b. Create a graph to show how far Maggie and Mike can travel based on the chart above.

Transcription

1 Final Exam Review 1. Find the midpoint, the distance and the slope between (4,-2) and (-5, 3) 2. Jacinta hangs a picture 15 inches from the left side of a wall. How far from the edge of the wall should she mark the location to nail the picture so that the right side of the picture is 37.5 inches from the wall s left side? 3. Point P is located on the segment between point point (1,4) and point D (7,13). The distance from to P is twice the distance from P to D. What are the coordinates of point P? 4. Parallel lines have slopes. 5. Perpendicular lines have slopes. 6. Determine whether the lines are parallel, perpendicular or neither. a. 2x + 3y = 4 b. y = -4x + 1 c. 2y = x 1 3x - 2y = 3 4x + y = 8 y = -2 x Maggie and Mike want to go to the music store near Maggie s house after school. They can walk 3.5 miles per hour and ride their bikes 10 miles per hour. a. reate a table to show how far Maggie and Mike can travel walking and riding their bikes. b. reate a graph to show how far Maggie and Mike can travel based on the chart above. c. What does the slope represent in the graph? d. Maggie s mom said that they can only go if they can make it to the music store and back in less than two hours. If they want to spend at least 30 minutes in the music store and it is four miles away, can they make it?

2 line a // line b 8. Given : m 1 = 3x + 1 m 6 = 5x + 3 m 8 = y x= y= 9. Given : m 2 = 13x + 4 m 3= 4z + 21 m 5= 7y + 2 m 6 = 6x + 25 x= y= z= 10. Name the types of angle pairs that are congruent with respect to parallel lines. 11. Name the types of angle pairs that are supplementary with respect to parallel lines. 12. Given: y = 3x + 7 Questions 12 14: re these lines parallel, perpendicular or neither y = 1 3 x Given: y = 2 x x 15 y = Given : 3x = 6y 15 2y = -4x Find the area and perimeter of the following regular polygons

3 rea = rea = in in. rea = Perimeter = rea = Perimeter = rea = Perimeter = rea = ircumference = Find the area of the shaded part rea = rea =

4 rea = rea = ngle of Elevation/Depression 25.) sonar operator on a cruiser detects a submarine at a distance of 500m and an angle of depression of 37. How deep is the sub? 26.) The top of a signal tower is 120m above sea level. The angle of depression from the top of the tower to a passing ship is 25m. How many meters from the base of the tower is the ship? 27.) ntonio is flying a kite. He lets out 500ft of kite string. The kite is flying so that ntonio s angle of elevation is 36 How high above the ground is the kite? Special Right Triangles 28.) 29.) x y y x

5 30.) ladder leaning against a wall makes a 60 angle with the ground. The base of the ladder is 3m from the building. How high above the ground is the top of the ladder? 31.) What is the perimeter of an isosceles right triangle whose hypotenuse is? Pythagorean Theorem Determine whether each set of numbers can be represent side lengths of a right triangle. 32.) 15, 36, ) 2, 3, 2 34.) 5, 7, ) List 4 Pythagorean Triples. For each, show that a 2 + b 2 = c 2. a.),, b.),, c.),, d.),, 36.) 2 3 = = = 5

6 Right Triangle Trigonometry 37.) The sin =. Find cos and tan. 38.) The cos =. Find sin and tan. cos = tan = sin = tan = 39) The acute angles of a right triangle are and add up to º 40) 2 angles of a triangles are 45º and 72º, what is the measure of the last angle? 41) 3 angles of a quadrilateral are 100º, 120º, and 40º, find the measure of the 4 th angle. 42) In a right triangle, the hypotenuse is 10 ft and a leg is 19, find the length of the other leg. 43) If one acute angle in a right triangle is 57º, find the measure of the other angle is 44) Supplementary angles add up to 45) 12 ft tree casts a 48 ft shadow at the same time a girl casts a 20 ft shadow. Find the height of the girl. 46) What parallelogram has congruent diagonals? and 47) Which parallelogram has congruent sides? and

7 48) Which parallelogram has perpendicular diagonals? and 49) In a triangle, an exterior angle is equal to the sum of the other 2 *** 50) n altitude in a triangle is a segment from a vertex to the opposite side and is to the opposite side 51) median in a triangle is a segment from a vertex to the opposite and the opposite side. 52) Given parallelogram D, write a similarity statement for the 2 triangles D 53) Name the longest side of if 63, 70and 47 54) Find the area of the figure below ) circle has a radius of 5, find the area and circumference = =

8 56) In a parallelogram, the sum of a pair of opposite angles is 200º. Find the measure of the other angles. onsecutive angles of a parallelogram add up to 57) Name the figures: 58) side of a regular octagon is 3, find the perimeter 59) 20 X = 10 + x x 60) Find the missing angle measure X 25 61) Find the missing angle measure In ircle D, 37 D

9 D 62) Find the area of the sector, Find the arc length Diameter = 10 63) The set of points in a plane equidistant to the center is called a 64) Find the area of a square with a diagonal of ) Find the altitude of an equilateral triangle with sides of length 10. Find the area. 66) Find the missing side length X Proportions 68. m m + 7 = = b 9 b = 5x - 4 x + 5 Similarity 71. What proportions could be used to find x? x 6

10 72. The scale factor of RST to XYZ is 3:4. Find the perimeter of XYZ. X R 4 10 Z T 15 S Y 73. T is the centroid of GHI and IH GO. Find the area of OTH G M 10 T N I O 6 H In the figures below, the triangles are congruent by which theorem/postulate: SSS, SS, S, S, or HL. 74. D; D 75. L and N are right angles; MO OP L N O D M P , D D bisects

11 x x 3 x D Given : Diameter 8in m ED 34 md 26 E 82). rc angle measurement of E 83). Minor rc angle measurement of DE 84). Minor rc angle measurement of 85). rea and ircumference of the circle. 86). Sector area ofd. Find the angle measurement of x. x

12 x ) 88) 89) thin wire is formed into a rectangle with an area of area of the new rectangle that is formed be increased or decreased? (and by how much). 2 36cm. If it is reshaped so that the 9cm side is decreased by 3cm, will the 90) Guiseppe s always made personal sized pizzas with a 6 inch radius. He decided to start making larger pizzas that had a 12 inch radius. He figured that if he kept the thickness of the crust, sauce, and cheese the same as his personal sized pizzas, he would just need to double the ingredients to make the larger pizzas. a) Determine how many pizzas Guiseppe will be able to make by doubling the ingredients. b) Explain why or why not Guiseppe s is correct. 91) The formula for the volume of a cylinder is the volume? V 2 r h. If the radius of a cylinder is doubled, how does the change affect 92) ylinder has a height of 12ft and a radius of 4 ft. ylinder has a height of 24 ft and a radius of 8 feet. How many times greater is the volume of ylinder? 93) How many times greater is the volume of a cube with 6 inch edges than that of a cube with 2 inch edges? nswer below if E is the centroid of and D 4 F G=9. 6 E G 7

13 94. E = 95. EF = 96. = 97. IF G=9, then E = 98. IF G=9, then GE =

14 Find the value of x, m D and m F 108 D 5x E 141 2x-3 F G

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16 111) Two cubes are shown. Use the figures to answers each question below. 5 ft. 10 ft.. Find the volume of figure. Show all your work here.. Find the volume of figure. Show all your work here.. Multiple hoice: Which of the following statements is true?. When the length of a cube doubles, the volume also doubles.. When the length of a cube doubles, the volume triples.. When the length of a cube doubles, the volume is four times bigger. D. If figure was filled with water, which weighs 8 pounds per cubic foot, how many pounds of water would the cube hold?

17 112.) Two cylinders are shown. Use the figures to answers each question below. 10m 30m 20m 20m. Find the volume of figure. Show all your work here.. Find the volume of figure. Show all your work here.. Multiple hoice: Which of the following statements is true?. When the radius of a cylinder tripled the volume stay the same.. When the radius of a cylinder tripled the volume also triples.. When the radius of a cylinder tripled the volume is eight times bigger.