Term 4 Cumulative (Kent, 2025)

📊 Statistics & Data Analysis

1. Measures of Center

   • Mean: Sum of all values ÷ number of values

   • Median: Middle number (when ordered)

   • Mode: Most frequent number

2. Standard Deviation Comparison

   • Wider spread = larger standard deviation

   • Closer cluster = smaller standard deviation

3. Shapes of Distributions

   • Symmetric: Mean ≈ Median

   • Skewed Left: Tail on left, Mean < Median

   • Skewed Right: Tail on right, Mean > Median

   • Uniform: All values equally likely

   • Irregular: No clear pattern

4. Mean vs. Median Based on Shape

   • Skew left: mean < median

   • Skew right: mean > median

   • Symmetric: mean ≈ median

5. Effect of Outliers

   • Mean is affected

   • Median is resistant

6. Interpreting a Histogram

   • Bars show frequency

   • Look for shape, center, spread

7. Scatterplots

   • Shows relationships between two variables

8. Line of Best Fit

   • Estimate future values using trend line

9. Equation of Line of Best Fit

   • y=mx+by = mx + by=mx+b, where m = slope, b = y-intercept

10. Interpreting Correlation

• Strength: Weak, Moderate, Strong

• Direction: Positive / Negative

🎲 Probability & Two-Way Tables

11. Sample Space

• All possible outcomes (e.g., {HH, HT, TH, TT})

12. Calculating Probability

• Favorable outcomesTotal outcomes\frac{\text{Favorable outcomes}}{\text{Total outcomes}}Total outcomesFavorable outcomes​

13. Two-Way Tables

• Fill based on given data (rows and columns)

14. Probabilities from Two-Way Tables

• Joint, marginal, conditional probabilities

15. Union, Intersection, Conditional

• Union (A or B): Either event happens

• Intersection (A and B): Both happen

• Conditional (A | B): A given B occurred

16. Independent vs. Dependent Events

• Independent: One event doesn’t affect the other

• Dependent: One event affects the other

17. Disjoint Events

• Cannot occur at the same time (no overlap)

📈 Functions and Polynomials

18. Function Notation

• f(x)=...f(x) = ...f(x)=...; input xxx, output f(x)f(x)f(x)

19. Evaluate for Given Domain

• Substitute the value of xxx

20. Evaluate for Given Range

• Solve for xxx given f(x)f(x)f(x)

21. Add/Subtract/Multiply Polynomials

• Combine like terms; use distributive property

22. Degree and Leading Coefficient

• Degree: Highest power of variable

• Leading coefficient: Coefficient of highest degree term

23. End Behavior

• Based on degree (even/odd) and leading sign

24. Graph: Degree & Leading Sign

• Use the graph to tell if degree is even/odd, sign +/–

25. Y-Intercept

• Set x=0x = 0x=0 and solve f(0)f(0)f(0)

26. X-Intercepts (Zeros)

• Set f(x)=0f(x) = 0f(x)=0 and solve

27. Factored to Standard Form

• Multiply factors out

28. Graph Polynomial by Hand

• Include:

  • a. End behavior

  • b. X-intercepts

  • c. Y-intercept

  • d. Intercept behavior

29. Determine Zeros

• Solve f(x)=0f(x) = 0f(x)=0

30. Classify Zeros

• Real (visible on graph) or Imaginary (not visible)

31. Invisible Zeros

• Imaginary zeros don’t show as x-intercepts

32. Multiplicity Impact

• Multiplicity 1: Pass through

• Multiplicity 2: Touch and turn around

33. Factoring Polynomials

• GCF, grouping, trinomials, special cases

34. Multiply/Divide Rational Expressions

• Factor all parts, cancel common terms

35. Simplify Rational Expressions

• Reduce to lowest terms

36. Standard to Factored Form

• Use factoring techniques

37. Determine Factor from Zero

• If zero is rrr, factor is (x−r)(x - r)(x−r)

38. Write Least Degree Polynomial

• Use: y-int, zeros, leading coeff., point(s), factors