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Math 20-2 Final Review Name: Class: Date of Final: Unit 1: Quadratics Vocabulary: Quadratic Relation: a relation that can be written in standard form π¦ = ππ₯ 2 + ππ₯ + π, where π β 0; for example, π¦ = 4π₯² + 2π₯ + 1. Vertex: The point at which the quadratic function reaches its maximum or minimum value. Axis of symmetry: A line that seperates a 2-D figure into two identical parts. For example, a parabola has a vertical axis of symmetry passing through its vertex. Maximum value: The greatest value of the dependent variable in a relation. Zero: in a function, a value of the variable that makes the value of the function equal to zero. Quadratic equation: a polynomial equation of the second degree; the standard form of the quadratic equation is ππ₯² + ππ₯ + π = 0. Quadratic Formula: a formula for determining the roots of a quadratic equation in the form ππ₯ 2 + ππ₯ + π = 0, where aβ 0; the quadratic formula is written using the coefficients of the variables and the constant in the quadratic equation that is being solved: βπ ± βπ 2 β 4ππ 2π This formula is derived from ππ₯ 2 + ππ₯ + π = 0 by isolating x. Inadmissible solution: a root of a quadratic equation that does not lead to a solution that satisfies the original problem. Math 20-2 Final Review 2 Unit 1: Quadratics Recall: Standard form: π(π₯) = ππ₯ 2 + ππ₯ + π Factored form: π(π₯) = π(π₯ β π)(π₯ β π ) Vertex form: π(π₯) = π(π₯ β β)2 + π Key Ideas: ο· ο· ο· ο· ο· The degree of all quadratic functions is 2 The standard form of a quadratic function is π¦ = ππ₯ 2 + ππ₯ + π The graph of any quadratic function is a parabola with a single vertical line of symmetry A quadratic function that is written in standard form, π¦ = ππ₯ 2 + ππ₯ + π has the following characteristics: The highest or lowest point on the graph of the quadratic function lies on its vertical line of symmetry - If a is positive, the parabola opens up. If a is negative, the parabola opens down. - Changing the value of b changes the location of the parabolaβs line of symmetry (positive moves left, negative moves right) - The constant term, c, is the value of the parabolaβs y-intercept When a quadratic function is written in factored form: y = a(x β r)(x β s) each factor can be used to determine a zero of the function by setting each factor equal to zero and solving. - - The zeros of a quadratic function correspond to the x-intercepts of the parabola that is defined by the function If a parabola has one or two x-intercepts, the equation of the parabola can be written in factored form using the x-intercepts and the coordinates of one other point on the parabola Quadratic functions without any zeros cannot be written in factored form Math 20-2 Final Review 3 Unit 1: Quadratics Practice Questions: Multiple Choice Identify the choice that best completes the statement or answers the question. y 5 ____ 1. Which set of data is correct for the graph to the right? 4 3 2 A. B. C. Axis of Symmetry x = β2 x = β0.25 x = β0.5 D. x=3 Vertex (β0.25, β3.125) (β0.25, 3.125) (β0.5, 3) (3, β0.5) Domain xοR xοR β2.5 ο£ x ο£ 1.5 β3 ο£ x ο£ 2 1 Range yοR y ο£ 3.125 yο£3 β5 β4 β3 β2 β1 β1 1 2 3 4 x 5 β2 β3 yο£5 β4 β5 ____ 2. What is the correct quadratic function for the parabola to the right? y 5 a. b. c. d. f(x) f(x) f(x) f(x) = = = = 4 (x + 1)(x + 3) (1 β x)(3 β x) (x β 1)(x + 3) β(x + 1)(x β 3) 3 2 1 β5 β4 β3 β2 β1 β1 1 2 β2 β3 β4 β5 ____ 3. How many zeros does f(x) = (x β c)2 + d have if d > 0? a. 1 b. 0 c. 2 d. It is impossible to determine. ____ 4. Solve 4p2 + 15p = β9 by factoring. a. p = β , p = β3 b. p = 4, p = 3 c. p = β4, p = 3 d. p = β , p = 3 Math 20-2 Final Review 4 Unit 1: Quadratics 3 4 5 x ____ 5. Solve x2 β 2x = 4 using the quadratic formula. a. b. c. d. x x x x = = = = 1+ β1 + β1 + 1+ ,x=1β , x = β1 β , x = β1 β ,x=1β Written Response 6. Fill in the table for the relation y = β2x2 + 2x β 1. Maximum or minimum Axis of symmetry Vertex 7. Determine the equation that defines a quadratic function with x-intercepts located at (β9, 0) and (β2, 0) and a y-intercept of (0, 18). Provide a sketch to support your work. 8. a) Sketch the graph of y = (x + 1)(x β 7). b) State the maximum or minimum value of the function. c) Express the function in standard form. Math 20-2 Final Review 5 Unit 1: Quadratics 9. Determine the quadratic function that defines the parabola in vertex form. y 16 14 12 10 8 6 4 2 β4 β2 β2 2 4 6 8 10 12 14 16 x β4 10. The underside of a concrete underpass forms a parabolic arch. The arch is 32 m wide at the base and 11.5 m high in the centre. What would be the minimum headroom on a sidewalk that is built 1.5 m from the base of the underpass? 11. A ball is thrown into the air from a bridge that is 15 m above a river. The function that models the height, h(t), in metres, of the ball over time, t, in seconds is h(t) = β4.9t2 + 9t + 15 Answer each of the following questions by writing the corresponding quadratic equation and solving the equation by graphing. a) When is the ball 17 m above the water? b) When does the ball hit the water? Math 20-2 Final Review 6 Unit 1: Quadratics 12. Solve 2x2 + 4x β 2.5 = 0.5x2 + 5x + 4. 13. Tori sells posters to stores. The profit function for her business is P(n) = β 0.3n2 + 4n β 5, where n is the number of posters sold per month, in hundreds, and P(n) is the profit, in thousands of dollars. a) How many posters must Tori sell per month to break even? b) If Tori wants to earn a profit of $6000 (P(n)= 6), how many posters must she sell? 14. Ty is an artist. He wants the matte around each of his square photographs to be 6.5 cm wide. He also wants the area of the matte to be twice the area of each photograph. What should the dimensions of each photograph be, to the nearest tenth of a centimetre? Use a labelled diagram to solve the problem. Math 20-2 Final Review 7 Unit 1: Quadratics 15. A small movie theatre sells tickets for $15. At this price, the theatre sells 200 tickets every show. The owners know from past years that they will sell 8 more tickets per show for each price decrease of $0.50. a) What function, E(x), can be used to model the ownersβ earnings, if x represents the price decrease in dollars? b) What lower price would let the owners earn the same amount of money they earn now? c) What should the owners charge per ticket to earn the maximum amount of money? Math 20-2 Final Review 8 Unit 1: Quadratics Unit 2: Logic Vocabulary: Conjecture: A testable expression that is based on available evidence but is not yet proved. Inductive reasoning: Draw a general conclusion by observing patterns and identifying properties in specific examples. Deductive Reasoning: Drawing a specific conclusion through logical reasoning by starting with general assumptions that are known to be valid. Invalid Proof: A proof that contains an error in reasoning or that contains invalid assumptions. Circular Reasoning: An argument that is incorrect because it makes use of the conclusion to be proved. Practice Questions: Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Ginerva made the following conjecture: The square of a number is always greater than the number. Is the following equation a counterexample to this conjecture? Explain. 52 = 25 a. b. c. d. Yes, it is a counterexample, because 25 is greater than 5. No, it is not a counterexample, because 25 is greater than 5. No, it is not a counterexample, because 25 is less than 5. Yes, it is a counterexample, because 5 is less than 25. ____ 2. What type of error, if any, occurs in the following deduction? All swimmers can swim one kilometre without stopping. Joan is a swimmer. Therefore, Joan can swim one kilometre without stopping. a. b. c. d. a false assumption or generalization an error in reasoning an error in calculation There is no error in the deduction. Math 20-2 Final Review 9 Unit 2: Logic ____ 3. Which number should appear in the centre of Figure 4? a. b. c. d. Figure 1 6 120 15 240 Figure 2 Figure 3 Figure 4 Short Answer 4. Examine the following example of deductive reasoning. Why is it faulty? Given: At 11:00 p.m. this evening, there will be a newscast on Channel 20. There is a newscast on Channel 20 starting right now. Deduction: It is now 11:00. 5. The square of an odd integer is subtracted from the square of an even integer. Develop a conjecture about whether the difference is odd or even. Provide evidence to support your conjecture. Math 20-2 Final Review 10 Unit 2: Logic 6. Tyler made the following conjecture:A polygon with four right angles must be a rectangle. Matthew disagreed with Tylerβs conjecture, however, because the following figure has four right angles, and it is not a rectangle. How could Tylerβs conjecture be improved? Explain the changes you would make. 7. What type of error occurs in the following proof? Briefly justify your answer. 7= 7 β 1 2(7) + 3= 2(7 β 1) + 3 14 + 3= 2(6) + 3 17= 12 + 3 17 = 15 Math 20-2 Final Review 11 Unit 2: Logic Unit 3: Geometry Vocabulary: Corresponding angles: One interior angle and one exterior angle that are non-adjacent and on the same side of a transversal. Interior Angles: Any angles formed by a transversal and two parallel lines that lie inside the parallel lines. a b c a, b, c, d are interior angles. d Exterior Angles: Any angles formed by a transversal and two parallel lines that lie outside the parallel lines. e f e, f, g, h are exterior angles. g h Supplementary angles: Two angles that add to 180Λ. Alternate interior angles: Two non-adjacent interior angles on opposite sides of a transversal. Math 20-2 Final Review 12 Unit 3: Geometry Alternate Exterior angles: Two exterior angles formed between two lines and a transversal, on opposite sides of the transversal. Non-adjacent interior angles: The two angles of a triangle that do not have the same vertex as an exterior angle. A B C D β A and β B are non-adjacent interior angles to exterior β ACD Convex polygon: A polygon in which each interior angle measures less than 180Λ. Key Ideas: If a transversal intersects two lines such that ο· ο· ο· ο· The corresponding angles are equal or The alternate interior angles are equal or The alternate exterior angles are equal or The interior angles on the same side of the transversal are supplementary, Then the lines are parallel. The sum of the measures of the interior angles of a convex polygon with n sides can be expressed as: 180Λ(n β 2). The measure of each interior angle of a regular polygon is: Math 20-2 Final Review 13 180°(πβ2) π . Unit 3: Geometry The sum of the measures of the exterior angles of any convex polygon is 360Λ If three pairs of corresponding sides are equal, then the triangles are congruent. This is known as side-side-side congruence, or SSS. If two pairs of corresponding sides and the contained angles are equal, then the triangles are congruent. This is known as the side-angle-side congruence or SAS If two pairs of corresponding angles and the contained sides are equal, then the triangles are congruent. This is known as the angle-side-angle congruence or ASA The following Acronym can be helpful in remembering the ratios: SOH sin = opposite hypotenuse CAH cos = TOA adjacent hypotenuse tan = opposite adjacent The sine law can be used to determine unknown side lengths or angle measures in acute triangles. You can use the sine law, sin π΄ π = sin π΅ π = sin πΆ π , to solve a problem modeled by an acute triangle when you know: ο· ο· Two sides and the angle opposite a known side Two angles and any side If you know the measures of two angles in a triangle, you can determine the third angle because the angles must add to 180Λ. Some oblique triangle cannot be solved using the Sine Law. Therefore when you are not given a side and its angle, you can use the Cosine Law, c² = a² + b² - 2abCosC. Math 20-2 Final Review 14 Unit 3: Geometry Practice Questions: Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Which angle property proves οDAB = 120°? a. b. c. d. alternate exterior angles corresponding angles vertically opposite angles alternate interior angles ____ 2. Which are the correct measures for οDCE and οCAB? a. b. c. d. οDCE οDCE οDCE οDCE = = = = 31°, 47°, 13°, 37°, οCAB οCAB οCAB οCAB = = = = 134° 109° 143° 119° ____ 3. Which are the correct measures for οNOK and οJON? a. b. c. d. οNOK οNOK οNOK οNOK = = = = 35°, 35°, 38°, 28°, οJON οJON οJON οJON = = = = 82° 36° 35° 63° ____ 4. Which angle is equal to οD? a. b. c. d. οA οB οC none of the above Math 20-2 Final Review 15 Unit 3: Geometry ____ 5. Determine the measure of ο± to the nearest degree. a. b. c. d. 40° 38° 36° 42° ____ 6. Determine the length of PQ to the nearest tenth of a centimetre. a. b. c. d. 8.8 8.5 9.1 9.4 cm cm cm cm ____ 7. A kayak leaves Rankin Inlet, Nunavut, and heads due south for 4.5 km. At the same time, a second kayak travels in a direction S75°E from the inlet for 3.2 km. In which direction, to the nearest degree, would the second kayak have to travel to meet the first kayak? a. b. c. d. S45°W S45°W S50°W S40°W ____ 8. How long, to the nearest inch, is the right rafter in the roof shown? a. b. c. d. 33β0β 34β6β 33β6β 34β0β Math 20-2 Final Review 16 Unit 3: Geometry Short Answer 9. Given QP || MR, determine the measure of οMOQ. 10. Determine the value of x. 11. Determine the sum of the measures of the interior angles of this seven-sided polygon. Show your calculation. 12. In οLMN, l = 10.0 cm, m = 13.2 cm, and οM = 79°. Determine the measure of οL to the nearest degree. 13. Determine the measure of ο‘ to the nearest degree. 14. In οGHI, g = 30.0 cm, i = 19.3 cm, and οH = 53°. Determine the measure of h to the nearest tenth of a centimetre. Math 20-2 Final Review 17 Unit 3: Geometry 15. Given οz = 115°. Determine the measure of y. 16. MO and LN are angle bisectors. What is the relationship, if any, between οL and οO? Explain. 17. HJKL is a rectangle. Prove: JM = NL 18. Determine the length of EF. Show your reasoning. 19. A radio tower is supported by two wires on opposite sides. On the ground, the ends of the wire are 235 m apart. One wire makes a 75° angle with the ground. The other makes a 55° angle with the ground. Draw a diagram of the situation. Then, determine the length of each wire to the nearest metre. Show your work. Math 20-2 Final Review 18 Unit 3: Geometry Unit 4: Radicals Vocabulary: Extraneous Root: A root that does not satisfy the initial conditions that were introduced while solving an equation. Root is another word for solution. Key Ideas: A radical is in simplest form when the exponent of the radicand is less than 3 the index of the radical. For example, 12β3 and 13 β4 are in simplest form, while 12β4 is not. If you express an answer as a radical, the answer will be exact. If you write a radical in decimal form, the answer will be an approximation, except when the radicand is a perfect square. For example, β12 expressed as 2β3 remains an exact value, while β12 expressed as 3.464β¦ is an approximation. Both β9 and 3 are exact values. The product of two square roots is equal to the square root of the product. β3 β β2 = β3 β 2 = β6 The product of two mixed radicals is equal to the product of the rational numbers times the product of the radicals. 3β2 β 5β7 = 15β14 The quotient of two square roots is equal to the square root of the quotient: β6 β2 = β3 The quotient of two mixed radicals is equal to the product of the quotient of the coefficients and the quotient of the radicals: 15β14 5β7 Math 20-2 Final Review = 3β2 19 Unit 4: Radicals Practice Questions: Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Which of these equations are true? I. II. III. a. b. c. d. II only I and II I, II, and III I only ____ 2. Which is the simplest form of β7 β2 β6 ? a. β47 b. β161 c. β15 d. ____ 3. Which expression is the rationalized form of ? a. b. c. d. Short Answer 4. Convert β 5. Express + β into mixed radical form. Then simplify. in mixed radical form and entire form. Math 20-2 Final Review 20 Unit 4: Radicals 6. A park has a width of the park. m and a length of m. Determine the area of 7. State any restrictions on the variable, then divide. 8. Highway engineers design on-ramps and off-ramps to be safe and efficient. The relationship between the maximum speed at which a car can travel around a curve without skidding is S = , where S is the speed in kilometres per hour and R is the radius in metres of an unbanked curve in metres. What is the maximum speed at which a car can travel on a ramp with a radius of 200 m, to the nearest tenth of a metre? 9. Buildings in snowy areas often have steeper roofs than buildings in drier areas. This steepness, or βpitch,β is expressed as the height of a roof divided by its width. Determine the pitch, in lowest mixed radical form, for a building whose roof is m high and m wide. Show your work. 10. Simplify Math 20-2 Final Review . Explain each step. 21 Unit 4: Radicals Unit 5: Statistics Vocabulary: Mean: What is commonly called the average, calculated by adding up all the numbers and dividing by how many numbers there are. The mean of a sample is π₯Μ . The mean of a population is π. Median: The middle value, provided the data has been organized in ascending order. The mean of the two middle values if there is an even number of values. Mode: The most frequent value. There can be more than one mode, if more than one value ties for the most frequent. If all values appear with the same frequency, there is no mode. Range: The difference between the top and bottom numbers in a data set. Outliers: A value in a data set that is far from the other values in the data set. Line Plot: A βgraphβ that shows each number in the data set as a point above a number line. Dispersion: A measure that varies by the spread among the data in a set; dispersion has a value of zero if all the data in a set is identical, and it increases in value as the data becomes more spread out. Frequency: is the number of times the data value occurs in a set. For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f. Frequency Table: a table constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies Histogram: a graph of a frequency distribution, in which equal intervals of values are marked on a horizontal axis and the frequencies associated with these intervals are indicated by the areas of the rectangles drawn for these intervals. Math 20-2 Final Review 22 Unit 5: Statistics Standard Deviation: A measure of the dispersion or scatter of data values in relation to the mean; a low standard deviation indicates that most data values are close to the mean, and a high standard deviation indicates that most data values are scattered farther from the mean. Normal Curve: a symmetrical curve that represents the normal distribution; also called the bell curve. ο· ο· ο· ο· ο· 50% of the data is above the mean 68.26% of the data is within one standard deviation of the mean 95.44% of the data is within two standard deviations of the mean 99.74% of the data is within three standard deviations of the mean Total area under the curve is 1 or 100% Normal Distribution: data that, when graphed as a histogram or a frequency polygon, results in a unimodal symmetric distribution about the mean. Z-Score: is a standardized value that indicates the number of standard deviations of a data value above or below the mean. Math 20-2 Final Review 23 Unit 5: Statistics Key Ideas: ο· ο· ο· A confidence interval is expressed as the survey or poll result, plus or minus the margin of error. The margin of error increases as the confidence level increases (with a constant sample size). The sample size that is needed also increases as the confidence level increases (with a constant margin of error). The sample size affects the margin of error. A larger sample results in a smaller margin of error. A larger sample results in a smaller margin of error, assuming that the same confidence level is required. Practice Questions: Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine the z-score for the given value. µ = 510, ο³ = 93, x = 412 a. 0.95 b. β0.95 c. 1.05 d. β1.05 ____ 2. Determine the percent of data between the following z-scores: z = 0.40 and z = 1.80. a. 7.72% b. 22.66% c. 15.44% d. 30.87% Short Answer 3. Joel researched the average daily temperature in his town. Average Daily Temperature in Lloydminster, SK Month Jan. Feb. Mar. Apr. May Jun. average daily β10.0 β17.5 β5.0 3.7 10.7 14.3 temperature (°C) Jul. 20.1 Aug. 14.0 Sep. 9.8 Oct. 4.8 Nov. Dec. β5.8 β14.8 Determine the median of the data. Math 20-2 Final Review 24 Unit 5: Statistics 4. A teacher is analyzing the class results for a computer science test. The marks are normally distributed with a mean (µ) of 77.4 and a standard deviation (ο³) of 4.2. Determine Sinaβs mark if she scored µ + 2.5ο³. 5. In a recent survey of high school students, 43% of those surveyed agreed that the lunch period should be extended. The survey is considered accurate to within 4.6 percent points, 19 times out of 20. If a high school has 1500 students, state the range of the number of students who would agree with the survey. 6. Leon keeps track of the amount he spends, in dollars, on weekly lunches during one semester: 25 19 36 19 17 10 24 33 24 28 25 31 28 26 29 26 18 32 a) Determine the range, mean, and standard deviation, correct to two decimal places. b) Remove the greatest and the least weekly amounts. Then determine the range, mean, and standard deviation for the remaining amounts. What effect does removing the greatest and the least amounts have on the three values? 7. Yumi always waits until her gas tank is nearly empty before refuelling. She keeps track of the distance she drives on each tank of gas. The distance varies depending on the weather and the amount she drives on the highway. The distance has a mean of 520 km and a standard deviation of 14 km. a) What percent of the time does she drive between 534 km and 562 km on a tank of gas? b) Between what two symmetric values will she drive 95% of the time? Math 20-2 Final Review 25 Unit 5: Statistics 8. Jackson raises Siberian husky sled dogs at his kennel. He knows, from the data he has collected over the years, that the masses of adult male dogs are normally distributed, with a mean of 23.6 kg and a standard deviation of 1.8 kg. Jackson has 48 puppies this year. How many of them could he expect to have a mass greater than 20 kg when they grow up? 9. A hardware manufacturer produces bolts that have an average length of 1.22 in., with a standard deviation of 0.02 in. To be sold, all bolts must have a length between 1.20 in. and 1.25 in. What percent, to the nearest whole number, of the total production can be sold? 10. Use confidence intervals to interpret the following statement and apply the result to a graduating class of 1400 students. In a recent survey, 72% of post-secondary graduates indicated that they expected to earn at least $6000/month by the time they were ready to retire. The survey is considered accurate within ±5.2%, 19 times in 20. 11. Two different market research companies conducted a survey on the same issue. Company A used a 90% confidence level and company B used a 95% confidence level. a) If both companies used the same sample size, what does this imply about the margin of error for each survey? b) If both companies used the same margin of error of ±3.5%, what does this imply about the sample size for each survey? Math 20-2 Final Review 26 Unit 5: Statistics Unit 6: Proportional Reasoning Formulas: 1 π΄π‘πππππππ = 2 πβ π΄ππππππ = ππ² π΄πππππππππππππ = πβ h b 1 π΄π‘πππππ§πππ = 2 β(π + π) a h b If the area of a similar 2-D shape and the area of the original shape are known, then the scale factor, k, can be determined using the formula: π2 = ππππ ππ π ππππππ 2 β π· π βπππ ππππ ππ ππππππππ π βπππ 1 ππ΄πππβπ‘ π‘ππππππ’πππ ππππ π = πβ + π(π + π + π) ππππβπ‘ π‘ππππππ’πππ ππππ π = 2 πβπ ππ΄πππβπ‘ ππ¦ππππππ = 2ππ 2 + 2ππβ ππππβπ‘ ππ¦ππππππ = ππ 2 β 1 ππ΄πππβπ‘ ππ¦πππππ = π² + 2ππ ππππβπ‘ ππ¦πππππ = 3 π²β ππ΄πππβπ‘ ππππ = ππ² + πππ ππππβπ‘ ππππ = 3 ππ²β 1 4 ππ΄π πβπππ = 4ππ² Math 20-2 Final Review ππ πβπππ = 3 ππ³ 27 Unit 6: Proportional Reasoning Key Ideas: π·ππππππ ππππ π’ππππππ‘ ο· To determine a scale factor: ο· ο· ο· Scale factor between 0 and 1 is a reduction Scale factor greater than 1 is an enlargement Two 3-D objects that are similar have dimensions that are π΄ππ‘π’ππ ππππ π’ππππππ‘ proportional. ο· The scale factor is the ratio of a linear measurement of an object to the corresponding linear measurement in a similar object, where both measurements are expressed using the same units. ο· To create a scale model or diagram, determine an appropriate scale to use based on the dimensions of the original shape and the size of the model or diagram that is required Practice Questions: Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. It costs $0.3172/lb to ship freight by barge along the Pacific coast. Which equation determines the cost, C, in dollars, to ship 2740 kg of building supplies from Vancouver to Prince Rupert? a. b. c. d. Math 20-2 Final Review 28 Unit 6: Proportional Reasoning ____ 2. The distance between two towns on a map is 16.5 cm. The map was made using a scale of 5 cm to 100 km. What is the actual distance between the two towns? a. b. c. d. 135 825 330 165 km km km km ____ 3. A Ferris wheel is 57.85 m tall and has a diameter of 54.4 m. What are the dimensions of a scale model built using a scale of 1 : 95? a. b. c. d. height height height height 64.22 57.26 60.89 60.89 cm, cm, cm, cm, diameter diameter diameter diameter 60.44 53.42 64.22 57.26 cm cm cm cm ____ 4. Cylinder A has a radius of 5 mm and a height of 30 mm. Cylinder B has a radius of 20 mm and a height of 120 mm. These two cylinders are similar. By what factor is the volume of cylinder B greater than the volume of cylinder A? a. b. c. d. 64 8 16 32 Short Answer 5. A reindeer can run 133.25 km in 2.5 h. A grizzly bear can run 12.5 km in 15 min. Determine the speed of each animal in kilometres per hour. Which animal can faster? 6. It takes 5 h 17 min to decorate 200 cupcakes. How many minutes will it take to decorate three dozen cupcakes? Math 20-2 Final Review 29 Unit 6: Proportional Reasoning 7. Today, gold is worth $1200.60/oz (1 oz = 28.3495 g). What is the value of 0.9 g of gold? 8. Leo has a microscope with a lens that magnifies by a factor of 80. He was able to capture the image of a slide containing human skin cells. In the image, the cell was about 5.6 mm long. Determine the length of the actual human skin cell, to nearest hundredth of a millimetre. 9. The radius of a circle with an area of 8 cm2 will be enlarged by a scale factor of 4. Determine the area of the enlarged circle. 10. Museum curators are building scale models of antique furniture for a children's activity area. A chair is 91 cm tall, 56 cm wide, and 58 cm long. They would like the scale model to be 13 cm tall. What scale factor should they use? 11. The following table shows the attendance figures for the Calgary Stampede over several years. During which period was attendance decreasing at the greatest rate? Justify your answer. Year 1990 1995 1999 2004 2008 2010 Math 20-2 Final Review Attendance 1 208 371 1 101 551 1 113 017 1 221 182 1 236 351 1 145 394 30 Unit 6: Proportional Reasoning 12. Monroe and Connie drove from Winnipeg to Lethbridge for a music festival. They took turns driving, so they only needed to stop for gas or food. They drove the 1202 km distance in 15 h 34 min. They used 127.8 L of fuel, which cost $142.54. a) Determine their average speed to the nearest tenth of a kilometre per hour. b) Determine their average fuel consumption per 100 km. c) What was the average cost of a litre of gas? 13. A cook has a set of four mixing bowls with lids. The bowls stack inside each other and are similar to each other. The surface areas of the two largest bowls are 2300 cm2 and 1100 cm2. The scale factor is the same from each bowl to the next smaller bowl. How would you find the scale factor for the diameters of the bowls? Math 20-2 Final Review 31 Unit 6: Proportional Reasoning