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Name _____________________________________________ Period ________________ Pre-Algebra Final Review Part II GEOMETRY Vocab: Fill in the blank with one of the following: line, point, line segment, ray, plane, angle a) A ___line segment__ is part of a line between 2 endpoints. b) A flat surface made up of points, extended infinitely in 2 directions is a __plane______________. c) A ___ray_________ is made up of points extended infinitely in one direction. d) The intersection of two rays at a common endpoint is an ___angle______________. e) A ___point________ is a location without shape or size. f) Points that are ___collinear________ are on the same line. g) Points that are on the same plane are called ___coplanar____________. h) In order for two rays to be the same, they must share the same ___endpoint______ and extend infinitely in the __same______ direction. Use the diagram to answer questions 26-30. Use the vocabulary words above to help you. 26. FH names a ___ray________. 27. < EFH names a ___(right) angle_____. 28. Name a ray that is the same as GF: ⃗⃗⃗⃗⃗ ________ ___𝐺𝐸 H E F G ⃗⃗⃗⃗⃗ _________. ⃗⃗⃗⃗⃗ ________ and ____𝐸𝐺 29. Name two different rays from the diagram: ____𝐹𝐻 30. Are EF and FG the same ray? ____no______ Why or why not? ______do not share same endpoint_ Line Relationships: Fill in the blank. a) ___parallel____________ lines share no points and are in the same plane. b) ___skew_______________ lines share no points and are NOT parallel. c) ___intersecting_________ lines share ONE point ONLY. e) ___coincidental_________ lines share ALL points. (lie on top of one another) 31) Name the line relationship of the following: Y D A VX E C B a) XB and BC ___intersecting________________ c) XY and DE ___skew_____________________ d) RA and AR ____coincidental_________ e) XY and BE ____parallel_____________ ANGLE CLASSIFICATION: a) ___vertical____________ angles are formed by intersecting lines. b) ___adjacent___________ angles are next to each other, share a common vertex, common ray and do not overlap. c) ___complementary_____ angles are angles whose measures add up to 90 degrees. d) ___supplementary_____ angles are angles whose measures add up to 180 degrees. (hint—“s” straight angle) 32. Find the measure of <B if <C is equal to 47 degrees and <B and <C are complementary. 90-47 = 43o Use the diagram to the right to answer questions 33-36. 33. Name two vertical angles: ___∠6&∠3___or _∠1&∠4___or __∠2&∠5___ 34. If the measure of <1 is 42 degrees, what is the measure of <2? _____________ 35. Name two angles that are adjacent: ______________ and ____________ 36. What is the measure of <3? ________ How do you know? Angle 3 and 6 are vertical angles. Since vertical angles have the same measure and angle 6 measures 90o, angle 3 measures 90o. ANGLE PAIRS: a) Angles that are on the opposite side of the transversal and inside the lines are ____________________ ___________________ angles. b) Angles that are on the same side of the transversal in the same position are ___________________ __________________ angles. c) Angles that are on the opposite side of the transversal outside the lines are ___________________ __________________ angles. Use the diagram to the right to answer the following questions. 37. Name an angle pair that are alternate exterior: _______ , ______ 38. Name an angle pair that are corresponding: ________, ________ 39. Name an angle pair that are alternate exterior: ______, _______ 40. If the measure of <3 is 78 degrees, what is the measure of <7? ______ <4?_______ <2? ________ 1 2 3 4 5 6 7 8 CLASSIFYING TRIANGLES: a) The sum of all the angles of a triangle are equal to _________ degrees. b) You can classify triangles by their _______________ and/or their ________________. c) An ___isosceles________________ triangle has 2 equal sides and 2 equal angles. d) A ____scalene_____________ triangle has all different sides and angles. e) An ______equilateral_______ triangle has all equal sides and angles. f) An _______acute__________ triangle has 3 angles less than 90 degrees. g) A ________right___________ has one angle that measures 90 degrees. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be _______greater_________ than the measure of the 3rd side. 41. The angles of a triangle measure 90 degrees, 38 degrees and x degrees. Find the value of x. 180-128=52 degrees 42. Could the following measures be the sides of a triangle? Why or Why not? 2 , 2, 4 ____No because 2+2=4, which is not greater than 4. 42. The angles of a triangle measure 90 degrees, 45 degrees and 45 degrees. The sides measure 6 cm, 4 cm and 4 cm. Classify the triangle: _____right (angles)________ and ______isosceles (sides)________ PROBABILITY: **We just completed this unit in class. Use your NOTES and/or your TEXTBOOK to help you. 43. In a bag of Sour Patch Kids, 6 are red, 4 are yellow, 5 are green and 2 are purple. What is the probability of choosing the following? Answer in a simplified fraction, decimal and percent. Total - 17 2 a) a purple: 17 ≈.12 ≈12% 5 b) a green: 17 ≈.29 ≈29% c) a red or a yellow: 6+4 17 = d) a yellow then a green: 10 17 4 ∙ ≈.59 ≈59% 5 17 16 = 5 68 ≈.07 ≈ 7% 44. In Mrs. Ellwood’s closet, she has 6 pairs of shoes, 4 skirts and 9 shirts. How many possible outfits are possible? 6*4*9 = 216 outfits 45. In a package of M and M’s , Jennifer found that 15% of the candies were yellow. There are 200 M and M’s in the package. How many M and M’s can be expected to be yellow? 15 P(red) = .15 OR P(red) = 100 𝑥 = .15 x = .15(200) x = 30 200 𝑥 15 = 100 100x = 3000 x = 30 200 Pre-Algebra Final Study Guide continued Name: ________KEY___________________ 1) Solve and check the following equations algebraically. Example: 5a 9 a 21 5a 9 ( a) 21 4a 9 21 9 9 4a 12 44 a 1 Change subtraction to adding the opposite Combine like terms Undo addition by subtracting 9 on each side Simplify Undo multiplication by dividing by 4 on each side Simplify a. x + 4x + 6 = 31 5x + 6 = 31 -6 -6 5x = 25 5 5 x=5 b. 5r + 3r – 6 = 10 5r + 3r + (-6) = 10 8r + (-6) = 10 +6 +6 8r = 16 8 8 r=2 c. 1 – 3y + y = 5 1 + (-3y) + y = 5 1 + (-2y) = 5 -1 -1 -2y = 4 -2 -2 y = -2 5r 3r 6 10 5(2) 3(2) 6 10 10 6 6 10 10 10 1 3y y 5 1 3(2) (2) 5 1 (6) (2) 5 1 6 (2) 5 7 (2) 5 55 Check: x 4 x 6 31 (5) 4(5) 6 31 5 20 6 31 25 6 31 31 31 2) Use the percent proportion or the percent equation to solve each problem. Example: What is 5% of 224? Percent Proportion is % Percent Equation of 100 part (% as decimal)( whole) x 5 x (.05)(224) 224 100 x 11.2 100 x 1120 x 11.2 a. What is 16% of 36.2? x = .16 (36.2) x = 5.792 OR x 16 36.2 100 100 x 579.2 100 100 x 5.792 b. 60 is 28% of what number? c. What percent of 48 is 0.6? 60 = .28 (x) p (48) = 0.6 .28 .28 48 48 214.29 = x p = 0.0125 = 1.25% 60 28 x 100 28 x 6000 28 28 x 214.29 0.6 x 48 100 48 x 60 48 48 x 1.25% 3) A dress originally priced at $75 is on sale for 30% off. What is the discount? What is the sales price? d %(op) d .30(75) sp 75 22.50 sp $52.50 d $22.50 4a) Graph y = -2x + 1 by first completing the table below and then graph on the coordinate plane. x Work y (x, y) -2 y = -2(-2) + 1 = 4 + 1 = 5 (-2, 5) -1 y = -2(-1) + 1 = 2 + 1 = 3 (-1, 3) 0 y = -2(0) + 1 = 0 + 1 = 1 (0, 1) 1 y = -2(1) + 1 = -2 + 1 = -1 (1, -1) 2 y = -2(2) + 1 = -4 + 1 = -3 (2, -3) b) Is the graph increasing or decreasing? (1 pt) ___decreasing_____________ c) Is the graph proportional? Explain why or why not. (2 pts) __No, the graph is not proportion because it does not pass through the origin._____________________ 5) Use the table to find the rate of change. Explain the meaning of the rate of change. Example Time (Hours) 4 Amount earned ($) $25 6 $40 b) Explain the meaning of the rate of change. 8 $55 For each additional hour, you earn $7.50 more. Δ𝑦 a) Rate of change = Δ𝑥 = 15 = $7.50 per hour 2 Use the table to find the rate of change. Explain the meaning of the rate of change. Time (min) 15 Energy burned (Calories) 60 30 120 b) Explain the meaning of the rate of change. 45 180 For each additional minute, on average 4 more calories are burned. Δ𝑦 a) Rate of change = Δ𝑥 = 60 = 4 calories per min 15 6) You are planning to sell school supplies at the school store for NJHS and you want to know what to sell. To answer your question, you survey the following groups below. Determine whether the following samples are random samples or biased samples and explain why. a) The students at your lunch table. Biased Sample; Each student does not have an equal chance of being chosen. Students at your lunch table are favored over others.________________________________ b) You select 20 names of students from a hat. Random sample; Each student has an equal chance of being chosen.______________________________________________________________________ 7) You roll a six sided die once. a) What is the theoretical probability that you roll a number less than 3 as a simplified fraction, decimal to the nearest tenth, and as a percent? P(less than 3) 2 1 0.33 33% 6 3 Rodejha rolls the die 25 times and records her results in the frequency table shown below. Number TALLY FREQUENCY 1 |||| 4 2 |||| | 6 3 |||| | 6 4 |||| 4 5 || 2 6 ||| 3 b) What is the probability that Rodejha rolled a number less than 3 as a simplified fraction, decimal to the nearest hundredth, and a percent? P(less than 3) 10 2 0.40 40% 25 5 c) Name the probability you found in question 7b. ___Experimental Probability_____________________ c) How does the probability in question 7a compare to the probability in question 7b? The theoretical probability is less than the experimental probability. _________________________ ________________________________________________________________________________