Microsoft Word - EM40S Exam Review.docx



EXAM REVIEW | GR 12 ESSENTIALVEHICLE FINANCEMakayla traveled a total of 150 km in the city and 400 km on the highway. Her car has a fuel economy of 10.9 L/100 km in the city, and 7.9L/100 km on the highway. Gasoline costs109.9 cents per litre. Calculate the number of litres of fuel used, and the cost for the fuel.Cole lives in Manitoba and decides to buy a Mustang two-door convertible. He pays the base price of $28 673 and takes an option package worth $2 419. He adds on the automatic transmission for an extra $695. There is a freight charge of $1 095 and the options package he selects has air conditioning. Andy receives a trade-in allowance of $7 500 for his old car. How much will he pay?Determine the resale value of the following new vehicles for the years and depreciation rates given.$19 000 Vibe at the end of three years (first year 20%, 15% a year thereafter)$36 408 F150 at the end of two years (first year 25%, 15% a year thereafter)Calculate the total purchase price of a used vehicle sold privately in Steinbach, MB. The seller is asking $8 600 for the vehicle. A lien search costs $26, and a diagnostic test costs$35. Your mechanic reports that the car needs the following repairs: electrical, $275; suspension, $250; and exhaust, $170. A safety check costs $40. The book value of the vehicle is $9 000.A 4x4 pickup in The Pas, MB, leases for $329 a month plus taxes for a lease term of 36 months. A down payment of $3 500 is required. The sale price is $30 050 and the guaranteed residual value rate is 75%.Calculate the total lease monthly payment.Calculate the total lease payment over the term of the lease.Calculate the guaranteed residual value (including tax).Calculate the total cost if the vehicle is purchased outright at the end of the lease.Calculate the difference between the total cost if the vehicle is purchased outright at the end of the lease and the cost of the vehicle if it is purchased outright at time of purchase.Home FinanceBailey is considering purchasing a condominium in Winnipeg for $225 000. She has saved up $25 000 for a down payment. The credit union is offering her a mortgage at 4.25% over 25 years.Find her monthly mortgage payment.Find the interest and principal payments for the first month.How much interest is paid over the life of the mortgage?Harley earns an income of $4 000 per month. He wants to buy a house with a monthly mortgage payment of $950. The heating costs will be $150 per month and the annual property taxes are $2 750.Determine his Gross Debt Service Ratio.Would the bank likely recommend that Harley go ahead and purchase the house? Justify your answer.Kyla has a gross monthly income of $4 000. She is interested in purchasing a $195 000 house, and the bank is offering to give her a mortgage at 6.5% over 20 years. The monthly heating costs are $160 and the property taxes are $185 per month. Calculate the maximum affordable mortgage that Kyla can afford.Anthony is buying a home in East Selkirk, Mb. He is paying $235 000. He is also paying a down payment of 10% and closing costs are 2%.How much will Anthony pay for a down payment and how much will he need at closing?How much is the land transfer tax on his house?Devin lives in a large apartment complex. He would like to insure the contents of his suite for $40 000.00. What will his premium be for the year if he selects a Comprehensive policy with a $200.00 deductible?Al and Briana have purchased a house with a replacement value of $285 000.00. They wish to buy Comprehensive insurance with a $500.00 deductible for their new home. They live in Metro Winnipeg. How much will they have to pay for house insurance?Bronte plans to insulate the walls of her basement. This should reduce her heating costs by 12%. The wall area is 940 sq ft. The cost is $7.28/sq ft with installation and taxes.What is the total cost to insulate the walls?Bronte’s current heating bill is $1 950/yr. How much will she save on heat per year if she decides to insulate?The Jonatanson family lives in Libau and they decide to relocate to Winnipeg after purchasing a home. Name three additional costs when purchasing the home and explain each of them.A house has a market value assessment of $150 000 with a land assessment of $55 000. If the property is portioned at 45%, what is the portioned assessment?The budget requirement for the City of Dixie is $25 000 000. The taxable portioned assessment of the city is $685 000 000. What is the mill rate?The Martin family owns a home with a market value assessment of $170 000.00 and a land assessment of $50 000.00. The portion percentage for this class of property is 45%. The municipal mill rate is 22 mills, the provincial education rate is 7.5 mills and the local school division rate is 20 mills. The lot has a frontage of 15 m and there was a local improvement tax for sewer upgrades at $2.87/m. What was the total property tax bill for the family?STATISTICSFor each of the following, determine the median, mode, mean, and trimmed mean (remove the highest and lowest values). Also identify any outlier(s).a. 20, 34, 20, 15, 3, 20, 6, 10, 13, 16, 10, 50, 21b. 44.8, 43.9, 39.9, 42.7, 43.2, 44.6, 45.0, 30.1Taylor compares her quiz results to the rest of her classmates. She scored 21 out of 25 (it must have been an easy quiz). The scores of the nine other classmates are 19, 14, 23, 16, 15, 13, 17, 22 and 20.What is the range of the scores?At what percentile is a score of 16?At what percentile is a score of 21?What score is at the 50th percentile?What score is at the 75th percentile?Calculate the trimmed mean by removing the highest and lowest values.Owen got these marks in Geography:WorkMarkPercent of final markquiz685essay7525project7020exam7850Determine Owen’s final mark in this class.José scores 84% on his law exam. Two hundred other students wrote the same exam, and 175 received a lower score.What is his percentile ranking?What percent of students scored higher than José?PROBABILITYWhat is the probability of rolling a sum of 6 with two different dice? Express your answer as a fraction, a decimal to two decimal places, and a percent.What is the probability of choosing a vowel from letters G-R-A-D-U-A-T-E?What are the odds against choosing a vowel from the letters H-I-G-H-S-C-H-O-O-L?You choose a letter from the letters S-E-N-I-O-R, twice in a row (if you put the letter back each time)?Draw a tree diagram to show the different possible sequencesWhat is the probability of choosing 2 vowels in a row from the letters?A gas station has a scratch-and-win promotion. You scratch three cards and win once. What percent of the time did you win?You find the odds of winning a game are 1 to 3. What is the probability of winning once, as a percent?It costs $1 to play the game of “Pick the Marble”. In this game, a bag contains four red marbles, one black marble and five white marbles. You randomly pick a marble from the bag. If it is red, you win $5 and if it is black you win $10. However, if it is white you do not win anything. Determine the expected value of this game. If you play this game 20 times, what would you expect to gain or lose?A community club raffles off a $1 500 big screen TV. The tickets are $3.00 each and there are 2 500 tickets sold. What is your expected value if you bought only one of these tickets?A bag contains 2 blue marbles, 8 green marbles, 10 white marbles and 20 red marbles. A blue marble pays $16, a green marble pays $7, a white marble pays $1 and a red marble pays nothing.If it costs $2 to play, calculate the expected value.What is the expected gain or loss if a person plays the game 20 times?A lake is stocked with 150 fish for a fishing derby. Ten fish are tagged 3rd Prize, five fish are tagged 2nd Prize, and one fish is tagged Grand Prize. Dylan catches the first fish.What is the probability that Dylan’s fish is the Grand Prize fish?What is the probability that Dylan’s catch is one of the 2nd Prize fish?What is the probability that Dylan’s catch is one of the 3rd Prize fish?What is the probability that Dylan’s catch is any one of the tagged fish?On the drive to school you pass two traffic lights.List all of the possible combinations of lights you could get. Use R for red, G for green, and Y for yellow.What is the probability of getting 2 red lights?What are the odds of getting 2 red lights?Scott is laying laminate flooring. He needs 80 boards of laminate. About 15% of the boards are not usable. How many boards should Scott have available?A store that sells electrical receptacle plates claims that about 2% of the plates they sell arrive at the store damaged. The plates are sold in packs of 10.On average, there is approximately one damaged plate in how many packs?A customer purchases 8 packs of plates. Predict how many plates will be damaged.A weather forecast says that the P.O.P (probability of precipitation) today in Gimli, MB is 80%.Are the odds in favour of or against precipitation?What are the odds in favour of precipitation?How can you use P.O.P to help in decision making?PRECISION MEASUREMENT (PRECISION AND ACCURACY)Marcus times his 400-m practice freestyle swim on his wristwatch at 7:31. At the swim meet, the official time for his 400-m freestyle was 7:15.68.Which time was measured with greater precision?Explain how both times could be accurate.What is the difference between an accurate measurement and a precise measurement? Use examples to explain.Norm is a tailor in Prince George. He uses a cloth measuring tape to measure lengths. What measuring errors could cause him to measure inaccurately?Complete the chart.MeasurementPrecisionUncertainty52.3?C0.355 mmIs 214 000 L an allowable volume for a 216 000-L pool with a tolerance of ±1200 L?State the precision and uncertainty of the measurements. a. 8.04 gb. 60 secondsMarnie is looking at a drawing of a bolt that has a tolerance of 0.20” and a nominal value of 0.70”. What is the acceptable range of the measurement?What are the maximum and minimum values for each of the tolerances listed below?a.5.5 kg ± 0.03 kg-3b.63 +o cmc.50 ± 1 (0.25)2TRIGONOMETRYEvaluate sin 42°to three decimal places.Determine the measure of ?A, to the nearest degree, when cos A = 0.515.418185517369Determine the measure of the unknown angle.4771644-64037Determine the length of side a, to the nearest tenth of a unit.4675632-95644Determine the measure of ?A, to the nearest degree.500024456868Determine the length of side a, to the nearest tenth of a metre.Determine the measure of ?A, to the nearest degree.1304544127796Determine the length of each side, to the nearest tenth of a unit.side eside iA lighthouse keeper spots an iceberg. The captain of a ship also sees the iceberg. The diagram shows their readings. How far is the ship from the iceberg? Express your answer to the nearest mile.14356082279502447544297787Determine the measure of each angle, to the nearest degree.?A221894475803?E2218944-33288?GA surveyor spots a ship that is 2.5 km away. Her line of sight with the ship makes a 40° angle with the shoreline. Her assistant along the shoreline spots the same ship 1.8 km away. What is the measure of the angle at the assistant?1321308145653Determine the length of side EF for the triangle below, to the nearest tenth of a unit.1280160134985Solve for ∠C, to the nearest degree.cos C ?222? 72? 16.522(22)(7)3136392861664An employee of a tunnel boring company measures an angle of 95°at the top of a mountain, between where the new tunnel will enter and exit the mountain. Using a laser range finder, she measures the distance from the top of the mountain to the tunnel entry as 1520 feet. She measures the distance to the tunnel exit as 2320 feet. How long will the tunnel be?Determine the measure of the specified angle, to the nearest degree.?E188976094269A certain type of triangular sail has the side lengths shown. To cut the material for the sail, the manufacturer must know the size of each angle. Solve the triangle by determining the three unknown angles, to the nearest degree.A surveyor records the distance around a triangular piece of land. The measurements are 12 miles, 15 miles, and 13 miles. Determine the measures of the interior angles.POLYGONS (GEOMETRY)What is the measure of each interior angle in a regular pentagon?1866900165466What is the sum of the interior angles in each shape?an equilateral trianglean octagona parallelogramPolygonNumber of Interior AnglesSum of Interior AnglesMeasure of Each Interior AngleScalene triangleParallelogramIsosceles trapezoidRegular hexagonRegular octagonComplete the table with the properties related to the angle measures of the polygons listed.Tiffany is the lighting director for a theatre in Edmonton. She wants to place a spotlight so that it shines on the centre of a rectangular stage. How can Tiffany use a property of rectangles to find the centre of the stage? Use the rectangle below in your explanation.Determine the unknown measurements.isosceles trapezoidTW = 5 UV =?TXU = 110°?WXV =?TXU + ?UXV + ?VXW + ?WXT =parallelogramIG = EG = GH = IH =SOLUTIONSLet me know if you think you’ve spotted an error in the solutions below.Vehicle Finance1. (a) $600(b) $13002. $2 1253. 47.95L, $52.704. $28 681.665. (a) $10 982(b) $23 210.106. $10 212.907. (a) $371.77(b) $16 883.72(c) $25 467.38(d) $42 351.10(e) $8 394.60Home Finance1. (a) $1080(b) I = $708.33, P = $371.67 (c) $124 0002. (a) 33.2%(b) No, greater than 32%. 3. $139 552.244. (a) DP = $23 500, C = $4700 (b) $23505. $295.906. $1068.507. (a) $6843.20 (b) $2348. Various…9. $92 25010. 36.496 mills11. GMT: $2178, LIT: $43.05, ED:$742.50, SCH DIV: $1980 =$4943.55Statistics1. (a) median: 16, mode: 20, mean: 18.3, trimmed mean: 16.8, outlier: 50(b) median: 43.55, mode: none, mean: 41.775, trimmed mean: 43.18, outlier: 30.12. (a) 10P30P70182118 3. 75.15%4. (a) 88th percentile(b) 12%Probability1.2.3.4.5.6.7.8.9.5 , 0.14, 14%361273(b)93633%1, 25%10.(a)4$2, $40 gain$2.40 loss$0.30 gain$6.00 gain1(b)(c)(d)15013011587511. (b) 19(c) 1812. 9213. (a) 5(b) 1-2 plates14. (a) favour(b) 80%Precision and Accuracy1.(a) 7:15.684.(a) 0.1℃, ±0.05℃(b) 0.001 mm, ±0.0005 mm5.no6.(a) 0.01 g, ±0.5 sec(b) 1 sec, ±0.5 sec 7.0.6-0.88.(a) 5.47 kg-5.53 kg(b) 60 cm-63 cm (c) 49.875-50.125Trigonometry1. 0.6692. 59°3. 45°4. 12.45. 39°6. 14.9 m7. 149°8. (a) 10.5 m(b) 142.0 m9. 24 miles 10. (a) 58°(b) 63°(c) 60° 11. 63°12. 16.1 in, 32°13. 2 882 ft14. 22°15. ∠A = 79°, ∠B = 43°, ∠C = 58°16. 50.1°, 73.6°, 56.3°Geometry1. 108°2. (a) 180°(b) 1 080°(c) 360°3. (a) 3, 180°, varies(b) 4, 360°, 2 = acute, 2 = obtuse (c) 360°(d) 6 720°, 120°(e) 8, 1 080°, 135°5. (a) 5, 110°, 360°(b) IG = 4, EG = 8, GH = 6, IH = 3 ................
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