Score: /42 Name: Grade 11 Essential Math Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following would not be a correct description of slope? rise a. run b. The height that a line rises. c. How gently or steeply something is slanted. d. The change in vertical distance compared to the change in horizontal distance. 2. Which of these instructions would give the following graph? a. Plot coordinate (12, 0), and continue plotting points 5 unit(s) in the negative x direction and 1 unit(s) in the negative y direction. b. Plot coordinate (0, 12), and continue plotting points 1 unit(s) in the negative x direction and 5 unit(s) in the positive y direction. c. Plot coordinate (0, 12), and continue plotting points 5 unit(s) in the positive x direction and 1 unit(s) in the negative y direction. d. Plot coordinate (12, 0), and continue plotting points 5 unit(s) in the positive x direction and 1 unit(s) in the negative y direction. 3. At the post office, Amaya sorted 43 letters in 19 minutes. After a total of 76 minutes, she has sorted 172 letters. What coordinates would represent her work? a. (43, 19) and (172, 76) c. (43, 19) and (76, 172) b. (76, 43) and (19, 172) d. (19, 43) and (76, 172) 4. If a rectangular face has an area of 120 square inches, which of the following dimensions could the rectangular face have? a. 5 in.! 8 in. c. 18 in.! 6 in. b. 15 in.! 8 in. d. 5 in.! 15 in.
5. What is the surface area of this cylinder? a. 413.0 m 2 c. 619.5 m 2 b. 516.2 m 2 d. 84.9 m 2 6. What is the lateral surface area of a cone with a radius of 26 feet and a slant height of 37 feet? a. 2115 ft 2 c. 3022 ft 2 b. 3626 ft 2 d. 3929 ft 2 7. What is the capacity, in litres, of a square-based pyramid with a height of 3.5 cm and side lengths of 8 cm? (1cubic cm = 1 ml) a. 0.056 L c. 0.09 L b. 0.075 L d. 0.068 L 8. Paul invests his savings of $1835.00 into a savings bond at a simple interest rate of 3.80% per annum. How much interest will his savings bond earn in 4 years? a. $278.92 c. $223.14 b. $334.70 d. $264.25 9. How much more interest would you pay per year on a $3300.00 credit card balance if the interest rate was 18.50% per annum instead of 14.30% per annum? a. $144.20 c. $135.04 b. $138.60 d. $145.30 10. What is the volume of this pyramid? a. 29640 cm 3 c. 18525 cm 3 b. 24700 cm 3 d. 22230 cm 3
Short Answer 1. What is the slope of a driveway that rises 1.1 m over a length of 10.9 m? (1 mark) 2. A theatre tracks ticket sales for every production that runs on their stage during a three-week run. Theatre Ticket Sales, by Production Legend Production A Production B Production C Danger at Noon The Kitchen Jumping Hoops a) Of the three productions, which one had the most ticket sales? Show your calculations. (2 marks) b) The theatre company is thinking of rerunning one of their productions. Why might you recommend The Kitchen? (1 mark)
3. What is the area of triangle DCE? (3 marks) D 40 0 7.5 cm C E 4. A standard bank account allows 20 free transactions per month and charges $0.50 for each additional transaction. How much will it cost if you make an average of 43 transactions each month for a length of 6 months? (1 mark) 5. A principal of $3500.00 was invested at a simple interest rate of 1.50% per annum. It earned $157.50 in simple interest. How long was it invested, in years? (1 mark) 6. If Tim s annual salary is $23050.00 and he gets a raise of 2.83% at the start of the new year, what is his new annual salary? (1 mark) 7. Andrei s average monthly spending on entertainment is $112.45. He is creating a conservative monthly budget and allocates $112.00 to entertainment. Give one reason why the rounded value Andrei has included in his budget is not appropriate. (1 mark)
Problem 1. A family returning from a camping trip has a 750-km drive ahead of them. They will travel at an average speed of 80 km/h. The following equation shows their progress: d = -80h + 1000 In this equation, d is the distance remaining and h is the number of hours travelled. a. What are the independent and dependent variables in this situation? (1 mark) b. Create a table of values showing the distance remaining at 1-hour intervals, up to 6 hours. (3 marks) Time travelled (h) Distance remaining (km) c. Plot the data and calculate the slope of the line. (4 marks) d. What does the slope represent? (1 mark)
2. Mike invests $10225.00 at a rate of 5.70% per annum, compounded monthly. Over a 9-month period, how much more money would Mike earn if the investment was compounded daily? Assume 1 year equals 365 days. (3 marks) 3. Peter has started creating a monthly budget. Peter s monthly budget Income Expenses Semi-monthly paycheque $890.00 Rent $595.00 Semi-monthly paycheque $890.00 Utilities, phone, internet $150.00 Groceries $300.00 Transportation $190.00 Entertainment $200.00 Clothing $150.00 Charitable donations $20.00 Miscellaneous $150.00 Savings TOTAL TOTAL a) Calculate how much money Peter can put into savings in one month. (3 marks) b) What percentage of his income goes to entertainment? (1 mark) c) If Peter wanted to begin saving more money, what are two changes he could make to his spending? (1 mark)
4. A surveyor is measuring the heights of various buildings. From the top of one building, the angle of elevation to the top of the neighbouring building is 20 and the angle of depression to the bottom of the building is 74. If the neighbouring building is 11 m away, how tall is it? Include a diagram. (4 marks)
Grade 11 Essential Math Practice Exam Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Easy REF: 1.1 OBJ: Algebra LOC: A-SO2 TOP: Rise Over Run KEY: slope 2. ANS: C PTS: 1 DIF: Moderate REF: 1.3 OBJ: Algebra LOC: A-SO2 TOP: Rate of Change KEY: plotting graph 3. ANS: D PTS: 1 DIF: Easy REF: 1.3 OBJ: Algebra LOC: A-SO2 TOP: Rate of Change KEY: plotting graph 4. ANS: B PTS: 1 DIF: Moderate REF: 3.1 OBJ: Measurement Algebra LOC: M-SO1 A-SO1 TOP: Surface Area of Prisms KEY: surface area 5. ANS: B PTS: 1 DIF: Easy REF: 3.2 OBJ: Measurement Algebra LOC: M-SO1 A-SO1 TOP: Surface Area of Pyramids, Cylinders, Spheres, and Cones KEY: surface area cylinder 6. ANS: C PTS: 1 DIF: Moderate REF: 3.2 OBJ: Measurement Algebra LOC: M-SO1 A-SO1 TOP: Surface Area of Pyramids, Cylinders, Spheres, and Cones KEY: surface area cone 7. ANS: B PTS: 1 DIF: Moderate REF: 3.4 OBJ: Measurement Algebra LOC: M-SO2 A-SO1 A-SO3 TOP: Volume and Capacity of Spheres, Cones, and Pyramids KEY: capacity pyramid 8. ANS: A PTS: 1 DIF: Easy REF: 6.2 OBJ: Number Algebra LOC: N-SO3 A-SO1 TOP: Simple and Compound Interest KEY: simple interest 9. ANS: B PTS: 1 DIF: Moderate REF: 6.3 OBJ: Number Algebra LOC: N-SO3 N-SO5 A-SO1 TOP: Credit Cards and Store Promotions KEY: simple interest unpaid balance 10. ANS: B PTS: 1 DIF: Easy REF: 3.4 OBJ: Measurement Algebra LOC: M-SO2 A-SO1 TOP: Volume and Capacity of Spheres, Cones, and Pyramids KEY: volume pyramid SHORT ANSWER 1. ANS: m = rise run m = 1.1 10.9 m! 0.101
The slope of the driveway is about 0.101. PTS: 1 DIF: Easy REF: 1.1 OBJ: Algebra LOC: A-SO2 TOP: Rise Over Run KEY: slope 2. ANS: a) Calculate the total sales for each production. Danger at Noon : 120 + 130 + 100 = 350 The Kitchen : 55 + 120 + 160 = 335 Jumping Hoops : 120 + 80 + 70 = 270 Danger at Noon had the most ticket sales. b) The Kitchen became more popular each week, so if it was brought back it might continue to grow in popularity. PTS: 1 DIF: Moderate REF: 2.2 OBJ: Statistics LOC: S-SO1 TOP: Bar Graphs KEY: reading a graph 3. ANS: Calculate length DC. cos! = adj hyp cos 40 = DC 7.5 7.5 cos 40 = DC 5.7 cm " DC DC is 5.7 cm. Calculate length CE. sin! = opp hyp sin 40 = CE 7.5 7.5 sin 40 = CE 4.8 cm " CE CE is 4.8 cm. Calculate the area of triangle DCE.
A = 1 2 bh A = 1 2 (CE)(DC) A = 1 2 (4.8)(5.7) A = 13.7 cm 2 The area is 13.7 cm 2. PTS: 1 DIF: Difficult REF: 4.1 OBJ: Geometry LOC: G-SO1 TOP: Solving for Angles, Lengths, and Distances KEY: cosine ratio sine ratio area 4. ANS: Calculate how many transactions will be charged at an additional fee on average each month. 43 20 = 23 Calculate the average cost per month. 23! $0.50 = $11.50 Calculate the cost over 6 months. 6! $11.50 = $69.00 Over 6 months, it will cost $69.00. PTS: 1 DIF: Moderate REF: 6.1 OBJ: Number LOC: N-SO4 TOP: Choosing an Account KEY: transaction fee 5. ANS: Use the simple interest formula to calculate the term length. I = Prt $157.50 = $3500.00! 0.015! t $157.50 $3500.00! 0.015 = t 3 = t The investment term was 3 years. PTS: 1 DIF: Moderate REF: 6.2 OBJ: Number Algebra LOC: N-SO3 A-SO1 TOP: Simple and Compound Interest KEY: simple interest 6. ANS: Calculate Tim s new salary as a percentage of his old salary.
new salary = old salary! (1 + raise percentage, as a decimal) new salary = $23050.00! (1 + 0.0283) new salary = $23050.00! 1.0283 new salary = $23702.31 Tim s new salary will be $23702.31. PTS: 1 DIF: Easy REF: 7.1 OBJ: Number LOC: N-SO2 TOP: Preparing to Make a Budget KEY: income 7. ANS: Answers will vary. Entertainment is a variable expense. In a conservative budget, variable expenses should be rounded up. Rounding a value to the nearest $1.00 will not account for the fluctuations in spending from month to month. Andrei should round the value up to the nearest $10.00. An appropriate entry for entertainment in Andrei s conservative monthly budget would be $120.00. PTS: 1 DIF: Moderate REF: 7.2 OBJ: Number LOC: N-SO2 TOP: The Budgeting Process KEY: conservative budget variable expenses PROBLEM 1. ANS: a. The independent variable is the number of hours travelled and the dependent variable is the distance travelled. b. Time travelled (h) Distance remaining (km) 0 750 1 670 2 590 3 510 4 430 5 350 6 270 c.
Choose two points on the graph, such as (1, 670) and (5, 350). m = y 2! y 1 x 2! x 1 m = m =!80 350! 670 5! 1 The slope of the line is 80. d. The slope represents a rate of change, the speed at which the family is driving. They are driving at 80 km/h. PTS: 1 DIF: Moderate REF: 1.3 OBJ: Algebra LOC: A-SO2 TOP: Rate of Change KEY: slope plotting graph 2. ANS: Use the compound interest formula to calculate the final value of the investment when compounded monthly. Ê A = P 1 + r ˆ Ë Á n Ê A = $10225.00 1 + 0.057 ˆ Ë Á 12 nt A = $10670.52 12! 0.75 Calculate the final value of the investment when compounded daily.
Ê A = P 1 + r ˆ Ë Á n Ê A = $10225.00 1 + 0.057 ˆ Ë Á 365 A = $10671.56 nt Calculate the difference earned between the two investments. $10671.56 $10670.52 = $1.04 If the investment were compounded daily rather than monthly, it would earn an extra $1.04. PTS: 1 DIF: Moderate REF: 6.2 OBJ: Number Algebra LOC: N-SO3 A-SO1 TOP: Simple and Compound Interest KEY: compound interest 3. ANS: a) Calculate Peter s total income. $890.00 + $890.00 = $1780.00 Calculate his total expenses. $595.00 + $150.00 + $300.00 + $190.00 + $200.00 + $150.00 + $20.00 + $150.00 = $1755.00 Calculate the difference between Peter s income and his expenses. $1780.00 $1755.00 = $25.00 Peter can put $25.00 into savings in one month if he follows this budget. b) Calculate what percentage of his income goes to entertainment expenses. $200.00! 100 " 11% $1780.00 About 11% of Peter s income goes to entertainment expenses. c) Answers will vary. 365! 0.75 If Peter wants save more money, he could: spend less on entertainment; spend less on donations; or spend less on transportation. PTS: 1 DIF: Moderate REF: 7.2 OBJ: Number LOC: N-SO2 TOP: The Budgeting Process KEY: conservative budget savings 4. ANS: Let x be the height from the top of building 1 to the top of building 2.
tan! = opp adj tan 20 = x 11 11 tan 20 = x 4 m " x Let y be the height of building 1. tan! = opp adj tan 74 = y 11 11 tan 74 = y 38.36 m " y The total height of building height is the sum of x plus y. Height = x + y Height = 4 + 38.36 Height = 42.36 m The neighbouring building is 42.36 m tall. PTS: 1 DIF: Moderate REF: 4.2 OBJ: Geometry LOC: G-SO1 TOP: Solving Complex Problems in the Real World KEY: tangent ratio!