# MATHEMATICS

MAP4C Grade 12 College and Apprenticeship Online Plus Final Summative Assignment

Name: _________________ Date:_____________________ MATERIALS: A dark pencil or dark blue or black pen. A ruler Graph paper Resources: A scientific calculator. Student’s Math Notes and Portfolio. A TI-83 or online TVM calculator may be used for Activity 4 This is an independent project to be completed on your own. INSTRUCTIONS:

1. Read over the instructions for each activity carefully. Make a plan to

solve the problem and execute your plan. 2. For full marks, complete solutions are required.

3. Good Luck!

Part Activity Date Time Earned Mark

Possible Mark

1 Trigonometry

9

2 Exponential Growth and Decay

8

3 Statistics and Mathematical Models

15

4 Financial Applications

11

Total Mark

43

MAP4C Grade 12 College and Apprenticeship Online Plus Final Summative Assignment

ACTIVITY 1 Trigonometry

Scenario While on a trip in Algonquin Park, two hikers (hiker A and B) separate from their group and each becomes lost. Both hikers go to a wide-open clearing where aircraft can see them. A rescue helicopter, flying at an altitude of 200 metres, spots both hikers at the same time. The first hiker is at an angle of depression of 9° and the second hiker is at an angle of depression of 13°. If the helicopter pilot is looking at the first hiker, she needs to turn her head 172° to see the second hiker.

/1 a) Label the angles of depression, and the location of hiker B. /8 b) How far apart are the two hikers? Show all your work.

MAP4C Online Plus Final

ACTIVITY 2

Exponential The population of Venus doubles in number every 30

model the population is � � 10 is the time in years. /3 1. Determine how many Venutians there will be after 400 years. /3 2. Unfortunately, just at the point when the population reaches 1

million, a virus attacks and the population starts falling in exponential decay. In fact, the population is cut in half every Determine the remaining population after 4

/2 3. If the temperature on Venus is

temperature be in Fahrenheit if

Grade 12 College and Apprenticeship Final Summative Assignment

Exponential Growth and Decay

The population of Venus doubles in number every 30 years. The formula to

10 �2� � �; where P is the total population and t

Determine how many Venutians there will be after 400 years.

just at the point when the population reaches 1 a virus attacks and the population starts falling in

exponential decay. In fact, the population is cut in half every year Determine the remaining population after 4 years.

If the temperature on Venus is , what would this

Fahrenheit if ?

Grade 12 College and Apprenticeship

The formula to

; where P is the total population and t

year.

MAP4C Online Plus Final

ACTIVITY 3

Statistics and Mathematical Models

A university would like to construct a mathematical model to predict first marks for incoming students based on their achievement in grade 12. A comparison of these marks for shown below.

Grade 12 Average 85 90 First-year Average 74 83

/5 1. Construct a scatter plot for these data. Which variable should be

placed on the vertical separate sheet (on graph paper… not using software).

/2 2. Estimate and draw a line of best fit for the data. /2 3. Classify the linear correlation for this data, based on /4 4. Calculate the slope and y

equation for it in the form /2 5. Use the linear model to predict the first

who had an 82 average in grade 12.

Grade 12 College and Apprenticeship Final Summative Assignment

Statistics and Mathematical Models

A university would like to construct a mathematical model to predict first-year marks for incoming students based on their achievement in grade 12. A comparison of these marks for a random sample of first-year students is

76 78 88 84 76 96 86 68 70 75 72 64 91 78

Construct a scatter plot for these data. Which variable should be placed on the vertical axis? Explain. Provide the scatter plot on a

(on graph paper… not using software).

Estimate and draw a line of best fit for the data.

/2 3. Classify the linear correlation for this data, based on the scatter plot.

Calculate the slope and y-intercept for this line and write an

equation for it in the form .

Use the linear model to predict the first-year average for a student who had an 82 average in grade 12.

Grade 12 College and Apprenticeship

year marks for incoming students based on their achievement in grade 12. A

86 85 78 86

Construct a scatter plot for these data. Which variable should be Provide the scatter plot on a

the scatter plot.

year average for a student

MAP4C Grade 12 College and Apprenticeship Online Plus Final Summative Assignment

ACTIVITY 4 Financial Applications

1. Sarah has recently graduated from community college and has found a

job with a good starting salary. Her financial goals include saving enough to buy a used car in 3 years. In addition, she has a $6000 student loan, which she would like to pay off within 10 years.

/3 a) She is saving money to buy her car by depositing $200 into a

savings account every month. What price of car will she be able to afford if the account earns interest at 3%, compounded monthly?

/3 b) What price of car will she be able to afford if her deposits remain

at $200, but she finds an investment that pays 6% compounded monthly?

2. A friend wants to sell Sarah his car and is offering a payment plan of $200 monthly for 3 years. The payment plan is a loan at 9% interest, compounded monthly. Her friend would prefer it if Sarah paid a lump sum equivalent to the present value of the payment plan.

/4 a) How much less will she pay for the car if she pays in a lump

sum instead of accepting the payment plan? /1 b) Why might Sarah prefer the payment plan even though it will

cost her more?