Honors Analysis. Fundamental Counting Principle Factorial Calculations (No Calculator!) ...

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 words1.2 COMBINATIONS

Combinations Formula (by hand) Combinations & Fundamental Counting

Principle Distinguish between perm/comb

1.3 INTRO TO PROBABILITY

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

1.4 EXTENDED PROBABILITY 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 Misleading graphs Quantitative vs. Categorical Variables Graph Types:

Bar graph vs. HistogramFrequency table vs. Relative Frequency TableStem PlotPie Chart/Circle GraphComparative Bar ChartDot Plot

UNIT 2 TOPICS (PART I) Five Point Summary (quartiles, IQR) Box Plot Standard Deviation (By hand, calc) Basic Normal Curve (given simple curve) Z-Scores

UNIT 2 TOPICS (PART II) Calculate probabilities using

Z-scores/Table Calculate std. dev. of sample proportion Calculate margin of error Determine confidence interval 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

PROGRAMMING TOPICS Make calculations using variables Print to screen using Disp command Enter data using Input statement Make decisions using If/Then/Else

statements Write simple loops Use counter within loop

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: 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 4 TOPICS

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

UNIT 4 TOPICS Solve distance = rate * time word

problems (use chart setup!) Calculate average rate of change of a

function from a table or function