Honors Analysis

 Fundamental Counting Principle  Factorial Calculations (No Calculator!)  Permutation Calculation (No Calculator!)  Arrangement Problems (Permutations): n!  Circular Arrangements: (n – 1)!  Unique arrangements of letters in words  Combinations Formula (by hand)  Combinations & Fundamental Counting Principle  Distinguish between perm/comb

 Calculate Probability/Odds  Create a sample space to determine prob.  Prob of Union of Events (OR Problems)  Remember: If events aren’t mutually exclusive, the intersection must be subtracted!!  Probability of Intersections (AND Problems)  Adjust for independent vs. dependent events (such as replacement)  Calculate probability of the complement  Reword probability scenarios using AND/OR

 Know & triangle patterns  Find basic areas (circles, triangles, rectangles, trapezoids…)  Subtract areas of shapes from other regions to find partial areas

 Misleading graphs  Quantitative vs. Categorical Variables  Graph Types:  Bar graph vs. Histogram  Frequency table vs. Relative Frequency Table  Stem Plot  Pie Chart/Circle Graph  Comparative Bar Chart  Dot Plot

 Five Point Summary (quartiles, IQR)  Box Plot  Standard Deviation (By hand, calc)  Basic Normal Curve (given simple curve)  Z-Scores  Calculate probabilities using Z-scores

 Solve linear equations  Write linear equations based on application problems  Write linear equations involving supplements and complements  Write median equation (passes through triangle vertex and mdpt of opposite side)  Write equation of perpendicular bisector of side (passes through midpoint; perpendicular to slope of side)  Write equation of altitude of triangle (passes through vertex; slope perpendicular to base)

 Solve systems using substitution  Solve systems using elimination  Find intersection point of medians (centroid), altitudes (orthocenter), perpendicular bisectors (circumcenter)  Solve systems of three variables  Write equation of parabola using a system of three variables.

 Solve distance = rate * time word problems (use chart setup!)  Calculate average rate of change of a function from a table or function  Estimate instantaneous rate of change of a function  Estimate definite integrals by counting blocks on a graph (WATCH OUT FOR GRAPH SCALE!!)  Calculate definite integrals by calculating areas (constant functions, linear functions, etc.)  Estimate definite integrals (area under the curve) using the Trapezoidal Rule (may be given function OR a table of values – always best to draw a graph first!!)  Determine units for rate problems (y unit divided by x unit!)  Determine units for integral/area problems (x unit times y unit!)

 Factoring Methods:  Factor out the GCF  Difference of Squares  Trinomial (FOIL Pattern)  Grouping  Find vertex of a parabola by completing the square  Solve a quadratic using the quadratic formula  Solve a quadratic by factoring