SUGGESTED ANSWER KEY DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN. Mathematics COMMON FINAL EXAM June 2014

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1 Name: Teacher: SUGGESTED ANSWER KEY HP DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN Mathematics 01 COMMON FINAL EXAM June 014 Value: 70 Marks Duration: Hours General Instructions Part I Selected Response (5 marks) Answer ALL questions in this section. Select the letter of the correct response from those provided and shade the letter on the computer scorable card and/or place the letter in the blank provided on the Selected Response Answer Sheet. Part II - Constructed Response (5 marks) Answer ALL questions completely and show workings in the space provided. NOTE: DIAGRAMS ARE NOT NECESSARILY DRAWN TO SCALE FORMULA SHEET AND Z-SCORE Z TABLE ARE PROVIDED Student Checklist Write your name and your teacher's name on this eam and on the Part I answer sheet. Check the eam to ensure that there are no missing pages.

2 Part I - Total Value: 5 marks Shade the letter of the correct response on the computer scorable card and/or place the letter in the blank provided on the Selected Response Answer Sheet. 1. What is the 6 term in the sequence { 5,9,1,...}? (A) 1 5 (C) 9 (D) 7. Which statement demonstrates using inductive reasoning to show that the product of two odd numbers is an odd number? (A) ( 5)(7) = 5 and ( 9)(7) = 6 ( 6)(8) = 48 and ( 4)(6) = 4 (C) ( )(y) = 4y (D) ( + 1)(y + 1) = 4y + + y + 1 = (y + + y) + 1. Which statement is correct regarding the conjecture that could be made, based on the table below? Multiples of Sum of Digits (A) (C) The sum of the digits of a multiple of 5 is an odd number. This conjecture is valid. The sum of the digits of a multiple of 5 is an odd number. This conjecture is not valid. The sum of the digits of a multiple of 5 is an even number. This conjecture is valid. (D) The sum of the digits of a multiple of 5 is an even number. This conjecture is not valid. 4. Brad, Lucy, Michelle and Patrick ran a race. Michelle and Brad finished before Lucy. Brad finished after Michelle. Brad and Lucy finished before Patrick. Who took second place? (A) Brad (C) (D) Lucy Michelle Patrick Mathematics 01 Common Final Eam 014 Page of 15

3 5. In which diagram is line L1 parallel to line L? (A) 70 L L L 1 L (C) L 1 L (D) 70 L L 6. If L1 L in the diagram below, what is the value of, in degrees? (A) (C) 100 (D) 10 L 1 L In the diagram below, what is the measure of ABC, in degrees? (A) 50 A C 60 B (C) 80 (D) 10 D E In the diagram below, what is the value of, in degrees? (A) (C) 110 (D) Mathematics 01 Common Final Eam 014 Page of 15

4 9. What is the congruence statement for the pair of congruent triangles below? (A) ABC FDE ACB FDE A 70 E F (C) (D) BAC BCA EDF EFD B 60 C D 10. In regular heagon ABCDEF below, what is the measure of angle, in degrees? (A) 0 A 60 F B (C) 90 (D) 10 E C D 11. If f = 1, degree? F = 40, and d = 10 in DEF, what is the measure of D E, to the nearest (A) F (C) 50 (D) 7 D 1. If j = 14, k = 19 and m = 17in JKM, what is the measure of K, to the nearest degree? J (A) (C) (D) 75 K 14 M Mathematics 01 Common Final Eam 014 Page 4 of 15

5 1. Simplify and order from least to greatest: 0, 64, 11 (A) 4, 4 5, 11 4, 11, 8 5 (C) 8, 4 5, 11 (D) 8, 11, Simplify: 6 ( + 5) (A) (C) (D) Simplify: 5 15 (A) (C) (D) What are the restrictions on the variable in the epression 5? (A) >, 5, 5 R R (C) (D) >, 5, 5 R R Mathematics 01 Common Final Eam 014 Page 5 of 15

6 17. Simplify: ( 8 )( ) (A) (C) (D) What is 5 written as an entire radical? (A) 10 0 (C) 40 (D) An advertisement for a new toothpaste states that 80% of users reported having better dental checkups. The results of the poll used to collect the data are accurate within 4 percentage points 9 times out of 10. What is the confidence interval? (A) 71% 89% 76% 84% (C) 81% 99% (D) 86% 94% 0. In Canada, IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What percent of the population would be epected to have an IQ lower than 85? (A) 9% 16% (C) 84% (D) 91% Mathematics 01 Common Final Eam 014 Page 6 of 15

7 1. Environment Canada compiled data on the number of millimetres of rain that fell at St. John s airport each day of April 01, and reported it in the frequency table below. How many days had less than 80 mm of rain? (A) 1 14 (C) 7 (D) 8 Rainfall (mm) Frequency At Harbour High School, 95% of the students weigh between 6 kg and 90 kg. Assuming that the data is normally distributed, what are the mean and standard deviation? Mean (kg) Standard Deviation (kg) (A) (C) (D) What are the domain and range for the quadratic function graphed below? Domain Range (A) { R} { y y 4, y R } { R} { y y 4, y R } (C) { 4, R } { y R} (D) { 4, R } { y R} y What is the y-intercept for the graph of y = ( + 1)? (A) 4 (C) (D) 1 Mathematics 01 Common Final Eam 014 Page 7 of 15

8 5. What is the verte of the quadratic function f ( ) = ( )( + 10)? (A) ( 4, 6) ( 4, 1) (C) ( 4,16) (D) ( 4,8) 6. What is the equation of the ais of symmetry for the graph of y = + 5? (A) = 5 = 1 (C) = 1 (D) = 5 7. Which equation describes the quadratic function graphed below? 1 (A) y = y = (C) y = (D) y = + 4 y Which describes the quadratic function y =? (A) It has a minimum value of 4 at = 1. It has a maimum value of 4 at = 1. (C) It has a minimum value of 0 at = 1. (D) It has a maimum value of 0 at = 1. Mathematics 01 Common Final Eam 014 Page 8 of 15

9 9. Which quadratic function has zeros = and = 6? (A) f ( ) = ( )( 6) f ( ) = ( )( + 6) (C) f ( ) = ( + )( 6) (D) f ( ) = ( + )( + 6) 0. Which quadratic equation has a root of =? (A) = 0 + = 0 (C) 9 = 0 (D) + 9 = 0 1. How many -intercepts would the function y = ( 1) + have? (A) 0 1 (C) (D). Which is the better buy? (A) L of apple juice for $ L of apple juice for $0.88 (C) 1 L of apple juice for $7.44 (D) 4 L of apple juice for $64.80 Mathematics 01 Common Final Eam 014 Page 9 of 15

10 . Which segment of the graph below represents the greatest rate of population increase? Population of Rocky Point (A) A 5000 (C) B C population A B C D (D) D year 4. The length and height of a tissue bo, in the shape of a rectangular prism, are 0 cm and 5 cm, respectively. A similar rectangular prism has length 5 cm, width 1.75 cm, and height 1.5 cm. What is the width, to the nearest tenth of a cm, of the original tissue bo? (A) cm 4. 0 (C) cm (D) cm 1.75 cm 1.5 cm 5. A spherical balloon with an initial volume of cm was leaking air. What was its volume, to the nearest cm, when the dimensions had been reduced by a factor of 4 1? (A) (C) 500 (D) Mathematics 01 Common Final Eam 014 Page 10 of 15

11 Part II - Total Value: 5 marks Answer ALL questions and show workings in the space provided. Value 6. Use deductive reasoning to prove that the product of an odd number and an even number is even. Let n = an even # n + 1 = an odd # Product = n(n + 1) = 4n + n = (n + n) Since (n + n) is divisible by, the product must be an even number 7. Use either a paragraph or two-column format to complete the given proof: A Given: AC BD C is the midpoint of BD Prove: AB AD B C D Statements Reasons 1. AC BD 1. Given. ACB = ACD = 90. lines form congruent. C is the midpoint of BD. Given 4. BC = CD 4. Definition of midpoint 5. AC = AC 5. Common side 90 angles 6. ABC ADC 6. SAS 7. AB AD 7. Corresponding parts of congruent triangles Mathematics 01 Common Final Eam 014 Page 11 of 15

12 Value 4 8. In the diagram below, QPR = 0, PRQ = 110, PQ = 45, and RS = 50. Determine the lengths of PR and PS, to the nearest tenth. Q # 1 : = = sin110 sin40 = 45 PR 45 sin40 PR = sin110 PR = 0.8 ******************** # : PRS = = 70 a r 40 = b + c bc cos A = (0.8)(50) cos70 r = 95. r = 95. r = 48.9 Q P 45 0 #1 # 110 R 50 S PR = 0.8 PS = Solve algebraically and check for etraneous roots: = = 4 Restr = 4 +1 = ( +1 ) = +1 = 4 = 4 1 = Check: LS = = + = 4 valid RS = 4 Mathematics 01 Common Final Eam 014 Page 1 of 15

13 Value 40. The area of rectangle ABCD is 15 and the length of AD is. Determine the lengths of DC and AC, in simplest form. A B Area DC = = = = width 5 D C ( ) + ( 5) = (AC) + 5 = (AC) 8 = (AC) 8 = AC = AC DC = 5 AC = Stewart s Snacks claims that their boes of crackers have a mean mass of 500 g with a standard deviation of 5 g. They promise to refund the purchase price of $.50 to customers if their bo of crackers has a mass less than 454 g. What is the maimum amount of money that Stewart s Snacks could be epected to refund to customers if there are 1 million boes sold per year? µ z = σ z = 5 46 z = 5 z = 1.84 From z-score table: 0.09 or.9% Maimum refund possible = $.50 = $8 50 Mathematics 01 Common Final Eam 014 Page 1 of 15

14 Value 4 4. A golf ball is hit from the ground and lands on the green after 4 seconds. The maimum height reached by the ball is 0 m. a) Algebraically determine the function, in the form y = a( h) + k, that models the path of the ball. b) Use that function to determine the height of the ball at.5 seconds. y = a( ) + 0 Verte (, 0) Sub in (0,0) 0 = a (0 ) = 4a + 0 4a 0 = 4 4 a = 5 0 y = 5( ) At =. 5, y = 5(.5 ) + 0 y = Function y = 5( ) + 0 Height m 4 4. Algebraically determine the eact roots, in simplest form: ( + ) = + 6 = + 6 = 0 b ± b 4ac = a 6 ± 6 4()( ) = () 6 ± = 6 6 ± 60 = 6 6 ± 4 15 = 6 6 ± 15 = 6 ± 15 = Mathematics 01 Common Final Eam 014 Page 14 of 15

15 Value Mary has a rectangular vegetable garden with dimensions 8 m by 6 m. She wishes to etend her garden as shown in the diagram below, so that the area of her new garden is twice the area of the original. Algebraically determine the dimensions of the new garden. Areanew = Areaoriginal = (6 8) = 96 New width = 6 + New length = 8 + new original ( 6 + )(8 + ) = = = 0 ( ) = 0 0 ( ) = = 0 8 m 6 m ( + 1)( ) = 0 = 1 = reject width = 6 + = 8 m length = 8 + () = 1 m 45. A scale drawing of River View High School s triangular school crest has a base of 8 cm and a height of 5 cm. The principal wants to place a poster of the enlarged crest in the school lobby. If the enlarged crest has an area of 0cm, what are the measurements of its base and height? 1 Area = bh 1 = (8)(5) = 0 RVHS Scale factor = k 0 k = 0 k = 16 k = 16 k = 4 Enlarged base = 4(8) = cm Enlarged height = 4(5) = 0 cm Mathematics 01 Common Final Eam 014 Page 15 of 15