This is the first of two 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 qua-dratic equations, inequalities, system of linear equations, polynomials and their properties.
Broad Learning Outcome:
Upon successful completion of the Math 1 course, students will be able to simplify and manipulate algebraic expressions and solve basic equations such as linear, quadratic, rational and those involving radical expressions.
Supporting Learning Outcome Statements
Upon successful 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.
- Demonstrate an understanding of powers with real number bases (excluding base 0).
- Explain and apply the exponent laws for powers of numbers and for variables with rational exponents.
- Examine the nature of relations with an emphasis on functions.
- Represent and analyze quadratic, polynomial and rational functions,
- Perform operations on algebraic expressions.
- Find the product of polynomials.
- Divide an integral polynomial by a monomial/binomial.
- 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.
- Determine the equation of a line, given information that uniquely determines the line.
- Solve problems using slopes of parallel lines and perpendicular lines.
- Describe a function in terms of ordered pairs, a rule, in word or equation form, a graph.
- Use function notation to evaluate and represent functions.
- Determine the domain and range of a relation from its graph.
- Determine the following characteristics of the graph of a linear function, given its equation: intercepts slope, domain, range.
- Classify numbers as natural, whole, integer, rational or irrational, and show that these number sets are nested within the real number system.
- Solve systems of linear equations, in two variables: algebraically (elimination and substitution) and graphically.
- Solve word problems that can be reduced to linear or quadratic equations.
- Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using:
- Factoring, completing the square, and the quadratic formula.
- Perform operations on functions and compositions of functions.
- Formulate and apply strategies to solve absolute value equations, radical equations, rational equations.
- Graph linear inequalities, in two variables.
Successful completion of Pure Math 10, 10C or equivalent course.