MAP 4CI MOCK EXAM

Complete all questions on lined paper. Be sure to include proper form.

Trigonometry

[4] 1. Identify all possible values for A, if 0˚<A<180˚.

a) tan A = -2.1453 b) cos A = 0.5166 c) sin A = 0.9634

[9] 2. Solve for x in each of the triangles below.

a) b) c)

[7] 3. Solve the following triangle.

[4] 4. Determine the value of P in obtuse triangle PQR, if q = 25 cm, r = 42 cm and R = 28˚. Include a diagram.

[6] 5. The point P makes a right triangle with the origin and the x-axis. Determine the trigonometric ratios, in fraction form, if P(-2, 9).

[3] 6. A person is standing 25 m from the base of a large structure when they measure the angle of elevation to be 37˚. How tall is the structure?

[3] 7. While parasailing, you are at a vertical height of 500 m. If the angle of depression to the back of the boat is 59˚, how long is the rope you are attached to?

Geometry / Measurement

[5] 8. Convert the following.

a) 1500 m to km b) 23 inches to feet c) 15 inches to cm

d) 3 lbs to kg e) 30 m to feet

[6] 9. Determine the perimeter and area of the following shape.

[6] 10. Determine the volume and surface area.

[3] 11. A farmer has 650 feet of fencing. Does she have enough fencing to enclose a rectangular area of half an acre? Justify your answer.

Note: 1 acre = 43 560 square feet

[6] 12. Mathew is constructing a rectangular prism with volume exactly 729 cubic inches. It will have the least possible surface area.

a) Describe the prism. What will be its dimensions?

b) What will be its surface area?

[6] 13. Jude is designing a plush activity toy for a baby. The toy will be a rectangular prism with surface area 864 cm2.

a) Determine the maximum volume of the toy.

b) What are the dimensions of the toy with maximum volume?

Two Variable Data

[4] 14. Refer to the graph to the right.

a) Describe the correlation.

b) Identify the independent and dependent variables.

c) Which buildings have the same height?

d) Which buildings have the same number of windows?

[10] 15. For each situation, state whether you think the two variables would have a positive correlation, a negative correlation, or no correlation. If there is a correlation, identify the independent and dependent variables.

a) Cost of a restaurant bill and the amount left as a tip

b) Blood pressure reading and IQ

c) Number of applicants for a job and probability that you will get the job

d) Speed of current and time taken to travel upstream

e) Number of kilometres driven and price of gas per litre

[3] 16. Which line is the line of best fit? Justify your choice by explaining what is wrong with the other two.

[7] 17. Use the graph to the right.

a) Sketch the line of best fit.

b) Determine the equation of the line of best fit.

c) Use your line of best fit to predict the cost of a 5 ft tree.

d) Predict the height of a tree that costs $50.

e) Would you use interpolation or extrapolation to determine the cost of a 10 ft tree?

f) Would you use interpolation or extrapolation to determine the height of a tree that costs $80?

[2] 18. A line of best fit has a different name in both Excel and Fathom. What are the other names?

[2] 19. A linear regression has a correlation coefficient of r = 0.89. How reliable is the data? Explain.

Statistical Literacy

[6] 20. Here are the exam marks for a class of 20 math students.

35 72 74 84 90 60 93 48 70 68

75 63 65 75 82 65 54 77 64 59

a) Determine the mean, median, and mode. Which measure of central tendency best represents the data?

b) What are the quartiles for this data set?

c) Vince’s mark is in the 37th percentile for this group. Explain what the percentile means. What is Vince’s mark?

[4] 21. There are 7 types of sampling techniques identify 4 of them.

[3] 22. The textbook identified 5 questions you can ask yourself to assess the validity of the conclusions to a survey. Identify 3 of them.

[1] 23. On a Food Price Index where New York = 100, Toronto has a value of 80.8. What does Toronto’s value mean?

Graphical Models

[3] 24. Identify which type of relation each equation represents.

a) y = 7x – 9 b) y = 6x2 c) y = 100(2)x

[3] 25. Identify which type of relation each graph represents.

[3] 26. Explain how a table of values can be used to determine if a relation is linear, quadratic or exponential.

[7] 27. The volume of dough for cinnamon buns is measured at 10-min intervals. Use the graphing calculator to perform the following three regressions. Be sure to turn the Diagnostics On before you start.

a) Linear Regression: b) Quadratic Regression: c) Exponential Regression:

a = a = a =

b = b = b =

r2 = c = r2 =

r = r2 = r =

d) This data is best represented by

e) The equation that best represents the data is

f) When did the Volume reach 2.0 L?

g) What was the Volume after 45 min?

Algebraic Models

[4] 28. Rewrite using radicals, then evaluate.

a) b)

[5] 29. Simplify then evaluate for x = 2, y = -3 and z = 5.

a) b)

[6] 30. Solve.

a) b) c)

[4] 31. An antique watch worth $2000 increases in value at a rate of 1.5% per year.

a) Write an equation to represent the value of the watch over n years.

b) How much with the watch be worth in 3 years?

c) How would the equation change if the value of the watch was decreasing instead of increasing? Write the new equation.

Annuities & Mortgages

[3] 32. Monthly payments of $500 are deposited into an investment earning 8% compounded monthly. What is the value of the investment at the end of 5 years?

[3] 33. You won a lottery and have the option of receiving a lump sum payment now or quarterly payments of $3000 for 10 years. If the money is invested at a rate of 9% compounded quarterly, what is the value of the equivalent lump sum payment?

[5] 34. Use the formula to answer the following questions.

a) What is the amount of the regular payment?

b) For how many years are payments being made, if payments are deposited semi-annually?

c) What is the annual rate of interest?

d) Would this be an investment or a loan?

e) What is the value of this annuity?

[2] 35. Under Canadian Law how often can a bank compound interest on a mortgage? How does this differ from an annuity?

[4] 36. A $450 000 mortgage is obtained a rate of 5.75% amortized over 20 years

a) Using the TVM Solver, determine the monthly mortgage payment.

b) Determine the total interest paid over the life of the mortgage.

[4] 37. Complete the following amortization table.

Payment
number / Monthly
payment / Interest
paid / Principal
paid / Outstanding
balance
0 / $600,000.00
1 / $3,404.73 / $2351.83 / $1,052.90 / $598,947.10
2 / $2,347.71 / $1,057.02 / $597,890.08
3 / $3,404.73 / $2,343.56 / $596,828.91
4 / $3,404.73 / $1,065.33

[3] 38. Identify 3 costs that you would have as a property owner that you would not have as a renter.

[2] 39. Identify 2 responsibilities each for a landlord and a tenant.

[7] 40. Complete the following table.

Description / Frequency / Estimated cost ($) / Annual cost ($)
Mortgage payment / Monthly / 2500.00
Food and restaurants / Bi-weekly / 300.00
Utilities and services / Bi-monthly / 350.00
Property tax / Quarterly / 375.00
Entertainment / Weekly / 60.00
Miscellaneous / Semi-annually / 2125.00
Annual Total

[3] 41. What is the most common time period used for a budget? Why would someone create a budget and why would they use this length of time?