Mathematics II

Upon completion of this course students will be able to:

1. Use, simplify, evaluate and perform operations with real numbers and expressions

1.1. write fractions as decimals and repeating decimals as fractions
1.2. add, subtract, multiply and divide rational numbers
1.3. evaluate powers with rational bases and integer exponents
1.4. demonstrate the order of operations with rational numbers
1.5. evaluate radicals with rational radicands and distinguish between exact answers and approximate answers
1.6. simplify, add, subtract, multiply and divide square roots

2. Solve first degree equations and inequalities

2.1. solve first degree equations, in one variable, including those involving parentheses
2.2. solve formulas for a given variable when other variables are known
2.3. solve formulas for a given variable
2.4. solve first degree inequalities in one variable
2.5. solve practical problems using a first degree equation

3. Classify, evaluate, factor and perform operations on polynomials and solve polynomial equations and applied problems

3.1. distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)
3.2. apply the laws of exponents to variable expressions with integral exponents
3.3. evaluate polynomials by substitution
3.4. add, subtract, and multiply polynomials
3.5. factor polynomials by removing the largest common factor
3.6. factor binomials of the form a²x² – b²y²
3.7. factor trinomials of the form ax² + bx + c
3.8. fully factor polynomials using a combination of factoring techniques
3.9. solve quadratic equations using the law of zero products

4. Interpret, simplify and perform operations on rational expressions and solve rational equations

4.1. simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial, or trinomial denominators
4.2. determine values for which a rational expression is undefined
4.3. multiply and divide rational expressions
4.4. add and subtract rational expressions consisting of monomial and/or binomial denominators
4.5. solve simple rational equations and check solutions
4.6. simplify expressions using exponent laws

5. Graph and solve linear equations and inequalities

5.1. graph a linear equation including the forms x = a and y = b
5.2. given a linear equation or its graph, determine its
   5.2.1. slope
   5.2.2. x- and y-intercepts
5.3. determine the equation of a line, y = mx + b, given
   5.3.1. its graph
   5.3.2. its slope and a point on the line
   5.3.3. two points on the line
5.4. graph a linear inequality

6. Solve systems of linear equations and applied problems

6.1. solve a system of first degree equations in two unknowns by graphing, substitution, and elimination methods
6.2. solve practical problems using a system of equations

7. Simplify and perform operations on radical expressions and solve radical equations

7.1. simplify square roots with variable radicands
7.2. add, subtract, multiply and divide square roots with variable radicands
7.3. solve equations with one square root containing a polynomial radicand and check for extraneous solutions

8. Solve right angle triangles

8.1. solve right triangles using one or more of
   8.1.1. the sine ratio
   8.1.2. the cosine ratio
   8.1.3. the tangent ratio
   8.1.4. the Pythagorean theorem
   8.1.5. the angle sum property of triangles

9. Solve and graph quadratic equations and applied problems

9.1. solve quadratic equations by factoring
9.2. solve equations of the form x² + bx + c = 0 by completing the square
9.3. solve quadratic equations by using the quadratic formula
9.4. graph y = ax² + bx + c and determine its
   9.4.1. x- and y-intercepts
   9.4.2. vertex
9.5. solve practical problems using a quadratic equation