MAP4C

Modelling Algebraically

SAMPLE PROBLEM: Which variable(s) in the
formula V = πr h would you need to set as
a constant to generate a linear equation?
A quadratic equation? Explain why you can
expect the relationship between the volume
and the height to be linear when the radius
is constant.

Representing

Solving Exponential Equations

SAMPLE PROBLEM: Use the graph of y = 3 to
solve the equation 3 = 5

Connecting + Representing

SAMPLE PROBLEM: Dye is injected to test pancreas function. The mass, R grams, of dye remaining in a healthy pancreas after t minutes is given by the equation R = I(0.96) , where I grams is the mass of dye initially injected.
If 0.50 g of dye is initially injected into a healthy pancreas, determine how much time elapses until 0.35 g remains by using a graph and/or table of values generated with technology.

Selecting Tools and Computational Strategies

Modelling Graphically

SAMPLE PROBLEM: Given the data table at the
top of page 139, determine an algebraic
model to represent the relationship between
population and time, using technology. Use
the algebraic model to predict the population
in 2015, and describe any assumptions made.

Reasoning and Proving

Solving Problems Involving Measurement and Geometry

SAMPLE PROBLEM: A car manufacturer wants to
display three of its compact models in a triangular arrangement on a rotating circular platform.
Calculate a reasonable area for this platform,
and explain your assumptions and reasoning

Reasoning and Proving

Investigating Optimal Dimensions

SAMPLE PROBLEM: You are constructing a rectangular deck against your house. You will use 32 ft of railing and will leave a 4-ft gap in the railing for access to stairs. Determine
the dimensions that will maximize the area of the deck.

Problem Solving

Solving Problems Involving Trigonometry

SAMPLE PROBLEM: Prepare a presentation to
showcase an occupation that makes use of
trigonometry, to describe the education and
training needed for the occupation, and to
highlight a particular use of trigonometry
in the occupation.

Connecting

Understanding Annuities

SAMPLE PROBLEM: Calculate the interest saved on a $100 000 mortgage with monthly payments, at 6% per annum compounded semiannually, when it is amortized over 20 years instead of 25 years.

Selecting Tools and Computational Strategies

Renting or Owning Accomodation

SAMPLE PROBLEM: Calculate the total of the
fixed and variable monthly costs that are
associated with owning a detached house
but that are usually included in the rent for
rental accommodation.

Problem Solving

Reflecting

Designing Budgets

SAMPLE PROBLEM: Determine, through investigation, if it is possible to change from renting to owning accommodation in your community in five years if you currently earn $30 000
per year, pay $900 per month in rent, and have savings of $20 000.

Reasoning and Proving

Connecting

Working with Two-Variable Data

SAMPLE PROBLEM: Given a table showing shoe
size and height for several people, pose a
question that would require one-variable
analysis and a question that would require
two-variable analysis of the data.

Communicating

Applying Data Management

SAMPLE PROBLEM: The headline that accompanies the following graph says “Big Increase in Profits”. Suggest reasons why this headline may or may not be true.

Reflecting