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Honors Geometry / Algebra II B Midterm Review Packet

2018-19

This review packet is a general set of skills that will be assessed on the midterm. This review packet MAY

NOT include every possible type of problem that is assessed on the midterm.

Unit 1: Area

1. Find the value of h in the parallelogram.

Not drawn to scale

2. The area of a square garden is 50 m2. How long is the diagonal?

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

3. 4.

Find the area of the trapezoid. Leave your answer in simplest radical form.

5.

Find the area of Polygon ABCD. Find the area of the rhombus.

6. 7.

Find the area of each regular polygon.

8. 9.

Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle.

Leave your answer in terms of .

10.

Find the area of the shaded region. Round to the nearest tenth.

11. 12.

.

Unit 2: Surface Area and Volume

1. A room is 14 ft long and 28 ft wide. The ceiling is 8 ft high. A particular brand of paint will cover 125 ft2 per

gallon. How many gallons of paint need to be bought to paint the walls of the room?

2. A ceramic brick is in the shape of a rectangular prism with dimensions 2” × 3” × 8”. The brick has a

density of 0.2 lbs per cubic inch. Find the weight of the brick.

Find the Lateral Area and Surface Area of the following figures. Leave each answer in simplest radical

form or in terms of pi.

3. 4.

5. 6.

Find the volume of the given prism. Round to the nearest tenth if necessary.

7. 8.

Find the volume of the cylinder in terms of π.

9.

Find the volume of the following figures, to the nearest whole number.

10. 11. 12.

Find the surface area and volume of the sphere. Give each answer in terms of π.

13.

14. Erin’s farm has two similar cylindrical grain silos. The smaller silo is 20 feet tall and the larger silo is 35

feet tall. If the smaller silo can hold 2000 cubic feet of grain, how much can the larger silo hold?

Unit 3: Circles

Assume that the lines that appear to be tangent are tangent. Find the value of x.

1. 2. 3.

Each polygon is circumscribed about the circle. Find the perimeter of each polygon.

4. 5.

Find the value of x. If necessary, round to TWO decimal places.

6. 7.

Find the value of each variable. If necessary, round to TWO decimal places.

8. 9. 10.

x

52

x

114

5x

9cm 12cm

8cm7cm

15in

18in

13in

6in

4in

97

x

58

23

x

y x

y

67

86

162

8

Find the area of the shaded region in each circle below. Round to the nearest tenth.

11. 12.

13. 14.

Find the length of AB . Round to the nearest tenth.

15.

Find the length of ABC . Round to the nearest tenth.

16.

3in

70

9 in

For 17-20, write the standard equation of each circle.

17. C(2, -7); r = 7 18.

19. C(-10, -5); passes through the point (-5, 5) 20. Endpoints of the diameter at (-5, 2) and (3, 6)

Identify the center and radius of the following.

21. 2 2( 5) ( 9) 72x y

Write the equation of the circle in standard form. Then state the center and radius.

22. 2 2 3 8 20x y x y

Find the center and the radius of the circle with the given equation. Then graph the circle.

23. 2 2 6 16 0x y y

Unit 4: Geometric Transformations

1. The x-axis 2. y x

3.

Use the diagram below to answer questions #5-8

5. Identify the image of C under the translation <4,-2>

6. Identify the vector that describes the translation F B

7. Identify the image of H under the translation <-2,4>

8. What vector describes the translation D H

Draw the image of each figure for the given rotation about the origin. Label the vertices of the image.

9. 90 clockwise 10. 180 counterclockwise

Identify the scale factor of each dilation. Assume the center is (0, 0).

11. 12.

Dilate the following about center (0, 0), given each scale factor. Be sure to label the images properly.

13. Scale factor of 1

2 14. Scale factor of 1.5

Unit 5: Algebraic Transformations

Find the inverse of each function.

1. 1

( ) 24

f x x 2. 2( ) 5f x x

3. 2

( ) 3f xx

4. 1

( ) 35

f xx

5. 6

( )5

xf x

x

6. {(5, -4), (6, 9), (-10, 1), (0, 8)}

Use compositions to state if the two functions are inverses.

7.

2( ) 1

3

3 6( )

2

f x n

ng x

8.

4 8( )

3

3( ) 2

4

xf x

g x x

Find the inverse of the function. Then graph the function, the inverse, and the identity function.

9. 6

( )3

xf x

Write an equation for each scenario and then find the constant of variation.

10. The amount of money spent at the gas station varies directly with the number of gallons purchased. When

11.5 gallons of gas were purchased the cost was $37.72.

11. For a fixed number of miles, the gas mileage of a car (miles/gallon) varies inversely with the number of

gallons. Aiden's truck averaged 24 miles per gallon and used 750 gallons of gas in one year.

Write an equation that relates the two variables. Then solve.

12. The time to complete a project varies inversely with the number of employees. If 3 people can complete the

project in 7 days, how long will it take 5 people?

13. The number of bricks laid varies directly with the amount of time spent. If 45 bricks are laid in 65 minutes,

how much time would it take to lay 500 bricks?

Graph each function.

14. 21( ) 2

3f x x 15.

3( ) 3 3f x x

16. 5

( ) 4 26

f x x 17. ( ) 2 5 3f x x

Write the function for each graph.

18. ______________________ 19. ______________________

20. ______________________ 21. ______________________

Unit 6: Quadratics

Solve by factoring.

1. 24 44 121 0x x 2. 29 49 0x 3. 212 40x x

4. 3 22 6 56 0x x x 5. 23 2 21x x 6. 28 14 4x x

Write a quadratic equation with the given roots.

7. 5,9 8. 2 1

,3 5

Simplify.

9. 256 10. 1081x 11. 6 24

12. ( 3 )( 5 )(9 )i i i 13. 23i 14. 3

6 5i i

15. (3 4 ) (1 8 )i i 16. (1 4 )(2 )i i 17. 2

3 4

i

i

Solve each equation by taking square roots.

18. 212 12 0x 19. 26 72 0x

Solve each equation. List all real and imaginary solutions.

20. 4 211 18 0x x 21. 3 216 0x 22. 364 1 0x

Find the value of the discriminant and determine the number and types of roots for the equations.

23. 22 16 33 0x x

a) One rational root b) Two rational roots c) Two irrational roots d) Two complex roots

24. 2 8 4 0x x

b) One rational root b) Two rational roots c) Two irrational roots d) Two complex roots

Find the exact solutions using the Quadratic Formula.

25. 28 1 4x x 26. 2 14 53 0x x

Solve each equation by completing the square.

27. 2 2 120 0x x 28. 22 3 5 0x x

29. 2 6 13 0x x 30. 23 5 1 0x x

Write each quadratic function in vertex form. Then identify the vertex and direction of opening.

31. 22 16 31y x x 32. 24 8 3y x x

Write each quadratic function in vertex form. Then graph the parabola.

33. 2 6 1y x x

Write an equation for the parabola with the following conditions.

34. Vertex is at 4,3 and passes through 3,6 .

Show all work to solve each word problem.

35. The sum of two numbers is 12 and their product is -28. What are the numbers?

36. The product of two consecutive integers is 462. What are the numbers?

37. An arrow is shot upward with an initial velocity of 112 feet per second. How long after the arrow is

released does it return?

38. An object is being propelled straight up from the ground with an initial velocity of 85 feet per second.

When will the object have a height of 50 feet?

Unit 7: Radical Functions

Simplify.

1. 5 818x y 2.

7

14

a

b 3. 5 20 24

4. 12 48 27 5. 5 6 2 5 3 6. 7 6

4 6

7. 33

4 8. 3 54 9. 5 4

41

81h k

Simplify each expression.

10. 4

2 3x 11. 2

327

12. 4

4

27

3

13. 37 49 14. 6 4 881a b 15. 3 100

Solve each equation.

16. 6 3 0z 17. 5 2 4 0x x

18. 12 2y y 19. 1 6 1b b

20. 3 2 3 4x 21. 34 2 11 2 10x