MATH-1050

Designed primarily for non-STEM students, this course will help you to develop your logical thinking and problem-solving skills; you will have the opportunity to apply your knowledge and to make connections of algebraic concepts to real life applications. You can find the current (or most recent) course syllabus here.

Learning Objectives

Upon successful completion of this course the student will demonstrate an understanding of and ability to apply each of the following topics:

• Solve and graph linear equations and inequalities, including applications
• Analyze and apply linear, quadratic, polynomial, rational, exponential, and logarithmic functions
• Solve the applied problems in mathematics of finance (simple and compound interest)
• Solve systems of linear equations and inequalities in two variables
• Apply the geometric approach to linear programming

Specific skills to be mastered

1. Arithmetic and algebraic preparations
   • Work with negative sign
   • Understand the distributive property $a(b+c) = ab + ac$
   • Add two fractions together
   • Multiplying two fractions together
   • Reduce a fraction into its simplest form
2. Linear equations
   • Solve a simple linear equation of the form $ax = b$
   • Solve a linear equation involving numbers
   • Solve a linear equation involving two symbols for one of them
   • Solve a linear equation involving several symbols for one of them
   • Solve a linear equation in the context of cost-vs-revenue
   • Solve a quadratic equation
3. Linear inequalities
   • Understand interval notations
   • Understand interval notations that involve infinity
   • Solve a simple linear inequality in one unknown
   • Solve a slightly more complicated linear inequality in one unknown
   • Solve chained inequalities in one unknown
   • Find the intersection of two intervals
4. Linear polynomial functions
   • Rewrite a linear polynomial function in the “slope-intercept” form
5. Quadratic polynomial functions
   • Understand the graph of a quadratic polynomial function
   • Finding the vertex of a parabola that is the graph of a quadratic function
   • Identify the degree of a polynomial function
6. General functions
   • Understand what is a function
   • Plug a number into a function (i.e. evaluate a function)
   • Plug an expression into a function
   • Understand the graph of constant functions
   • Understand the graph of piecewise linear function
   • Compose two functions together
   • Determine if two functions are inverse of each other
7. Algebra involving polynomials and power expressions
   • Add/subtract two polynomials and combine liked terms
   • Multiply two polynomials together
   • Understand the basic meaning of a power expression, e.g., “$b^a$”
   • Understand the meaning of negative exponents
   • Compute the product of two powers
8. Rational functions
   • Identify the domain of a rational function
   • Identify the zeros of a rational function
   • Identify the horizontal asymptotes of a rational function
   • Identify the vertical asymptotes of a function
9. Systems of equations
   • Solve a system of two linear equations in two unknowns in which one equation involves only one variable
   • Solve a system of two linear equations in two unknowns
   • Solve a system of three linear equations in three unknowns
10. Exponential and logarithm functions
    • Distinguish between the graphs of an exponential function and a logarithms function
    • Identify the base of an exponential function
    • Identify the base of a logarithm function
    • Simplify expressions involving logarithm
    • Solve simple equations involving exponential and logarithm
11. Interest rate
    • Understand simple interest rate
    • Understand compound interest rate
12. Systems of inequalities and linear programming
    • Describe solution set of systems of inequalities in two variables using graphs
    • Solve linear programming problems using graphical methods