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# Semester 1 REview - PowerPoint PPT Presentation

Semester 1 REview. Honors Analysis. 1.1: Counting Problems. 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.

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### Semester 1 REview

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

1.2 Combinations

• 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

• Use combinations to calculate complex probabilities (specifically when order doesn’t matter)

• Conditional Prob: P(A | B) (Probability of Event A given that Event B has occurred)

• P(A | B) =

1.5 Geometric Probability

• Know 30-60-90 & 45-45-90 triangle patterns

• Find basic areas (circles, triangles, rectangles, trapezoids…)

• Subtract areas of shapes from other regions to find partial areas

1.6 Mathematical Expectation (Expected Value)

• (Calculated as sum of the products of the probability of each event and the gain/loss)

Unit 2 Topics

• 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

Unit 2 Topics

• 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

Unit 3 topics

• Calculate Slope

• Graph linear equations using a table

• Graph linear equations using x & y intercepts

• Graph linear equations using slope-int form

• Horizontal lines: y = k

• Vertical lines: x = k

• Perpendicular lines: Negative Recip. Slopes

• Graph functions to find intersection point

• Write equations of lines using pt-slope form:

Unit 3 topics

• Graph 2-variable data using a scatter plot

• Approximate equation of line of best fit

• Use graphing calculator (STAT/lists) to create linear regression line

• Use linear equations to make predictions about data

• Evaluate positive/negative correlation of data

• Calculate midpoint:

Unit 3 topics

• 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)

UNIT 3 topics

• 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.

• Evaluate, analyze, and graph piecewise functions

• Write the equation of piecewise functions

• Determine domain and range of a function using the graph (or given a function such as

• Determine values that make piecewise functions continuous

• Evaluate Greatest Integer Function values

• Modular Arithmetic

• 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