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# Intermediate Algebra

1. Algebra of functions
Find the domain of a function and write it in interval notation.
Know the range of simple functions .
Read the domain, range, and values of functions from their graphs.
Evaluate f(x), (f+g)(x), (f–g)(x), (fg)(x), (f/g)(x),
Use the vertical and horizontal line tests.
Test if a function is one-to-one.
Test if a function has an inverse and find the inverse function.

2. Inequalities
Solve linear inequalities .
Solve compound linear inequalities.
Convert absolute value inequalities to compound linear inequalities and solve.

3. Linear systems
Solve systems of 2 linear equations in 2 unknowns.
Evaluate a 2x2 determinant.
Solve systems of 3 linear equations in 3 unknowns.
Know Cramers rule for solutions of linear systems.
Interpret geometrically a system of 2 linear equations in 2 unknowns.
Interpret geometrically a system of 3 linear equations in 3 unknowns.
Identify linear systems as consistent or inconsistent.
Identify if a linear system is dependent.
Identify if a 3-d linear systems is a book, tent, or corner.
Know how to tell if two planes are parallel, coincident, or intersect in a line given their equations.

4. Polynomials
Know the definition of a polynomial.
Find the degree of a monomial.
Find the degree of a polynomial.
Add, subtract, and multiply polynomials .
Divide polynomials using long division.
Factor polynomials
Memorize special products.
Solve polynomial equations by factoring and using the zero product rule.
Understand the remainder theorem.
Factor a polynomial by finding the roots of the equation “polynomial = 0”.

5. Rational Expressions
Find the LCD of polynomials by factoring and finding the common factors.
Simplify rational expressions by finding the LCD.
Solve rational equations by multiplying both sides by the LCD.

6. Radical notation and rational exponent notation
Know the laws of exponents .
Know the definitions of negative exponents and fraction exponents .
Understand the definition of square root, cube root , and nth root.
Write roots using both radical notation and rational exponent notation.
Simplify expressions with rational exponents.
Know what simplified means for rational exponent expressions with and without negative exponents.
Convert between rational exponent notation and radical notation.

7. Radical equations and rational exponent equations
Solve equations with one square root expression by squaring both sides.
Solve equations with 2 square root expressions by squaring both sides.
Solve equations with 2 square root expressions and a linear expression by squaring both sides twice.
Solve equations with radical (roots) by undoing .
Solve equations with rational exponents by raising to the reciprocal power.
Know when an extra solution might be introduced.
Check the domain to see if the solution is allowed.

8. Complex numbers Learn definition of i.
Simplify expressions with square roots of negative numbers.
Know the definition of a complex number and the standard form of a complex number.
Find the real and imaginary parts of a complex number by putting it in standard form.
Remember the imaginary part of a complex number is the coefficient of i . It does not contain i.
Evaluate i to any integer power.
Simplify expressions with complex numbers.
Multiply complex numbers by foiling.

9. Logarithm Functions
Know the definition of a logarithm.
Graph log functions.
Find the domain and range of log functions.
Convert between log and exponential expressions.
Memorize the basic properties of logs .
Convert between expanded notation and single log notation.
Simplify log expressions.
Know how to use and simplify expressions with ln.
Solve equations with logs with the unknown in any of three possible positions.
Approximate values on calculator, rounding off correctly.
Use log for base 10 and ln for base e on the caluclator.

10. Exponential Functions
Memorize laws of exponents.
Know the definition of an exponential function.
Identify exponential functions as growth or decay.
Graph exponential functions.
Find the domain and range of exponential functions.
Convert between log and exponential expressions.
Simplify exponential expressions.
Solve exponential equations.
Approximate values with a calculator, rounding off correctly.
Find an exponential model for population growth given data.
Find growth constants and doubling time given data or formulas for population growth.

Evaluate the disciminant of a quadratic equation.
Identify the nature of the roots of a quadratic equation from the discriminant.
Given the roots of a quadratic equation find the equation.
Solve a quadratic equation by square root method or factoring or quadratic formula.
Graph and identify all relevant points for horizontal and vertical parabolas.

12. Circles and binomial theorem
Find the midpoint of a line segment connecting two points.
Find the distance between two points.
Complete the square to write the equation of a circle in standard form.
Identify the center and radius of a circle given the equation.
Graph the equation of a circle.
Expand binomials using the binomial formula.
Evaluate binomial coefficients.
Simplify expressions with factorials.

13. Graphs
Memorize the basic graphs for powers, roots, exponentials, logs, parabolas, and circles.
Know how to translate graphs horizontally and vertically.
Know how to reflect graphs about the line y = x.
Know how to reflect graphs about the x or y axis.

Exams
Monday December 8 on 2,3,5 (inequalities, linear systems, rational expressions)
Tuesday December 9 on 4,6,7 (polynomials, radical and rational exponent notation in expressions and equations)
Wednesday December 10 on 1,9,10,11 (algebra of functions, log functions, exponential functions, quadratics)
Thursday December 11 on 8,12,13 above (complex numbers, circles and binomial theorem, graphs)

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