Lessons

Keep up-to-date with your notes: IMPORTANT: If you have missed a topic listed here, ask a classmate to see what notes you have missed.

1. Fractions:

A. Adding fractions: a. Only work wih fractions and improper fractions (change whole numbers and mixed numbers into improper fractions) b. Look for common denominator (Methods: LCM, prime factorization, multiplying the two denominators together) c. Add numerators together; keep common denominator

B. Subtracting fractions: a. Only work with fractions and improper fractions (change whole numbers and mixed numbers into improper fractions) b. Look for common denominator (Methods: LCM, prime factorization, multiplying the two denominators together) c. Add numerators together; keep common denominator

C. Multiplying fractions: a. Only work with fractions and improper fractions (change whole numbers and mixed numbers into improper fractions) b. Cross cancellation c. Multiply numerators together; multiply denominators together

D. Dividing fractions: a. Only work with fractions and improper fractions (change whole numbers and mixed numbers into improper fractions) b. Take reciprocal of right side fraction; change the sign from division to multiplication c. Cross cancellation d. Multiply numerators together; multiply denominators together

2. Real Numbers

A. Rational Numbers

a. Integers b. Whole numbers c. Natural numbers

B. Irrational Numbers

C. Properties of Real Numbers

a. Associative - Group b. Commutative - Order c. Identity d. Inverse e. Distributive

3. Equations

A. One-step B. Multi-step C. Variables on both sides D. Absolute Value

4. Inequalities

A. Simple B. Compound (and/or) C. Absolute Value

5. Radicals

A. Rules of exponents a. Product rule - add exponents b. Quotient rule - subtract exponents c. Zero-exponent rule - anything to the zero power is 1 d. Negative exponent rule - take the reciprocal and make the exponent positive e. Power rule - multiply exponents f. Product to power g. Quotient to power

B. nth roots

a. Radical Notation i.. Index - identifies the root ii. Radicand - number or variable under the radical iii. Power - exponent

b. Rational exponent notation i. Index - denominator of the fractional exponent ii. Base iii. Power - numerator of the fractional exponent

6. Graphing

A. Linear Equations - Different forms a. Standard form: Ax + By = C b. Point-slope form: y - y1 = m (x - x1) c. Slope-intercept form: y = mx + b i. b = y - intercept ii. m = slope iii. Plot the y - intercept, then use the slope to find a few other points to graph the linear equation

B. Slope a. m = (y2 - y1) / (x2 - x1) b. Vertical lines: undefined slope c. Horizontal lines: zero slope d. Parallel lines: same slope e. Perpendicular lines: slopes are negative reciprocals

C. Linear Inequalities a. Put the inequality into slope-intercept form, plot the y - intercept, use the slope to find other points for the linear inequality b. If the inequality is less than / greater than, the graph will have a dotted line c. If the inequality is less than or equal to / greater than or equal to, the graph will have a solid line d. Test a point on either side of the line. e. If the test point makes the inequality true, shade on the side of the test point (this is where your solutions lie) f. If the test point makes the inequality false, shade on the side opposite of the test point (this is where your solutions lie)

7. Scatter Plots / Line of Best Fit

A. Scatter plots a. Positive correlation - points rise from left to right (similar to a positive slope) b. Negative correlation - points fall from left to right (similar to a negative slope) c. No correlation - no pattern to the points whatsoever

B. Line of best fit a. See the notes on calculator instructions for finding the line of best fit

8. Variation

A. Direct variation a. y = kx or (y) / (x) = k

B. Inverse variation a. xy = k or y = (k) / (x)

C. Joint variation a. z = kxy

9. Systems of Linear Equations

A. Graphing a. Perpendicular lines - exactly one solution b. Parallel lines - no solutions c. Lines have the same graph - infinite solution

B. The Substitution Method a. See notes for the steps to solve using the substitution method

C. The Elimination Method a. See notes for the steps to solve using the elimination method

10. Solving Problems Using Linear Systems

A. Steps for solving problems using linear systems a. Write a verbal model b. Assign variables c. Write an algebraic model d. Solve the model e. Answer the question

11. Systems of Linear Inequalities

A. Steps for graphing linear inequalities a. Graph each inequality b. Lightly shade each solution set c. The graph of the system is the shaded intersection of the inequalities

12. Linear Programming

A. Steps to solve a linear programming problem a. Write objective function and all constraints b. Graph the constraints c. Identify all vertices d. Find value of objective function at each vertex e. Find optimum value

13. Matrices

A. Operations a. Adding b. Subtracting c. Multiplying

B. Determinants a. 2 x 2 method b. 3 x 3 - expansion by minors c. 3 x 3 - diagonals

C. Inverse Matrices a. 2 x 2 method b. 3 x 3 - calculator

D. Matrix Equation a. A x = B b. Find the inverse of A c. Multiply the inverse of A by B

E. Systems of equations with matrices a. Set up the matrices using the equations given b. Solve the same as a matrix equation problem

14. Polynomials

A. Operations a. Adding b. Subtracting c. Multiplying - FOIL d. Multiplying - Distributive Property

B. Special product patterns

C. Factoring a. Factoring trinomials b. GCF c. Grouping

D. Rational Zero Theorem

15. Quadractic Equations

A. Completing the square B. The quadratic formula( (x=-b+/-sqrt(b^2-4ac))/2a) C. Discriminant (b^2-4ac) 16. Circles A. Standard form (r^2=(x-0)^2+(y-0)^2)

17. Functions

A. Shifts a. a-value: direction (reflection) and steepness b. h-value: moves graph left and right c. k-value: moves graph up and down d. Quadratic, cubic, absolute value, and radical functions

B. Operation of functions a. Addition b. Subtraction c. Multiplication d. Division

C. Composition of functions a. Start from the inside and work outward (f(g(x)).

D. Inverse Functions a. Start with original function b. Switch x and y values c. Solve for y

18. Exponential Fucntions

A. Shifts

19. Logarithms

A. Introduction a. Exponential form and logarithmic form

B. Natural Logarithms