Math 20-2 Final Review

Class: Date: Math 20-2 Final Review Multiple Choice Identify the choice that best completes the statement or answers the question 1 Guilia created the following table to show a pattern Multiples of 9 18 27 36 45 54 Sum of the Digits 9 9 9 9 9 Which conjecture could Guilia make, based solely on this evidence? Choose the best answer a The sum of the digits of a multiple of 9 is equal to 9 b The sum of the digits of a multiple of 9 is an odd integer c The sum of the digits of a multiple of 9 is divisible by 9 d Guilia could make any of the above conjectures, based on this evidence 2 Siddartha made the following conjecture When you divide two whole numbers, the quotient will be greater than the divisor and less than the dividend Which choice, if either, is a counterexample to this conjecture? 1 2 4 8 = 05 12 4 = 3 a Choice 1 only b Neither Choice 1 nor Choice 2 c Choice 1 and Choice 2 d Choice 2 only 3 Which of the following choices, if any, uses deductive reasoning to show that the sum of three even integers is even? a x + y + z = 2(x + y + z) b 2 + 4 + 6 = 12 and 4 + 6 + 8 = 18 c 2x + 2y + 2z = 2(x + y + z) d None of the above choices 1

4 Which type of reasoning does the following statement demonstrate? All birds have feathers Robins are birds Therefore, robins have feathers a inductive reasoning b deductive reasoning c neither inductive nor deductive reasoning 5 Determine the unknown term in this pattern 3, 6, 12, 24,, 96, 192 a 48 b 102 c 96 d 36 6 Which number should appear in the centre of Figure 4? Figure 1 Figure 2 Figure 3 Figure 4 a 36 b 24 c 41 d 11 7 In which diagram(s) is AB parallel to CD? 1 2 a Choice 1 only b Choice 2 only c Choice 1 and Choice 2 d Neither Choice 1 nor Choice 2 2

8 Which angle property proves DAB = 120? a alternate exterior angles b corresponding angles c vertically opposite angles d alternate interior angles 9 Which are the correct measures of the interior angles of ΔCDE? a DCE = 56, CDE = 101, and CED = 23 b DCE = 46, CDE = 101, and CED = 33 c DCE = 32, CDE = 83, and CED = 65 d DCE = 76, CDE = 91, and CED = 13 10 Which are the correct measures for WXZ, UZY, and VYX? a WXZ = 162, UZY = 106, and VYX = 88 b WXZ = 166, UZY = 109, and VYX = 89 c WXZ = 152, UZY = 116, and VYX = 88 d WXZ = 162, UZY = 106, and VYX = 92 3

11 Determine the sum of the measures of the angles in a 12-sided convex polygon a 1080 b 3600 c 2160 d 1800 12 Determine the sum of the measures of the angles in a 9-sided convex polygon a 1720 b 1440 c 1260 d 1080 13 Which expression describes the ratios of side-angle pairs in ΔQRS? a q(sin R) = r(sin S) = s(sin Q) b q sin S = r sin Q = s sin R c s sin S = q sin Q = r sin R d q(sin Q) = r(sin R) = s(sin S) 14 Determine the measure of θ to the nearest degree a 40 b 38 c 36 d 42 4

15 In ΔDEF, d = 239 cm, e = 168 cm, and f = 270 cm Determine the measure of D to the nearest degree a 61 b 64 c 58 d 54 16 In ΔXYZ, x = 18 cm, y = 14 cm, and z = 17 cm Determine the measure of Y to the nearest degree a 43 b 47 c 45 d 49 17 Which choice expresses these numbers as the product of two radicals? 1089, 1764, 225, 1024 a 3 11, 6 7, 3 5, 4 8 b 9 121, 36 49, 9 25, 16 64 c 33 33, 42 42, 15 15, 32 32 d 3 11, 6 7, 3 5, 4 8 18 Which set contains like radicals? a 14 2, 5 16, 8, 21 6 b 6 3, 12, 2 3, 27 c 25, 9 15, 5 2, 3 5 3 d 17( 64 ), 10 4, 7 16, 4 19 Which is the simplest form of 7 8 2 72 50? a 0 b 3 2 c 21 2 d 9 2 5

20 How many solutions are there for 45 + 12x 6 = x? a one: 2 b none c two: 3, 3 d one: 3 21 Environment Canada compiled data on the number of lightning strikes per square kilometre in Alberta and British Columbia towns from 1999 to 2008 042 004 081 040 003 074 028 003 070 023 003 066 013 002 061 012 001 058 010 000 049 007 108 043 005 091 042 004 088 What value goes in the fourth row of this frequency table? Lightning Strikes (per square kilometre) Frequency 000 019 13 020 039 2 040 059 6 060 079 080 099 3 100 119 1 a 5 b 6 c 3 d 4 22 At the end of a bowling tournament, three friends analyzed their scores Erinn s mean bowling score is 92 with a standard deviation of 14 Declan s mean bowling score is 130 with a standard deviation of 18 Matt s mean bowling score is 116 with a standard deviation of 22 Who had the highest scoring game during the tournament? a Declan b Matt c Impossible to tell d Erinn 6

23 A company measured the lifespan of a random sample of 30 light bulbs Times are in hours 985 1001 1024 1087 952 910 938 931 1074 1081 1078 1080 982 1108 1022 937 922 1017 1093 1115 880 1048 917 1086 935 936 986 1038 954 966 Determine the standard deviation, to one decimal place a 585 h b 385 h c 685 h d 485 h 24 Which description does not describe the normal curve? a starts off increasing b symmetrical c shaped like a bell d always increasing 25 A teacher is analyzing the class results for a physics test The marks are normally distributed with a mean (µ) of 76 and a standard deviation (σ) of 4 Determine Olivia s mark if she scored µ σ a 84 b 68 c 80 d 72 26 Determine the percent of data between the following z-scores: z = 045 and z = 015 a 7668% b 4404% c 3264% d 1140% 27 In a recent survey of high school students, 42% of those surveyed said that the food in the cafeteria was overpriced The survey is considered accurate to within 6 percent points, 19 times out of 20 If a high school has 1000 students, state the range of the number of students who would agree with the survey a 520 640 b 360 420 c 420 480 d 360 480 7

28 Which relation is the factored form of f(x) = x 2 + 2x 8? a f(x) = (x + 2)(x 4) b f(x) = 2(x + 2)(x 2) c f(x) = (x 1)(x + 8) d f(x) = (x 2)(x + 4) 29 Which relation is the factored form of f(x) = x 2 4x + 4? a f(x) = (x 2) 2 b f(x) = (x + 4)(x 1) c f(x) = 4(x 1) 2 d f(x) = (x 2)(x + 2) 30 Which quadratic function represents this parabola? a f(x) = 4(x + 15) 2 2 b f(x) = 4(x + 15) 2 + 2 c f(x) = 4(x + 15) 2 + 2 d f(x) = 4(x 15) 2 2 8

31 Which quadratic function defines this parabola in vertex form? a y = (x + 5) 2 6 b y = (x + 4) 2 5 c y = (x + 6) 2 5 d y = (x + 6) 2 4 32 Solve 2x 2 24x + 75 = 0 by graphing the corresponding function and determining the zeros a x = 5, x = 3 b x = 3, x = 5 c There are no zeros d x = 0, x = 8333 33 A bridge is supported by three arches The function that describes the arches is h(x) = 02x 2 + 30x, where h(x) is the height, in metres, of the arch above the ground at any distance, x, in metres, from one end of the bridge How tall is each arch? a 97 m b 113 m c 108 m d 135 m 34 Which situations could be described using the rates $1556/lb, 80 km/h, and $158/L? a price of nails, average human running speed, price of sunflower oil b price of coffee, cruising speed of an airplane, price of milk c price of lobster, highway speed limit, price of apple juice d price of crude oil, average speed of a truck, price of cola 9

35 A picture is 46 cm by 32 cm A scale diagram of the picture must fit in a space that is 3 m by 2 m Which scale would be the most reasonable one to use for the scale diagram? a 60% b 1 cm:60 cm c 6 cm:1 m d 1 cm:6 cm 36 Data for triangle ABC is shown on the first line of the table Triangle ABC is reduced so the height is 15 cm Which triangle is the reduction of triangle ABC? Triangle Name Length of Base (cm) Height of Triangle (cm) Scale Factor Area (cm 2 ) Area of Scaled Triangle Area of O riginal Triangle ABC 50 30 10 75 100 DEF 100 15 20 25 400 GHI 15 15 05 30 025 JKL 25 15 05 1875 025 MNO 25 15 025 175 050 a DEF b GHI c JKL d MNO 37 Data for rectangle ABCD is shown on the first line of the table Rectangle ABCD is reduced to an area of 13 cm 2 Which rectangle is the reduction of rectangle ABCD? Rectangle Name Length (cm) Width (cm) Scale Factor Area (cm 2 ) Area of Scaled Rectangle Area of O riginal Rectangle ABCD 9 13 1 117 1 EFGH 3 4 1 9 13 1 81 JKLM 4 3 1 1 13 1 3 3 9 NOPQ 1 1 1 1 13 1 3 9 3 RSTU 3 4 1 1 13 1 3 3 9 a EFGH b JKLM c NOPQ d RSTU 10

38 A large city map book will be changed so that it can be used as a street guide To maintain the same number of pages, the page dimensions will be halved and the maps will be less detailed The same type of paper will be used for the smaller map book By what factor will the volume of the paper change? a 1 4 b 1 2 c 1 16 d 1 8 Short Answer 39 What type of error occurs in the following deduction? Briefly justify your answer People wear hats to prevent sunstroke Eldon is wearing a hat Therefore, Eldon is wearing the hat to prevent sunstroke 40 Does the following statement demonstrate inductive reasoning or deductive reasoning? For the pattern 4, 13, 22, 31, 40, the next term is 49 41 What number should go in the grey square in this Sudoku puzzle? 11

42 Solve for the unknown side length Round your answer to one decimal place v sin 84 = 150 sin 40 43 In ΔQRS, r = 41 cm, s = 27 cm, and R = 88 Determine the measure of S to the nearest degree 44 Convert 24 150 54 into mixed radical form Then simplify 45 Rationalize the denominator in 5 324 8 46 The ages of members in a hiking club are normally distributed, with a mean of 32 years and a standard deviation of 6 years What percent of the members are between 32 and 44? 12

47 Is the data in this set normally distributed? Explain Interval 10 19 20 29 30 39 40 49 50 59 60 69 Frequency 1 8 11 13 9 3 48 Determine the quadratic function that contains the factors (x + 5) and (x 9) and the point (5, 20) Express your answer in vertex form 49 Determine the roots of the corresponding quadratic equation for the graph 50 Determine the roots of the equation 4 5 b2 4b + 5 = 0 13

51 On Wednesday a crew paved 12 km of road in 7 h On Thursday, the crew paved 8 km in 6 h On which day did they pave the road at the faster rate? 52 A standard music CD has an exterior diameter of 120 mm and an interior diameter of 15 mm Draw a scale diagram of a CD using a scale factor of 60% 53 Sooki enlarges this figure by a scale factor of 2 Determine the area of the enlarged figure, to the nearest square unit 14

54 Triangle A has an area of 1900 cm 2 and similar triangle B has an area of 11875 cm 2 Determine what scale factor makes triangle B an enlargement of triangle A 55 The giant statue of a white fox in White Fox, SK, is 27 m long and 14 m tall Suppose the town council wants to create scale models of the statue that are 9 cm tall to sell to tourists What scale factor should they use? Problem 56 Jamie created a math trick in which she always ended with 5 When Jamie tried to prove her trick, however, it did not work Jamie s Proof n I used n to represent any number 3n Multiply by 3 3n + 15 Add 15 n + 15 Divide by 3 15 Subtract your starting number Identify the error in Jamie s proof and write the proof without error 15

57 Prove: FG HI 58 Given z = 115 Determine the measures of y 59 Rationalize each expression to compare the radical expressions Show each step A 7 B 3x 14 3 x 60 Gravity affects the speed at which objects travel when they fall Suppose a rock is dropped off a 75 m cliff on Mars The height of the rock, h(t), in metres, over time, t, in seconds could be modelled by the function h(t) = 19t 2 + 30t + 75 (The acceleration due to gravity on Mars is 377 m/s) a) How long would it take the rock to hit the bottom of the cliff? b) The same rock dropped off a cliff of the same height on Earth could be modelled by the function h(t) = 49t 2 + 30t + 75 Compare the time that the rock would be falling on Earth and on Mars 16

Math 20-2 Final Review Answer Section MULTIPLE CHOICE 1 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 11 OBJ: 11: Make conjectures by observing patterns and identifying properties, and justify the reasoning TOP: Conjectures and Inductive Reasoning KEY: conjecture inductive reasoning 2 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 13 OBJ: 14 Provide and explain a counterexample to disprove a given conjecture TOP: Disproving Conjectures: Counterexamples KEY: conjecture disproving conjectures counterexamples 3 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 14 OBJ: 13 Compare, using examples, inductive and deductive reasoning 15 Prove algebraic and number relationships, such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks 16 Prove a conjecture, using deductive reasoning (not limited to two column proofs) TOP: Proving Conjectures; deductive reasoning KEY: conjecture proving conjectures reasoning deductive reasoning 4 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 16 OBJ: 19 Solve a contextual problem involving inductive or deductive reasoning TOP: reasoning to solve problems KEY: reasoning inductive reasoning deductive reasoning 5 ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 16 OBJ: 19 Solve a contextual problem involving inductive or deductive reasoning TOP: reasoning to solve problems KEY: reasoning inductive reasoning deductive reasoning 6 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 16 OBJ: 19 Solve a contextual problem involving inductive or deductive reasoning TOP: reasoning to solve problems KEY: reasoning inductive reasoning deductive reasoning 7 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 21 OBJ: 11 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology 15 Verify, with examples, that if lines are not parallel the angle properties do not apply TOP: Parallel lines KEY: parallel lines transversals 8 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 22 OBJ: 12 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle 14 Identify and correct errors in a given proof of a property involving angles 21 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning 22 Identify and correct errors in a given solution to a problem that involves the measures of angles 23 Solve a contextual problem that involves angles or triangles 24 Construct parallel lines, using only a compass or a protractor, and explain the strategy used 25 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal TOP: Angles formed by parallel lines KEY: parallel lines transversals angles 9 ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 23 OBJ: 12 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle 21 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning TOP: Angles in triangles KEY: angles triangles 1

10 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 23 OBJ: 12 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle 21 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning TOP: Angles in triangles KEY: angles triangles 11 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 24 OBJ: 13 Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology 14 Identify and correct errors in a given proof of a property involving angles 22 Identify and correct errors in a given solution to a problem that involves the measures of angles 23 Solve a contextual problem that involves angles or triangles TOP: Angle properties in polygons KEY: polygons angle properties 12 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 24 OBJ: 13 Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology 14 Identify and correct errors in a given proof of a property involving angles 22 Identify and correct errors in a given solution to a problem that involves the measures of angles 23 Solve a contextual problem that involves angles or triangles TOP: Angle properties in polygons KEY: polygons angle properties 13 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 31 OBJ: 33 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the reasoning TOP: Side-angle relationships in acute triangles KEY: primary trigonometric ratios 14 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 32 OBJ: 33 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the reasoning TOP: Proving and applying the sine law KEY: sine law 15 ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 33 OBJ: 33 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the reasoning TOP: Proving and applying the cosine law KEY: cosine law 16 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 33 OBJ: 33 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the reasoning TOP: Proving and applying the cosine law KEY: cosine law 17 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 41 OBJ: 31 Compare and order radical expressions with numerical radicands 32 Express an entire radical with a numerical radicand as a mixed radical 33 Express a mixed radical with a numerical radicand as an entire radical TOP: Mixed and entire radicals KEY: radical 18 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 42 OBJ: 34 Perform one or more operations to simplify radical expressions with numerical or variable radicands TOP: Adding and subtracting radicals KEY: radical 19 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 42 OBJ: 34 Perform one or more operations to simplify radical expressions with numerical or variable radicands TOP: Adding and subtracting radicals KEY: radical 2

20 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 46 OBJ: 41 Determine any restrictions on values for the variable in a radical equation 42 Determine, algebraically, the roots of a radical equation, and explain the process used to solve the equation 43 Verify, by substitution, that the values determined in solving a radical equation are roots of the equation 45 Solve problems by modelling a situation with a radical equation and solving the equation TOP: Solving simple radical equations KEY: radical 21 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 52 TOP: Frequency tables, histograms, and frequency polygons KEY: frequency distribution histogram frequency polygon 22 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 53 OBJ: 13 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve TOP: Standard deviation KEY: mean standard deviation 23 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 53 OBJ: 12 Calculate, using technology, the population standard deviation of a data set 13 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve TOP: Standard deviation KEY: standard deviation 24 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 54 OBJ: 13 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve TOP: The normal distribution KEY: normal curve 25 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 54 OBJ: 17 Solve a contextual problem that involves the interpretation of standard deviation 19 Solve a contextual problem that involves normal distribution TOP: The normal distribution KEY: normal distribution mean standard deviation 26 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 55 OBJ: 18 Determine, with or without technology, and explain the z-score for a given value in a normally distributed data set TOP: Applying the normal distribution: z-scores KEY: z-score standard normal distribution 27 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 56 OBJ: 21 Explain, using examples, how confidence levels, margin of error and confidence intervals may vary depending on the size of the random sample 22 Explain, using examples, the significance of a confidence interval, margin of error or confidence level TOP: Confidence intervals KEY: margin of error confidence interval confidence level 28 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 63 OBJ: 26 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function TOP: Factored form of a quadratic function KEY: quadratic relation zero 29 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 63 OBJ: 26 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function TOP: Factored form of a quadratic function KEY: quadratic relation zero 3

30 ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 64 OBJ: 13 Determine the coordinates of the vertex of the graph of a quadratic function, given the equation of the function and the axis of symmetry, and determine if the y-coordinate of the vertex is a maximum or a minimum 26 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function TOP: Vertex form of a quadratic function KEY: quadratic relation parabola zero 31 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 65 OBJ: 26 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function TOP: Solving problems using quadratic function models KEY: quadratic relation parabola 32 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 71 OBJ: 15 Sketch the graph of a quadratic function 21 Determine, with or without technology, the intercepts of the graph of a quadratic function TOP: Solving quadratic equations by graphing KEY: quadratic equation roots 33 ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 74 OBJ: 11 Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function 16 Solve a contextual problem that involves the characteristics of a quadratic function TOP: Solving problems using quadratic equations KEY: quadratic equation roots 34 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 82 OBJ: 11 Interpret rates in a given context, such as the arts, commerce, the environment, medicine or recreation 18 Describe a context for a given rate or unit rate TOP: Solving problems that involve rates KEY: rate 35 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 83 OBJ: 22 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shape or a 3-D object and its representation TOP: Scale diagrams KEY: scale scale diagram 36 ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 84 OBJ: 22 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shape or a 3-D object and its representation 31 Determine the area of a 2-D shape, given the scale diagram, and justify the reasonableness of the result TOP: Scale factors and areas of 2-D shapes KEY: scale scale factor area 37 ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 84 OBJ: 22 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shape or a 3-D object and its representation 31 Determine the area of a 2-D shape, given the scale diagram, and justify the reasonableness of the result TOP: Scale factors and areas of 2-D shapes KEY: scale scale factor area 38 ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 86 OBJ: 36 Explain, using examples, the relationships among scale factor, area of a 2-D shape, surface area of a 3-D object and volume of a 3-D object 38 Solve a contextual problem that involves the relationships among scale factors, areas and volumes TOP: Scale factors and 3-D objects KEY: scale scale factor volume 4

SHORT ANSWER 39 ANS: There is an error in reasoning: there are many other reasons why Eldon might wear a hat, such as style, or being on a baseball team PTS: 1 DIF: Grade 11 REF: Lesson 15 OBJ: 17 Determine if a given argument is valid, and justify the reasoning 18 Identify errors in a given proof; eg, a proof that ends with 2 = 1 TOP: invalid proofs; deductive reasoning KEY: valid proofs invalid proofs deductive reasoning 40 ANS: inductive reasoning PTS: 1 DIF: Grade 11 REF: Lesson 16 OBJ: 19 Solve a contextual problem involving inductive or deductive reasoning TOP: reasoning to solve problems KEY: reasoning inductive reasoning deductive reasoning 41 ANS: 3 PTS: 1 DIF: Grade 11 REF: Lesson 17 OBJ: 21 Determine, explain and verify a strategy to solve a puzzle or to win a game 22 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game 23 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game TOP: analyzing puzzles and games KEY: reasoning solving puzzles 42 ANS: 232 PTS: 1 DIF: Grade 11 REF: Lesson 31 OBJ: 33 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the reasoning TOP: Side-angle relationships in acute triangles KEY: primary trigonometric ratios 43 ANS: S = 41 PTS: 1 DIF: Grade 11 REF: Lesson 32 OBJ: 33 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the reasoning TOP: Proving and applying the sine law KEY: sine law 44 ANS: 2 6 5 6 3 6 = 6 6 PTS: 1 DIF: Grade 11 REF: Lesson 42 OBJ: 34 Perform one or more operations to simplify radical expressions with numerical or variable radicands TOP: Adding and subtracting radicals KEY: radical 5

45 ANS: 45 2 2 PTS: 1 DIF: Grade 11 REF: Lesson 43 OBJ: 34 Perform one or more operations to simplify radical expressions with numerical or variable radicands 35 Rationalize the monomial denominator of a radical expression TOP: Multiplying and dividing radicals KEY: radical rationalize the denominator 46 ANS: 475% PTS: 1 DIF: Grade 11 REF: Lesson 54 OBJ: 17 Solve a contextual problem that involves the interpretation of standard deviation 19 Solve a contextual problem that involves normal distribution TOP: The normal distribution KEY: normal distribution mean standard deviation 47 ANS: Yes The graph of the data has a rough bell shape PTS: 1 DIF: Grade 11 REF: Lesson 54 OBJ: 14 Determine if a data set approximates a normal distribution, and explain the reasoning TOP: The normal distribution KEY: normal distribution mean standard deviation 48 ANS: y = 05(x + 2) 2 245 PTS: 1 DIF: Grade 11 REF: Lesson 65 OBJ: 16 Solve a contextual problem that involves the characteristics of a quadratic function 26 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function TOP: Solving problems using quadratic function models KEY: quadratic relation parabola 49 ANS: x = 0, x = 4 PTS: 1 DIF: Grade 11 REF: Lesson 71 OBJ: 21 Determine, with or without technology, the intercepts of the graph of a quadratic function 24 Explain the relationships among the roots of an equation, the zeros of the corresponding function, and the x-intercepts of the graph of the function 25 Explain, using examples, why the graph of a quadratic function may have zero, one or two x-intercepts TOP: Solving quadratic equations by graphing KEY: quadratic equation roots 50 ANS: b = 5 2 PTS: 1 DIF: Grade 11 REF: Lesson 72 OBJ: 22 Determine, by factoring, the roots of a quadratic equation, and verify by substitution TOP: Solving quadratic equations by factoring KEY: quadratic equation roots 6

51 ANS: Wednesday: 17 km/h Thursday: 13 km/h They paved the road faster on Wednesday PTS: 1 DIF: Grade 11 REF: Lesson 81 OBJ: 11 Interpret rates in a given context, such as the arts, commerce, the environment, medicine or recreation 13 Determine and compare rates and unit rates TOP: Comparing and interpreting rates KEY: rate unit rate 52 ANS: The CD should have an exterior diameter of 72 mm and an interior diameter of 9 mm PTS: 1 DIF: Grade 11 REF: Lesson 83 OBJ: 23 Determine, using proportional reasoning, an unknown dimension of a 2-D shape or a 3-D object, given a scale diagram or a model 24 Draw, with or without technology, a scale diagram of a given 2-D shape, according to a specified scale factor (enlargement or reduction) TOP: Scale diagrams KEY: scale scale diagram scale factor 53 ANS: 46 units 2 PTS: 1 DIF: Grade 11 REF: Lesson 84 OBJ: 31 Determine the area of a 2-D shape, given the scale diagram, and justify the reasonableness of the result TOP: Scale factors and areas of 2-D shapes KEY: scale scale factor area 54 ANS: 25 PTS: 1 DIF: Grade 11 REF: Lesson 84 OBJ: 22 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shape or a 3-D object and its representation 36 Explain, using examples, the relationships among scale factor, area of a 2-D shape, surface area of a 3-D object and volume of a 3-D object TOP: Scale factors and areas of 2-D shapes KEY: scale scale factor area 7

55 ANS: 9 or about 0064 140 PTS: 1 DIF: Grade 11 REF: Lesson 85 OBJ: 22 Determine, using proportional reasoning, the scale factor, given one dimension of a 2-D shape or a 3-D object and its representation TOP: Similar objects: scale models and scale diagrams KEY: scale scale factor similar objects PROBLEM 56 ANS: For example, in the 4th step, Jamie did not divide the term 15 by 3, which she should have done This throws out the rest of the calculations Here is the correct proof n I used n to represent any number 3n Multiply by 3 3n + 15 Add 15 n + 5 Divide by 3 5 Subtract your starting number PTS: 1 DIF: Grade 11 REF: Lesson 15 OBJ: 17 Determine if a given argument is valid, and justify the reasoning 18 Identify errors in a given proof; eg, a proof that ends with 2 = 1 TOP: invalid proofs; deductive reasoning KEY: valid proofs invalid proofs deductive reasoning 57 ANS: FHG + GHI + IHJ = 180 Sum of angles in triangle is 180 94 + GHI + 73 = 180 Substitute known values GHI = 180 94 73 Determine GHI GHI = 13 GHI = FGH Therefore, FG HI equal alternate interior angles PTS: 1 DIF: Grade 11 REF: Lesson 23 OBJ: 12 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle 21 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning TOP: Angles in triangles KEY: angles triangles 8

58 ANS: z + a = 180 Supplementary angles 115 + a = 180 Substitute a = 65 n + a + a = 180 Angle sum of a triangle n + 65 + 65 = 180 Substitute n = 50 n + m + 90 = 180 Angle sum of a triangle 50 + m + 90 = 180 Substitute m = 40 m + b + b = 180 Angle sum of a triangle 40 + 2 b = 180 Substitute 2 b = 140 b = 70 b + y = 180 Supplementary angles 70 + y = 180 Substitute y = 110 PTS: 1 DIF: Grade 11 REF: Lesson 23 OBJ: 12 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle 21 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning TOP: Angles in triangles KEY: angles triangles 9

59 ANS: A 7 3x 3x 3x = 21x 9x 2 B 14 3 x = 14 3 x x x 7 3x 3x 3x = 21x 3x 14 3 x = 14 x 3 x 2 7 3x 3x 3x = 21 x 3x 14 3 x = 14 x 3x The restriction of both expressions is x > 0 since x cannot be 0 or a negative number Since the denominators are the same, compare the numerators Since both numerators contain x and 21 < 14, then 7 3x < 14 3 x PTS: 1 DIF: Grade 11 REF: Lesson 44 OBJ: 34 Perform one or more operations to simplify radical expressions with numerical or variable radicands 35 Rationalize the monomial denominator of a radical expression 36 Identify values of the variable for which the radical expression is defined TOP: Simplifying algebraic expressions involving radicals KEY: radical restrictions rationalize the denominator 10

60 ANS: a) 0 = 19t 2 + 3t + 75 a = 19, b = 30, c = 75 t = b ± b 2 4ac 2a b) 0 = 49t 2 + 30t + 75 a = 49, b = 30, c = 75 t = b ± b 2 4ac 2a t = 30 ± ( 30 ) 2 4 ( 19) ( 75) 2 ( 19) t = 30 ± ( 30 ) 2 4 ( 49) ( 75) 2 ( 49) t = t = 3 ± 66 38 3 + 66 38 t = 1348 or t = 3 66 38 t = 2927 Time cannot be a negative value, so the time it takes for the rock to hit the bottom of the cliff on Mars is 29 s t = t = 3 ± 156 98 3 + 156 98 t = 0968 or t = 3 156 98 Difference in times = 2927 s 1580 s Difference in times = 13 s The difference in times between the two planets is 13 s t = 1580 Time cannot be a negative value, so the time it takes for the rock to hit the bottom of the cliff on Earth is 16 s PTS: 1 DIF: Grade 11 REF: Lesson 73 OBJ: 23 Determine, using the quadratic formula, the roots of a quadratic equation 27 Solve a contextual problem by modelling a situation with a quadratic equation and solving the equation TOP: Solving quadratic equations using the quadratic formula KEY: quadratic equation roots quadratic formula inadmissible solution 11