : 11. What is the measure of the
smaller angle?
Do the three given sides form a triangle? If so, will it be right, acute, or obtuse?
6. 12, 14, and 18
7. 9, 15, and 3√34
Unit 3: Trigonometry
8. Find the value of the variable in the following figures using Pythagorean Theorem, special right triangle rules, or
trigonometry.
a.
b.
c.
9. Solve the right triangle.
PQ = ________________
P = ________________
R = ________________
10. Max needs to reach his cat, Fuzzy, who is stuck in a tree 12 feet above the ground. Max is a terrible tree climber
so he will use a 16 foot ladder to get to Fuzzy the cat. How far away from the base of the tree should he place
the bottom of the ladder so that he can reach Fuzzy?
11. Find the missing angle, 𝜃.
12. Find the missing angle, 𝜃.
13. You lean a 20 foot ladder against a wall. The base of the ladder is 4 feet from the wall. What angle  does the
ladder make with the ground?
14. A sonar operator on a ship detects a submarine at a distance of 500 meters and an angle of depression of
40°. How deep is the submarine?
15. Find the area of each triangle:
46
Unit 4: Area and Volume
1. A sugar cone has a diameter of 4 cm and is 12 cm deep. A similar jumbo sized sugar cone is 18 cm deep. Find
the volume of the jumbo sized sugar cone.
2. Find the area of the figures.
a.
b.
3. Find the volume of each solid.
a.
c.
b.
4. A standard size mailbox is 6 inches wide, 19.5 inches long and 7 inches tall. The mailbox is constructed from a
rectangular prism and half a cylinder. A standard letter with envelope has dimensions of 6.125 inches high, 11.5
inches long, and .25 inches thick. What is the maximum amount of letters that can fit into the mailbox? (Do not
worry about whether or not the letters get bent)
5. What is the horizontal cross section of the solid?
6. A cylindrical thermos has a radius of 2 in. What is the volume of a similar thermos with a radius of 3 in. hold
Unit 5: Coordinate Geometry
1
1. Write an equation of a line perpendicular to 𝑦 = 3 𝑥 + 7
that passes through (2, 4).
2. Klaus the mouse is scampering across a kitchen floor. His hole is at (0, 8) and he sees some cheese at (11, 2).
Starting from his hole, Klaus runs exactly one third of the way to the cheese, then stops to stretch his tail and
straighten his whiskers. What are his coordinates when he stops?
3. Write the equation in vertex form for the
parabola with vertex (−2,3) and
directrix 𝑥 = 2.
4. M is the midpoint of AB . What are the
coordinates of the endpoint A if M = (3, 6) and
B= (-2, 3)
4. Given the information below, explain in words what type of shape it is and how you know!
Slopes
𝑃𝐻 =
𝐻𝐼 =
2
3
−3
2
𝐼𝑍 =
2
3
𝑍𝑃 =
−3
2
5. Given the information below, explain in words what type of shape it is and how you know!
Slopes
1
𝐻𝐼 =
4
𝐼𝐽 = −5
𝐽𝐾 =
1
4
𝐾𝐻 = 5
Unit 6: Circles
1. Find the arc length.
2. Find the area of the sector
3. Area of sector ∠𝐴𝐶𝐵 is 30 cm2.
What is the area of the entire
circle?
4. Find the radius of the circles with the given information.
5. Write the standard equation of the circle below.
6. Find the measure of the missing angles indicated below.
c.
d.