MAT 064 - College Prep Math

1. Practice study strategies that lead to math success.
   1. Explain thinking skills used in the study of mathematics.
   2. Demonstrate effective math study techniques.
   3. Identify resources for math help.
2. Apply the four arithmetic operations to whole numbers, fractions, and decimals.
   1. Apply the four arithmetic operations to whole numbers.
   2. Apply the four arithmetic operations to integers
   3. Apply the four arithmetic operations to fractions.
   4. Apply the four arithmetic operations to decimals.
   5. Apply the four arithmetic operations to any expression involving whole numbers, integers, fractions and decimals.
   6. Evaluate algebraic expressions using the four arithmetic operations.
3. Relate number theory to arithmetic calculations.
   1. Write related sentences.
   2. Write true number sentences using < or >.
   3. Round numbers to a given place value.
   4. Simplify expressions using the rules for order of operations.
   5. Find the factors and multiples of a number.
   6. Find the GCF of two or more numbers.
   7. Find the LCM of two or more numbers.
4. Execute calculations involving ratios, proportion, and percent
   1. Write ratios and percents in fractional notation.
   2. Write percents in decimal notation.
   3. Write ratios and proportions for verbal problems.
   4. Translate percent problems into proportions.
   5. Solve proportions using variables.
5. Develop basic understanding of simple statistics and probability.
   1. Interpret data from tables, charts, and various graphs.
   2. Compute mean, median, and mode.
   3. Determine sample space and basic probabilities.
6. Recognize measurable attributes of objects and the units, systems, and processes of measurement.
   1. State the common units of measure of weight, mass, capacity, length, time and temperature.
   2. Make decisions about units and scales that are appropriate for problem situations involving measurement.
   3. Calculate perimeter and circumference.
   4. Find the area of parallelograms (including squares and rectangles), triangles, trapezoids, and circles.
   5. Calculate the volume of a rectangular solid, cylinder, sphere, and cone.
   6. Calculate perimeter and area using variables.
   7. Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.
7. Identify patterns and relations
   1. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
   2. Analyze how both repeating and growing patterns are generated.
   3. Describe, extend, and make generalizations about geometric and numeric patterns
   4. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
   5. Identify patterns as linear or nonlinear and contrast their properties from tables, graphs, or equations.
   6. Generalize patterns using explicitly defined and recursively defined formulas.
   7. Find the nth term of an arithmetic and geometric sequence.
8. Simplify algebraic expressions.
   1. Evaluate an expression for a given value of the variable.
   2. Use the commutative or associative property to simplify a given expression.
   3. Use the distributive property to simplify an expression.
   4. Use the properties of 0 or 1 to simplify an expression.
   5. Identify the value of a given expression with exponents.
   6. Implement the order-of-operations rules.
9. Solve first-degree equations and inequalities in one variable.
   1. Classify statement as identity, contradiction, or conditional.
   2. Solve linear equations/inequalities involving one-step transformations using the
   3. addition property of equality.
   4. Solve linear equations/inequalities involving one-step transformations using the
   5. multiplication property of equality.
   6. Solve linear equations/inequalities involving two transformations.
   7. Solve linear equations for one variable in terms of other variables.
10. Write models for verbal problems that produce first-degree equations and inequalities in one variable.
    1. Translate phrases and sentences written in words into algebraic expressions.
    2. Write an equation to solve a given word problem.
11. Simplify expressions involving exponents.
    1. Define a positive exponent.
    2. Define the zero exponent.
    3. Define a negative exponent.
    4. Use exponent rules for products, quotients, and powers.
    5. Perform basic operations using scientific notation.
    6. Define and evaluate square roots of real numbers.
12. Write the equation of a specified line.
    1. Define slope.
    2. Determine the slope, given two points.
    3. Determine the slope, given the equation of a line.
    4. Write an equation for a line given the slope and the y-intercept.
    5. Write an equation for a line given the slope and one point (not the y-intercept).
    6. Write an equation for a line given two points.