Lecture Notes

Chapter 5: Key Concepts

5.1.2

• Problem 5-22: Solve by showing all steps in arithmetic operations.
• Problem 5-23: Use the formula ( \frac{y^2-y^1}{x^2-x^1} ) for slope; substitute values to find the line equation.
• Problem 5-24: Interpret variance in dependent variable from linear relationship.
• Problem 5-25: Formulate equations ( y=mx+b ) to find intersections.
• Problem 5-26: Utilize tables to identify proportional relationships.
• Problem 5-27: Confirm a point on a line by substitution.

5.1.3

• Problem 5-35: Calculate ratios for rebounding heights.
• Problem 5-36: Use tables for clarity; round to whole numbers.
• Problem 5-37: Define slope ( m ) and y-intercept ( b ).
• Problem 5-38: Remember correlation does not imply causation.
• Problem 5-39: Simplify expressions using whole numbers.
• Problem 5-40: Understand shapes like isosceles triangles and rectangles.

5.2.2

• Problem 5-66: Solve sequences using ( t(n) ) formulas.
• Problem 5-67: Only positive term numbers are valid.
• Problem 5-68: Recognize similarities between ( t(n)=mn+t(0) ) and ( y=mx+b ).
• Problem 5-69: Comprehend exponential growth variations.
• Problem 5-70: Residual plots indicate prediction accuracy.
• Problem 5-71: Pythagorean theorem insights.

5.3.1

• Problem 5-86: Differentiate geometric and arithmetic sequences.
• Problem 5-87: Verify arithmetic accuracy.
• Problem 5-88: Solve for angles by equating expressions.
• Problem 5-89: Use known formulas for solving areas.
• Problem 5-90: Simplification of exponential expressions.
• Problem 5-91: Incorporate slope to find equations.

5.3.2

• Problem 5-102: Adjust multipliers for percentage changes.
• Problem 5-103: Distinguish linear (arithmetic) and exponential (geometric) trends.
• Problem 5-104: Reference similar methods in 5-91.
• Problem 5-105: Employ whole numbers in calculations.
• Problem 5-106: Validate linear relationships with statistical tools.
• Problem 5-107: Contextual understanding in problem-solving.

5.3.3

• Problem 5-120: Domains for sequences and undefined expressions.
• Problem 5-121: Recognize limits for variable values.
• Problem 5-122: Explore recursive and explicit equations.
• Problem 5-123: Familiarize with terminology.
• Problem 5-124: Importance of units.
• Problem 5-125: Intersection at origin effects.

6.1.1

• Problem 6–7: Show all work; isolate variables.
• Problem 6-8: Use area models; correct misconceptions of multiplication.
• Problem 6-9: R-value proximity indicates association strength.
• Problem 6-10: Arithmetic sequences explorations.
• Problem 6-11: Function notation reminders.
• Problem 6-12: Solve for unknowns with structured work.

6.1.2

• Problem 6-15: Identify target variables.
• Problem 6-16: Clarify notation in equations.
• Problem 6-17: Determine POI by equating and solving equations.
• Problem 6-18: Comprehend similarities to ( y=mx+b ).
• Problem 6-19: Scale transformations understanding.
• Problem 6-20: Reinforce knowledge on POIs and scaling.

Chapter 7

• 7.1.1: Congruence through geometric theorems and scale factors.
• 7.1.2: Parallel lines and consistent slopes.
• 7.1.3: Flowcharts in reasoning; scientific notation clarity.
• 7.1.4: Triangle congruence and recursive equations.
• 7.1.5: Validity of congruence conditions and system solutions.
• 7.1.7: Triangle theorems and associations in systems.

Chapter 8

• 8.1.2: Exponential equations and congruence conditions.
• General: Consistent use of units, ensure correct scientific notation, and validate solutions with real-world context.