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Semester 1 REview

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

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  1. Semester 1 REview Honors Analysis

  2. 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 1.2 Combinations • Combinations Formula (by hand) • Combinations & Fundamental Counting Principle • Distinguish between perm/comb

  3. 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

  4. 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

  5. 1.6 Mathematical Expectation (Expected Value) • (Calculated as sum of the products of the probability of each event and the gain/loss)

  6. Unit 2 Topics • 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

  7. 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

  8. 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:

  9. 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:

  10. 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)

  11. 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.

  12. 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

  13. 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 • 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!)

  14. Unit 5 Topics • 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

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