Page 141 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

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3.3 make connections between formulas and lin- ear, quadratic, and exponential functions [e.g., recognize that the compound interest formula, A = P(1 + i)n, is an example of an exponential function A(n) when P and i are constant, and of a linear function A(P) when i and n are con- stant], using a variety of tools and strategies (e.g., comparing the graphs generated with technology when different variables in a formula are set as constants)
3. Modelling Algebraically Sample problem: Which variable(s) in the formula V = πr2h would you need to set as
By the end of this course, students will: a constant to generate a linear equation?
3.1 solve equations of the form xn = a using rational exponents (e.g., solve x3 = 7 by raising both sides to the exponent 31 )
3.2 determine the value of a variable of degree no higher than three, using a formula drawn from an application, by first substituting known values and then solving for the vari- able, and by first isolating the variable and then substituting known values
Sample problem: Use the formula V = 34 πr3
to determine the radius of a sphere with a volume of 1000 cm3.
A quadratic equation? Explain why you can expect the relationship between the volume and the height to be linear when the radius is constant.
3.4 solve multi-step problems requiring formulas arising from real-world applications (e.g., determining the cost of two coats of paint for a large cylindrical tank)
3.5 gather, interpret, and describe information about applications of mathematical modelling in occupations, and about college programs that explore these applications
MATHEMATICAL MODELS
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Foundations for College Mathematics
MAP4C