Labrador School Board. Mathematics 1201 Final Examination June 2012 ANSWER KEY

Transcription

1 DO NOT OPEN THIS EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN Labrador School Board Mathematics 0 Final Examination June 0 ANSWER KEY Total Value: 00 marks Time: Hours. Candidates are required to do all items. GENERAL INSTRUCTIONS. The examination has a total of pages consisting of the following parts: Part I: 0 Multiple Choice Items Value: 0% Part II: 7 Constructed Response Questions Value: 60%. Page is a formulae sheet to be used for the exam. This page may be removed.. Part I should be completed on the answer sheet provided on Page of the exam. This page may be removed.. Answers to the constructed response questions for part II are to be placed in this paper in the spaces provided. 6. For PART II items, candidates are reminded to show ALL necessary steps and calculations. Partial credit may be awarded for logical work even though you might not arrive at the correct solution. Correct answers without appropriate calculations will not merit full marks. 7. A self powered calculator may be used for calculations and to obtain special values. Graphing calculators are to be reset before the examination begins. REGULATIONS FOR CANDIDATES Candidates are expected to be thoroughly familiar with all regulations pertaining to their conduct during examinations. Candidates must comply with all requirements governing the following matters. Materials required Leaving the room Materials not permitted Models of calculators permitted Use of pen or pencil Use of unauthorized means and penalties Completion of required information Communication during the exam

2 PART I Total Value: 0% Item Level Outcome(s) Answer. I M. A. I M. B. II M. C. II M. C. II M.6 D 6. II M.8 D 7. I M., M. C 8. I M., M., M. A 9. II M., M. C 0. II M. C. I AN., AN. A. II AN.6, AN.7 B. I AN. D. I AN., AN. C. I AN., AN. C 6. II AN., AN., AN., AN. D 7. II AN., AN. C 8. II AN., AN. D 9. I AN. A 0. I AN., AN., AN. C. I AN., AN., AN., AN. A. I AN. B. I AN., AN., AN.7 D. II AN. B. II AN. A 6. II AN., AN., AN. C 7. I RF. B 8. I RF. A 9. II RF8. C 0. II RF.6 B. I RF. A. II RF., RF6., RF6., RF7. B. II RF., RF.9 A. I RF7. C. II RF6. C 6. I RF., RF6., RF7. C 7. II RF9., RF9. A 8. II RF9., RF9., RF9.6 C 9. I RF6., RF6.6, RF9.8 B 0. I RF9., RF9. D

3 PART II Total Value: 60% value. The right square pyramid is such that BC 0 cm and AF cm. Find the volume of the right square pyramid to the nearest cubic centimeter. Find perpendicular height: h 0 A h 00 6 h 6 00 marks h h Find Volume: E h cm D V B h F V 0 0 marks V 8000cm B 0 cm C. A farmer wishes to paint the exterior of his grain storage facility with dimensions as shown. If a can of paint covers 60 ft, how many cans of paint will the farmer need to purchase? (Note: the bottom of the storage facility is not to be painted.) Find Surface Area: S. A. lateral cone lateral cylinder S. A. rs rh S. A marks SA S. A ft 7 ft ft. Determine number of cans: mark 7 cans need to be purchased. 60 ft.

4 . Solve triangle PQR. Find QR or Q first. Find QR: a b c. QR 8 0. QR 6 QR QR marks Q. cm P 8 cm R QR Find P : a. cosp h 8 P. 8 P 6or.8 cos. marks Find R : R R 90 6 R 90.8 R. mark Measurements (assuming R ) are: P 6 Q 90 R side p 6.6 cm side q 8 cm side r. cm

5 . A lighthouse keeper spots two sailboats in distress. Sailboat A is observed at an angle of depression of and sailboat B at an angle of depression of 8. If the lighthouse keeper is. m above the ground, what is the distance (x) between the two sailboats? Find Distance from lighthouse to sailboat A:. tan y. y tan y.6.marks. m A x B Find Distance from lighthouse to sailboat B:. tan8 z. z tan8 z 88.9.marks Find Distance Between Both Sailboats : x z y x mark x 6. m is the dis tan cebetween the boats.. Shannon's rectangular dining room is ft by ft. There is a square rug that covers one-fourth the area of the floor. Determine the side length of the square rug. Express your answer in mixed radical form. Find Area of Room: Areaof Room ft. ft. 80 ft. 0.mark Determine Area of Rug: 80.. Areaof Rug ft ft mark Determine Side Length: Side Length Side Length ft. 9 ft mark Side Length ft 0. mark

6 6a. The volume of a sphere is 8. cm. What is the radius correct to the nearest tenth of a centimetre? Find Volume to Find Radius (r): V r 8. r 0.mark r 8. r 7. r mark 9. r 0. mark r 9,.9cm 0.mark 6b. What is the surface area of the sphere? Use the radius (r) to find Surface Area: S. A. r SA.. (.9) 0.mark SA.. (9.) S. A. (.)(9.) 0. mark SA r

7 7. Stephen completed a math problem and made a mistake. In which step does his error occur? Rewrite Stephen s solution so that it is correct. Error is instep mark Rewrite Solution Correcting Error: 6 0 x y x y x y x y y x y x y x y 0 0. mark x y mark Step Step Step Step 0 x y x y x y 6 0 x y x y x y x y y x y x y x y x y x 0.mark Step x y 8. Expand and simplify: x x 6x x x x x x x x 6 x x mark 0x x 6x x 0x x 0x x 8 mark 0x x x x 8 mark

8 9. Factor completely: 6x x 8x By Factoring: x(x x ) mark x(x x x ) 0. mark x[ x( x ) ( x ) 0. mark x ( x ) (x ) mark Using an Area Model: x(x x ) mark Area Model scores mark x - x x - x x - x (x x ) x (x )( x ) mark 0. Use an area model to multiply the binomials ( x 9) x. Area Model Setup is mark. x - Completing the model with the four terms (x, -x, 9x and -6) is mark. x x - x Determining the area is mark. ( x 9)( x ) x x 9x 6 x x x -6

9 . Determine an expression, in simplest form, to represent the area of the shaded region. Find Area of Rectangle: A (x )( x ) R A x x x 6 mark R A x x 6 R Find Area of Square: A ( x 6)( x 6) S A x 6x 6x 6 mark S A x x 6 S Find Shaded Area: x x 6 x + A A A Shaded R S A x x x x Shaded Shaded ( 6) ( 6) A x x x x 6 6) AShaded x x mark. A taxi company charges an initial fee of $ plus $ for every kilometer driven. Illustrate this relationship using each of the four methods requested in the table below. (Note: d is the distance travelled in km and C is the cost in dollars). The solution in each box is valued at mark. Table of Values: Equation: d 0 6 C Initial fee: $.00 Charge per km: $ C d Graph: Ordered Pairs: C = d + (0, ), (, 7), (, 9), (, ), (, ), (, ), (6, 7)

10 Note: Students should not be penalized if they did not include the value 0 in the domain and the value in the range. However, their table and graph should reflect this as well. Whether or not the point (0, ) should be included would make for a great class discussion during the unit.. The graph shows Brent leaving home at point A and travelling by truck to a friend s cabin located at point F. distance from home (km) 0 F(,0) 0 D(0,0) E(,0) 0 A B(, ) C(0, 0) time (minutes) a) What was his maximum rate of change (i.e. speed)? Occurs Between Point C and D. change in dist. 0 mi. mi./min. mark change in time 0min. b) Brent forgot his compass and had to turn around and go back home. How far was he from home when he had to go back? miles mark c) Brent stopped to repair a flat tire. How long was he stopped? he wasstopped for min. mark d) How many kilometres did Brent put on the truck from the time he left home (at point A) until he arrived at the cabin? 0miles mark

11 . A line passes through the points (8, -) and (6, ). Determine the equation of the line in general form (i.e. Ax By C 0 ). Find the Slope of the Line: slope 68 slope slope mark Determine the Equation of the Line y x b 0.mark Using the point (6, ): (6) b b 0.mark Write equation of the line: y x 0. mark Write equation in general form: y x 0. mark x y 0 mark

12 . Determine the equation of the line that passes through (6, -) and is parallel to the line x y 0. xy 0 y x mark y x m y x b mark 6 b 8 b mark b 0 y x 0 mark 6. Solve this system of equations by graphing. 8x y y x 8xy y 8x 0.mark 8 y x y x y x 0.mark y x y x 0. mark for each line correctly graphed as shown at the right. mark for clearly stating the solution as (, -7) or labelling the point on the graph.

13 7. Solve this system of equations using substitution or elimination. x 7y x y 8 Using Substitution: x7y 0. mark x7y xy 8 (7y) y 8 8y 0 y 8 98y 9 9 y 98 y x 7() x 8 0.mark x 7 Solution :( 7, ) 0.mark.marks Using Elimination: Mult. eq by - or 0. mark xy 70 mark x y 8 Vertically add equations to find x: x 98 mark x 7 Solve for y: x7y 7 7y 7y 8 y mark Solution :( 7, ) 0.mark