Part 1 - Multiple Choice Graphing Calculators or on-line graphing tools are permitted Circle the correct letter response

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1 1 MATH 30S APPLIED FINAL EXAM REVIEW ANSWERS TO SELECTION OF TYPICAL QUESTIONS Part 1 - Multiple Choice Graphing Calculators or on-line graphing tools are permitted Circle the correct letter response 1. The vertex of the parabola at right is: a. (0, ) b. (3, ) c. (, 3) d. no solution 0 y x. The line of symmetry for the parabola at the right is given by: 10 y - a. x = b. y = c. < y < x d. x x The vertex of the parabola: y = x x + is: a. (, ) b. (, ) c. (, ) d. (0, 0) (Tactical Hint: Never leave a multiple choice unchosen ; guess if you must! Teachers often make multiple choice questions a bit tougher because they know there is a 5% chance you will correctly guess the answer anyway!). The line of symmetry and the minimum value of the function: y = x 9 is: a. x = 9; y min =5 b. x = 0; y min = 9 c. x = 9; y min =5 5. The zeros (or roots) of the quadratic equation y = x + 5x + are: a and 5.70 b. 0 and 5 c. 3.1 and +3.1 d. 5 and - MA30SA_FinalExamReviewAns.doc Revised:011019

2 . The y intercept of the quadratic equation y = x 5x +3 is: a. 3 b. c. 5/ d The range of the quadratic equation y = x 7x + is: 1 a. < x < b. y < c. y > 0 d. none of these. Kyle found the following temperatures of his coffee as it cooled outside on the steps. Time M [Minutes] Temperature T [ C] What is an equation that best models this cooling? a. T = 0*0.5 M b. T = 3M + c. T = constant d. T = M % of $130 is: a. $0.9 b. $9.00 c. $. d. $10 exactly 10. One US dollar ($1 USD) will cost you $1.15 Canadian at the bank to buy. How much will $10 USD cost you? a. $13 Cdn b. $10.35 Cdn c. $11.15 Cdn d. $ The city and school board have set a combined mill rate of 39 mills for taxation on property. The portioned assessment value of your home is $5,000. How much annual property tax will you pay? a. $3,900 b. $5.00 c. $,1 d. $15 1. A six pack of 355ml cans of coke costs $1.. What is the unit cost in dollars per litre? a. $19.93/L b. $0.31 per litre c. $1./L d. $0./litre 13. A 0.5 kg package of steak costs $.5. What is the unit cost of the steak per Kg? a. $7.33 b. $.7 c. $0.1 d. $.3

3 3 1. Mathilde gets paid at an hourly rate of $10.50 per hour. She works the following hours in one week. What is her gross pay if overtime is paid at time-and-a-half after hours in any one day. Day M T W Th F Hours 10 1 a. $395.5 b. $375 c. $0.00 d. $ Brian has a gross income of $35 per week. He contributes $0/week to an RRSP. His income tax rate is 1%. How much tax is taken off his pay cheque? a. $.0 b. $1 c. $55.0 d. $ A system of linear equations that has no solutions is called: a. independent b. inconsistent c. dependant d. a solution 17. The solution to the system of linear equations: is: y = x + 1 y = 5x a. (, 1) b. (5, ) c. (3, 7) d. no solution; inconsistent 1. The solution to the system of linear equations: (same as question17!) y = x + 1 y 5x = is: a. (3, 7) b. 0 = 0 c. y 3x = 7 d. (, ) 19. The solution to the system of linear equations: 1 1 y = x and x + y = 1 is: a. (½, ¼) b. (, 1) c. (1, ) d. no solution 0. The sum of two numbers is 1 their difference is 5. Find the two numbers. a. (.5, 3.5) b. (17, 5) c. (7, 7) d. (7,1) (Hint: Often for multiple choice you can just test each answer to see if it works!)

4 1. Solve the inequality x + 1 > 5 a. x > 5 b. x > 3 c. x > d. x (Tactical Hint: Answer d. is obviously false! Where did the equals part come from?). Which (x, y) point is a solution to the linear inequality y > 5x? a. (0, ) b. (10, 0) c. ( 5, ) d. (0, 5) 3. The solution to the system of linear inequalities: y x + y 3x 9 is: a. region A b. region B c. region C d. region D D A B C. Points of equal elevation above sea-level on a geographic map are called: a. isoclines b. isotherms c. isobars d. icicles 5. On a weather map, the large Hs and Ls indicate: a. areas of High and Low temperature b. areas of High and Low bird migration c. areas of High and Low Ultraviolet exposure d. areas of High and Low atmospheric pressure. A tangent segment is to a radius at the point of tangency. a. parallel b. congruent c. perpendicular d. supplementary 7. Inscribed angles that share the same intercepted arc as a central angle are: a. half the measure of the central angle b. supplemental to the central angle c. pass through the centre of a chord d. always exactly 90 -

5 5. A line that goes through the centre of a circle and is perpendicular to a chord a. bisects a tangent b. is congruent c. bisects the chord d. is equidistant from the radius 9. If you invest $300 at 10% compounded quarterly how much is you investment worth after 1 years? a. $91. b. $0 c. $30.00 d. $ You loan your friend $00.00 and you charge him simple interest. He pays you back $0 after 1 months. What annual interest rate were you charging him? a. 15% b. 10% c. 13.3% d. 10% 31. How long does it take an investment of $1,000 to become $,500 if it is invested at % annual interest compounded daily? a. years b..5 years c years d. 1 months (Tactical Hint: sometimes many of the answers are just intuitively wrong, so eliminate them. Eg: if you could make $1,500 interest on $1,000 after only.5 years then sign me up for that program! More than double your money investment of $1,000 to $,500 after.5 years??!!; that would be so sweet)

7 7 Part - OPEN RESPONSE Graphing Calculators are permitted Show work for best marks 3. Accurately graph the quadratic function f(x) = x x a. state the vertex (3, 9) b. state the y intercept when x = 0, y = 0 c. state the domain of the function < x < d. state the range of the function y 9 e. state the minimum value of the function Y min = 9 f. state the zeros (x-intercepts) of the function 0 and ( the values of x that make y = 0 ) 33. Accurately graph the equation y = 0.1 * x a. what is the value of y when x =? y = 1. when x = b. what is the range of the y? y > 0 c. state the y-intercept? 0.1 (when x = 0, the y-axis)

8 3. Rachel makes Saskatoon pies! When she charges $3.00 she has 0 customers. For every increase in price of $0.50 she loses two customers. What price should she charge to optimize her income? Price $3.00 $3.50 $.00 $.50 Customers Income $0 $3.00 $.00 $3.00 She should charge $.00 per pie to optimize her income! 35. Terrance was counting bacteria in a petrie dish in biology class. There were initially 100 bacteria when he started his stop watch and he kept the following table of data for several days: Hours 0 0 Number a. Find the exponential equation that best models the bacteria growth y = 100*1.19 x b. how many bacteria were there after exactly 10 hours? 5 (depending on how accurately you calculate) c. how long would it take for there to be exactly 1000 bacteria? 13.9 hours

9 9 3. Nathan earns $1.50 per hour regular pay and gets time-and-a-half after 0 hours in a week. He worked 5 hours. He contributes $0/week to an RRSP and pays Union dues of $.00 per week. CPP contributions are deducted at.95% of his gross pay and EI takes 1.9% of his gross. He pays $1 for weekly parking. His income tax rate is 17%. What is Nathan s net (take-home) weekly pay? Net Pay is $ The Lavallee family has a house that has a market value of $10,000 and a frontage of 15 meters. The portion percentage applied is 5%. The city has set a mill rate of 0 mills and the school district a mill rate of 17 mills. Their new street sewer system costs them a frontage charge of $3.30 per meter. What is the Lavallee family annual tax bill? Annual tax bill is $07.50

10 10 3. You are going to St. Paul, Minnesota to shop. You want to take 00 US Dollars with you. Your bank posts a sign of exchange rates: Exchange Rate in We Buy We Sell Canadian Dollars US Dollar $1.15 $1.0 UK Pound $.0 $.0 a. how much will it cost you for your $00 USD to take to St. Paul? It will cost you $0.00 CDN b. if you return with $0.00 USD, how much Canadian $ can you exchange it for? You will get back $ CDN 39. Would you rather work for $9.50 per hour for 0 hours per week and 5% commission on all weekly sales of $5,00; Or Would you rather work for $1.00 per hour for 35 hours a week and a 10% commission on sales over $,000 based on weekly sales of $5,00? Option 1 is $0 per week, Option is $50. So option Solve the system of linear equations by substitution method y =x 5 x + y = ( 0.7,.333) or better yet : ( /3, 1/3)

11 11 1. Solve the system of linear equations by elimination method: x + y = 5 y = x + (1, 3). Solve the system of linear equations using a graphing calculator: x + 5y = y = x +5 a. Sketch the lines from your graphing calculator to the right b. Clearly state the solution to the system (.15, 0.75) 3. Solve using any method the system of linear equations: x + y = x y = 1 3 Clearly state your answer 1 This one is crazy!! But the exact answer is:, 7 (13.0, 3.57) 7 1 or approximately:

12 1. Six years ago my daughter was half my age. When I was she was two. What are our ages now? I am now, my daughter is now. 5. When I walk up an up-going escalator I am going miles per hour. When I walk down the up-going escalator I am going miles per hour. How fast am I walking and how fast is the escalator going? I am walking at 5 mph, the elevator moves at 3 mph. Ray paddles downstream for km in 30 minutes. He paddles back up stream in 5 minutes. What is the speed of the current and how fast does Ray paddle in still water? (in km/hr) Ray paddles at. and the current is at (The answers are not always nice round integer numbers!!!) 7. Solve the two separate linear inequalities: a. x + 1 > b. 3 x 0 a. x > 3.5 b. x 3/

13 13. Show the solution to the Linear Inequality for x and y. x + 5 y Show the solution to the system of linear inequalities: y > x x + 3y > You have a Canada Savings Bond (CSB) for $500. It pays % simple interest. You have had it for 15 years, how much is it worth now? $950.00

14 1 51. You invest $1,000 at 1% interest compounded monthly. How much is it worth after six years? $ You had an investment that earned $0 interest on a principal of $00 after 5 years. What was the interest rate if the interest was simple interest? % 53. Given centre O; radius = 5 cm, m BAC = 70. Find: A a. m BOC 10 b. m BDC 100 O c. m OBC 0 B C d. Area of OBC (area = ½*b*h).03 cm D

15 15 5. Given centre at O, Chord BD through the centre and length 10, m CAD = 30, find and explain why: A B a. m CBD m CBD = 30 since inscribed angles that share the same arc are congruent O b. m BCD m BCD = 90 since inscribed angles in a semi-circle are right angles c. radius of the circle. Radius = 5 since it is just half the length of the diameter BD D C

16 1 G E O B D C Z H A 55. Given O at centre, Line DE runs through centre and bisects chord GH, radius 10; measure length BC = 1; Lines AC and BC are tangents; and OE is bisected by chord GH find and explain how you found: a. distance CO Ans: 15. due to Pythagoras. Angle CBO is 90 since tangents are perpendicular to radii at the point of tangency; so : BC + radius = OC b. length GO Ans: 10 units long since GO is a radius! c. m BCZ Ans: 100. Since m BCO = tan -1 (OB/BC) = 39. ; so ACB = * 39. or 79. since triangle BOC and triangle OAC are congruent. So BCZ is the supplement of ACB or d. length GH Ans: GH is * 75 long or about 17.3 units. e. the area of sector AOB Ans: 7. units e. the area of the shape enclosed by the arc AB and between line segments AC and BC. Ans: 3. units.

17 B x C A 900 River 5. Here is a geographic map. The contour interval is 00 feet. a. If you walk from A to B are you going uphill or down hill? Ans: Downhill b. In which direction is the river flowing? North (to the top) or down (to the south)? Ans: It is flowing towards north (the top). c. If you are the x at point C at approximately what height would you be? Ans: Somewhere between 500 feet and 300 feet, so approximately 00 ft if it is a straight slope in that area.

4. The line of symmetry and the minimum value of the function: y = x 2 9 is:

4. The line of symmetry and the minimum value of the function: y = x 2 9 is: MATH 30P PRECALCULUS FINAL EXAM REVIEW SELECTION OF TYPICAL QUESTIONS Part - Multiple Choice Graphing Calculators or on-line graphing tools are not permitted Circle the correct letter response. The vertex