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Course Description

This is the second of three courses designed to prepare you for university entrance. The course covers the properties of real numbers, a brief introduction to number theory, exponents and radicals, algebraic expressions, factoring, linear and quadratic equations, inequalities, system of linear equations, polynomials and their properties.

Course Details

Broad learning outcome:

Upon completion of this course, successful students will be able to:

  • Simplify and manipulate algebraic expressions.
  • Use a variety of techniques to solve equations such as quadratic, radical, trigonometric, or rational.
  • Use quadratics or other functions to model real world problems mathematically and interpret the solutions.
  • Develop algebraic reasoning and number sense through the study of various relations and functions as well as sequences and series.
  • Develop trigonometric reasoning through the study of rotational trigonometry, as well as obtuse or acute triangles.

Supporting Learning Outcome Statements

Upon completion of this course, successful students will be able to:

  • Identify and differentiate the two types of sequences (arithmetic/geometric) and apply their properties to find the general term of the sequence, the sum of any number of terms of the sequence and series.
  • Investigate infinite geometric sequences to determine if they are convergent or divergent.
  • Convert entire radicals with rational coefficients or radicands to mixed radicals.
  • Convert mixed radicals with rational coefficients or radicands to entire radicals.
  • Add, subtract, multiply, and divide radicals.
  • Solve radical equations.
  • Identify and explain characteristics of graphs of quadratic functions such as:  the vertex, maximum or minimum values, the intercepts, domain and range.
  • Identify and explain the different forms of quadratic functions.
  • Graph a quadratic function given its equation in any form.
  • Determine the equation of a quadratic function given information that uniquely determines the function.
  • Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using: factoring, completing the square, and the quadratic formula.
  • Solve word problems that can be reduced to linear or quadratic equations.
  • Determine equivalent forms of single-variable rational expressions with polynomial numerators, and denominators that are monomials, binomials or trinomials that can be factored.
  • Determine the non-permissible values for the variable in single-variable rational expressions.
  • Perform the operations of addition, subtraction, multiplication and division on single-variable rational expressions.
  • Find and verify the solutions of rational equations that reduce to linear equations.
  • Formulate and apply strategies to solve absolute value equations, radical equations, rational equations.
  • Graph linear and quadratic inequalities in two variables.
  • Solve systems of equations (in two variables) that have at least one quadratic equation using algebra and graphing.
  • Identify and explain characteristics of reciprocal functions such as end behaviour and asymptotes.
  • Graph linear and quadratic reciprocal functions.
  • Demonstrate and understanding of rotational trigonometry using positive angles from 0 to 360 degrees.
  • Analyze special triangles and how they are used to determine trigonometric ratios in exact form.
  • Solve problems using the sine law and the cosine law.

Prerequisites

Successful completion of Math 10-C, Pure Math 10, UPG 010 Math Fundamentals, or equivalent course. Questions about placement? Call: 403.220.2866 or E-mail: conted@ucalgary.ca 
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