MTH 099 - Mathematical Reasoning

Credits: 5
Instructional Contact Hours: 6

1. Demonstrate understanding of mathematical computations with rational numbers.
   1. Compute (add, subtract, multiply and divide) with signed numbers without the use of a calculator.
   2. Simplify numerical expressions with multiple operations and grouping symbols using the order of operations.
   3. Compute the opposite, reciprocal, and absolute value of a given real number.
   4. Estimate sums, difference, products, and quotients of integers, fractions, or decimals.
   5. Evaluate square roots and exponential numerical expressions.
   6. Estimate the value of a numerical expression.
   7. Approximate answer to an application problem prior to working it out.
   8. Identify the appropriate unit of an answer to a word problem.
2. Demonstrate understanding of proportions.
   1. Set up and simplify ratios and rates.
   2. Solve proportions.
   3. Carry out fraction, decimal, and percent conversions.
   4. Solve percent equations including percent increase and percent decrease.
   5. Estimate the percent of a number.
3. Demonstrate basic algebra skills.
   1. Combine like terms.
   2. Use the distributive property.
   3. Add, subtract, and multiply polynomial expressions.
   4. Simplify algebraic expressions with multiple operations and grouping symbols using the order of operations.
   5. Simplify algebraic expressions using the rules of exponents (no negative exponents).
   6. Compute the opposite and reciprocal of a given algebraic expression.
   7. Identify and give examples of linear, quadratic and exponential expressions.
   8. Compare and contrast expressions and equations.
   9. Evaluate algebraic expressions including linear, quadratic and exponential.
4. Demonstrate understanding of Cartesian graphs.
   1. Understand the Cartesian (rectangular) coordinate system.
   2. Construct the graph of a line if given the equation of the line.
   3. Identify an appropriate scale for both axes when constructing a graph.
   4. Approximate one coordinate of a point on a graph if given the other.
   5. Identify graphs as linear or non-linear.　
5. Demonstrate understanding of linear functions.
   1. Solve linear equations algebraically.
   2. Solve systems of linear equations algebraically and graphically.
   3. Compute the slope of a line in a variety of contexts.
   4. Identify the slope of a line as positive, negative, zero, or undefined.
   5. Interpret the slope of a line in context.
   6. Compute the y-intercept of a line in a variety of contexts.
   7. Interpret the y-intercept of a line in context as an initial amount.
   8. Compute the equation of a line in y=mx+b form in a variety of contexts.
6. Solve quadratic equations.
   1. Solve a variety of quadratic (using the quadratic formula) equations.
   2. Verify the solution of an equation.
7. Solve linear equations.
   1. Solve a variety of linear equations.
   2. Verify the solution of an equation.
8. Solve linear inequalities.
   1. Solve a variety of one-dimensional linear inequalities.
   2. Verify the solution of a linear inequality.
   3. Use interval notation, relational symbols (<, >, <, >) or a verbal description to describe a set of numbers.
9. Solve systems of linear equations.
   1. Solve a variety of systems of linear equations. (no higher than 2x2).
   2. Verify the solution of a system of linear equations.
   3. Recognize situations in which a system of linear equations has no solution or multiple solutions.
10. Demonstrate understanding of statistical graphs.
    1. Construct pie charts, bar graphs and line graphs.
    2. Interpret bar graphs, pie charts, line graphs and scatterplots.
11. Solve real world problems using mathematics.
    1. Set up an equation or expression if given a word phrase or sentence.
    2. Solve a variety of real world problems using the tools of algebra and mathematical modeling (linear models primarily).
    3. Solve real world problems involving integers, fractions, decimals, percent, proportions, perimeter and area, measurement, linear equations, the Pythagorean Theorem and probability.
12. Demonstrate understanding of concepts related to modeling.
    1. Generate a scatter plot from a set of data.
    2. Identify which model is appropriate (linear, quadratic or exponential) for a data set on a scatterplot.
    3. Use the generated model to determine predicted values.
    4. Determine if a predicted value is reasonable.
13. Apply concepts of elementary probability.
    1. Demonstrate an understanding of the basic definition of probability.
    2. Use sample spaces, to represent the possible outcomes and use them to calculate probabilities.
    3. Create a probability distribution based on sample spaces and tree diagrams.
    4. Determine whether two events, A and B, are dependent or independent.
    5. Determine whether two events, A and B, are mutually exclusive.
    6. Compute probabilities, that involve unions, intersections and complements.
14. Communicate effectively about mathematics.
    1. Provide complete written solutions to problems using appropriate terminology.
    2. Articulate orally and in writing important ideas and conclusions.