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
