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Study Guide Semester 2: 2nd 4.5 Exam Get your study guide signed for 4 bonus points on the test! Name: __KEY_____________________ Parent Signature(+4) : __________________________ Vocabulary words to know! Write a short definition in your own words for each vocabulary word. Word To Know Definition Word To Know Definition Sample Space Sample Space shows all possible Probability The chance that an event outcomes. will occur Compound Probability The probability of more than 1 event Scalene Triangle A triangle with no congruent sides Acute Angle A angle less than 90 degrees Isosceles Triangle A triangle with at least two congruent sides Equilateral Triangle A triangle where all sides are congruent Acute Triangle A triangle with three acute angles Complementary Angles 2 angles who have a sum equal to 90 degrees Right Angle An angle which measures exactly 90 degrees Obtuse Angle Supplementary Angles An angle which measures more than 90 degrees 2 angles who have a sum equal to 180 degrees Right Triangle A triangle with one right angle Obtuse Triangle A triangle with one obtuse angle Cross-section The 2d shape that is formed when a 3D figure is sliced by a plane Fundamental counting Principle A 3D figure composed of two congruent polygon faces, all other faces are rectangles Circumference A method for determining the number of possible outcomes by multiplying the total outcomes for each event The distance around the outside of a circle Prism Part 1: Geometry Find the circumference and area of each circle. C= πd 1 C= 3.14(18)= 56.52 cm A= 3.14(9²)=254.34 cm² A=πr² 2. C= 3.14(12)=37.68 cm A= 3.14(6²)=113.04cm² 3. C= 3.14(16)=50.24 cm A= 3.14(8²)=200.96cm² Find the volume and surface area for each figure: Formulas- Prisms- V= (area of the base)x(height) 1. 2. 3. V= _200 cm³_ V= _972 cm³__ 4. V= __192 cm³___ V= __12 inches ³_____ SA= 220 cm²____ SA= _208 cm²___ Find the area for the composite figure: Formulas: Rectangle- a= lw Triangle a=½bh Circle a= πr² Trapezoid a= ½h(b1 + b2) 1. a=_31.73 mi²_ 2. a= 160 m²_ Find the missing angle for each triangle and classify the triangle by its angles. <1 <2 <3 Classification by angles: Right, Acute or Obtuse 44⁰ 68⁰ 68⁰ acute 121⁰ 7⁰ 52⁰ obtuse 56⁰ 103⁰ 21⁰ obtuse 72⁰ 18⁰ 90⁰ right Name the Faces, Vertices and Edges for each 3-D figure. Shape Faces Vertices Edges Rectangular 6 12 8 Prism Triangular 4 4 6 pyramid Hexagonal 8 12 16 Prism Classify the triangle by the sides and the angles. Congruent sides and angles are indicated. Right, Isosceles Obtuse, Scalene Acute, Equilateral Acute, Scalene Right, Scalene Name each 3-D figure & Sketch the cross-section for each slice. Figure(name each) Cut by a plane parallel to the base Circle Cut by a plane perpendicular to the base Triangle Cut by a plane diagonal to the base Ellipse/Oval Rectangle Square/Rectangle Parallelogram Circle Rectangle Ellipse/Oval Rectangle Triangle Parallelogram _____Cone______ ______Right Prism _____ ___Cylinder______ ____Rectangular Pyramid______ Find the value of x and find the missing angles. 3x 5x+20 3x + 5x + 20 = 180 8x + 20 = 180 8x = 160 X = 20 Part 2: Probability City Athens Berlin London Paris Rome 2x-6 X 2x – 6 + x = 90 x – 6 =90 x= 96 x 3x x-12 3x + x + x – 12 = 180 5x – 12 = 180 5x = 192 X = 38.4 1. Keisha’s family is planning a trip to Europe. If they want to visit each of the cities listed in the table at the right, in how many different orders can they visit the cities? (Use fundamental counting principle) 5 x 4 x 3 x 2 x 1 = 120 possible orders 2. Employees at a company are given a three digit employee identification code. If each digit cannot be repeated, how many different codes are possible? 9 x 8 x 7= 504 different id codes are possible 3. There are 26 students in Mr. Everly’s social studies class. Mr. Everly will randomly select one student as spokesperson and a second student as an alternate spokesperson for an upcoming presentation. In how many different ways can they be chosen? 26 x 25= 650 different ways 4. Drew spun a spinner with 5 equal sections 75 times. Each section of the spinner was a different color. One of the colors was blue. The outcome of “blue” occurred 30 times. Compare the theoretical to the experimental probability of spinning blue. (Show both fractions and compare them using the words greater than or less than. Give a reason the probabilities may be different. Theoretical P = 1/5 Experimental P= 2/5 The experimental probability was greater than the theoretical probability, a reason for the discrepancy is the frequency of the experiment. If the frequency of the experiment was increased the experimental probability would be closer to the theoretical probability. 5. A coin is flipped then a spinner with 3 equal sections that are yellow, blue and red is spun. Draw a tree diagram to show the sample space for the events. HR Sample Space- HR, HY, HB, TR, TY, TB Y B TR Y B Permutations: For 6 and 7, find the total number of outcomes that will be in each sample space. 6. buying bedroom furniture if you can select one each from 7 dressers, 4 beds, 6 lamps, and 9 night tables 7 x 4 x 6 x 9 = 1512 7. tossing a dime, a quarter, a penny, a nickel, and rolling a number cube 2 x 2 x 2 x 2= 16 8. How many ways can 4 friends sit together at the movies in 4 seats? 4 x 3 x 2 x 1= 24 Use the spinner to find each probability. Write each probability as a fraction, decimal and percent. Round to the nearest percent. 9. P(even number) 4/8 = ½ 10. P(2 or 3) 2/8 = ¼ 11. P(not 4) 7/8 12. The spinner is spun twice. Find P(5, then 8) 1/8 x 1/8 = 1/64 A bag contains 4 white beads, 6 red beads, 5 yellow beads, and 5 blue beads. One bead is selected, kept, and another bead is selected. Write the probability as a simplified fraction. 13. Find P(blue, then blue) 5/20 x 4/19 = 4/76 = 1/19 14. Find P(white, then red) 4/20 x 6/19= 6/95 15. Find P(red, then red) 6/20 x 5 / 19 = 3/38 Permutations: Find each value. (Remember the first number is the starting number, the second tells you how many times it is permutated!) 16. P(8, 5) 17. P(10, 2) 18. P(11, 4) 8 x 7 x 6 x 5 x 4= 6720 10 x 9 = 90 11x10x9x8= 7920 19. Explain the difference in independent and dependent events? In independent events the outcome of the first event does NOT affect the outcome of the second event. In dependent event the outcome of the first event does affect the outcome of the second event. 20. Explain the difference in theoretical and experimental probability. Experimental probability can only be determine if an experiment has taken place and the results have been recorded. Theoretical probability is the number of favorable outcomes over the number of total possible outcomes.