Unit 1: Area Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Transcription

1 Name Per Honors Geometry / Algebra II B Midterm Review Packet 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. 1. Find the value of h in the parallelogram. Unit 1: Area Not drawn to scale. The area of a square garden is 50 m. 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.. 4. Find the area of the trapezoid. Leave your answer in simplest radical form. 5.

2 Find the area of Polygon ABCD. Find the area of the rhombus Find the area of each regular polygon 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.

3 Find the area of the shaded region. Round to the nearest tenth Unit : Surface Area and Volume 1. A room is 14 ft long and 8 ft wide. The ceiling is 8 ft high. A particular brand of paint will cover 15 ft per gallon. How many gallons of paint need to be bought to paint the walls of the room?. A ceramic brick is in the shape of a rectangular prism with dimensions 8. The brick has a density of 0. lbs per cubic inch. Find the weight of the brick.

4 Find the Lateral Area and Surface Area of the following figures. Leave each answer in simplest radical form or in terms of pi Find the volume of the given prism. Round to the nearest tenth if necessary

5 Find the volume of the cylinder in terms of π. 9. Find the volume of the following figures, to the nearest whole number Find the surface area and volume of the sphere. Give each answer in terms of π Erin s farm has two similar cylindrical grain silos. The smaller silo is 0 feet tall and the larger silo is 5 feet tall. If the smaller silo can hold 000 cubic feet of grain, how much can the larger silo hold?

6 Unit : Circles Assume that the lines that appear to be tangent are tangent. Find the value of x x x 8 x Each polygon is circumscribed about the circle. Find the perimeter of each polygon. 4. 9cm 1cm 5. 6in 15in 4in 18in 7cm 8cm 1in Find the value of x. If necessary, round to TWO decimal places Find the value of each variable. If necessary, round to TWO decimal places y 10. x x 58 x y 67

7 Find the area of the shaded region in each circle below. Round to the nearest tenth in in Find the length of AB. Round to the nearest tenth. 15. Find the length of ABC. Round to the nearest tenth. 16.

8 For 17-0, write the standard equation of each circle. 17. C(, -7); r = C(-10, -5); passes through the point (-5, 5) 0. Endpoints of the diameter at (-5, ) and (, 6) Identify the center and radius of the following. 1. ( x 5) ( y 9) 7 Write the equation of the circle in standard form. Then state the center and radius.. x y x y 8 0 Find the center and the radius of the circle with the given equation. Then graph the circle.. x y y

9 Unit 4: Geometric Transformations 1. The x-axis. y x. Use the diagram below to answer questions # Identify the image of C under the translation <4,-> 6. Identify the vector that describes the translation F B 7. Identify the image of H under the translation <-,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 clockwise counterclockwise

10 Identify the scale factor of each dilation. Assume the center is (0, 0) Dilate the following about center (0, 0), given each scale factor. Be sure to label the images properly. 1. Scale factor of Scale factor of 1.5 Unit 5: Algebraic Transformations Find the inverse of each function f ( x) x. 4 f x ( ) x 5. f( x) 4. x 1 f( x) x 5

11 5. 6x f( x) 6. {(5, -4), (6, 9), (-10, 1), (0, 8)} x 5 Use compositions to state if the two functions are inverses. f ( x) n n 6 gx ( ) 4x 8 f( x) g( x) x 4 Find the inverse of the function. Then graph the function, the inverse, and the identity function. 6 x 9. f( 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 $ 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 4 miles per gallon and used 750 gallons of gas in one year.

12 Write an equation that relates the two variables. Then solve. 1. The time to complete a project varies inversely with the number of employees. If people can complete the project in 7 days, how long will it take 5 people? 1. 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 f ( x) x 15. f x x ( ) f ( x) x f ( x) x 5 6

13 Write the function for each graph Solve by factoring. Unit 6: Quadratics 1. 4x 44x x x 40 x 4. x 6x 56x 0 5. x x x 14x 4

14 Write a quadratic equation with the given roots. 7. 5,9 8. 1, 5 Simplify x ( i)( 5 i)(9 i) 1. i 14. 6i 5i 15. ( 4 i) (1 8 i) 16. (1 4 i)( i) 17. i 4i Solve each equation by taking square roots x x 7 0 Solve each equation. List all real and imaginary solutions. 0. x 11x x x 1 0

15 Find the value of the discriminant and determine the number and types of roots for the equations.. x 16x 0 a) One rational root b) Two rational roots c) Two irrational roots d) Two complex roots 4. x 8x 4 0 b) One rational root b) Two rational roots c) Two irrational roots d) Two complex roots Find the exact solutions using the Quadratic Formula. 5. 8x 1 4 x 6. x 14x 5 0 Solve each equation by completing the square. 7. x x x x x 6x x 5x 1 0

16 Write each quadratic function in vertex form. Then identify the vertex and direction of opening. 1. y x x y x x 4 8 Write each quadratic function in vertex form. Then graph the parabola.. y x x 6 1 Write an equation for the parabola with the following conditions. 4. Vertex is at 4, and passes through,6. Show all work to solve each word problem. 5. The sum of two numbers is 1 and their product is -8. What are the numbers?

17 6. The product of two consecutive integers is 46. What are the numbers? 7. An arrow is shot upward with an initial velocity of 11 feet per second. How long after the arrow is released does it return? 8. 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? Simplify. Unit 7: Radical Functions x y. a b

18 hk Simplify each expression x a 4 b Solve each equation. 16. z x 5 x y 1 y 19. b 1 b x x 11 10