MAP4C

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MAP4C

Data Management

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.

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

Personal Finance

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.

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.

Reflecting

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.

Geometry and Trigonometry

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

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 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

Mathematical Models

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 Exponential Equations

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

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

Connecting + Representing

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