Formula Sheet: Basic arithmetic, no specific formula listed.
Desmos/Excel: Use for the division calculation: 460 / 28.
2. Unit Conversion (Time):
Concept: Dimensional analysis.
Formula Sheet: No specific conversion formulas listed, but requires knowing: 1 year ≈ 365 days, 1 day = 24 hours.
Desmos/Excel: Use for calculation: 2 * 365 * 24.
3. Unit Conversion (Weight):
Concept: Using a given conversion factor.
Formula Sheet: No specific conversion formulas listed, but the factor (1 lb = 0.4536 kg) is provided in the question.
Desmos/Excel: Use for calculation: 16 * 0.4536.
4. Temperature Conversion:
Concept: Applying specific conversion formulas.
Formula Sheet: The necessary formulas ($C = (F-32)/1.8$, $F = 1.8C + 32$) are provided in the question itself.
Desmos/Excel: Use for plugging values into the formulas.
5. Percentage Calculation:
Concept: Understanding percentage decrease. 50% less means the price is (1 - 0.50) = 0.50 times the original price.
Formula Sheet: Basic percentage concept, related to Relative Change if needed, but simpler here.
6. Weighted Averages:
Concept: Understanding that averaging percentages directly only works if the quantities they represent have equal weight (which is often not the case with course grades where exams might be weighted differently).
Formula Sheet: No specific formula, relies on conceptual understanding of averages.
7. Scientific Notation Conversion:
Concept: Converting from scientific notation (with a negative exponent) to ordinary notation by moving the decimal point to the left.
Formula Sheet: No specific formula, relies on understanding scientific notation.
8. Scientific Notation Conversion:
Concept: Converting from ordinary notation to scientific notation (with a positive exponent).
Formula Sheet: No specific formula, relies on understanding scientific notation.
9. Prorating Expenses:
Concept: Calculating total annual cost from monthly cost (Monthly * 12) and comparing annual costs.
Formula Sheet: Basic arithmetic.
Excel: Useful for organizing and calculating: Cell A1: =75*12, Cell A2: 350, then compare A1 and A2.
10. Prorating Expenses:
Concept: Finding the average monthly cost by converting all expenses to monthly equivalents (Semiannual / 6, Annual / 12) and summing them.
Formula Sheet: Basic arithmetic.
Excel: Useful for calculation: =(600/6) + 105 + (400/12).
11. Compound Interest (Monthly):
Concept: Calculating future value with compound interest.
Formula Sheet: Financial Formulas -> Compound Interest -> Compounded n times/year: $ A = P \times \left(1 + \frac{APR}{n}\right)^{(nY)} $. A = P * (1 + APR/n)^(nY) (Here P=6000, APR=0.06, n=12, Y=13).
Excel: Use the FV function: =FV(0.06/12, 13*12, 0, -6000).
Desmos: Calculate using the formula directly: $6000*(1 + 0.06/12)^(12*13)$.
12. Compound Interest (Annually):
Concept: Calculating future value with annual compounding.
Formula Sheet: Financial Formulas -> Compound Interest -> Compounded Annually: $ A = P \times (1 + APR)^Y $. A = P * (1 + APR)^Y (Here P=2000, APR=0.05, Y=2).
Excel: Use the FV function: =FV(0.05, 2, 0, -2000).
Desmos: Calculate using the formula directly: $2000*(1 + 0.05)^2$.
13. Savings Plan Balance (Future Value of Annuity):
Concept: Calculating the future value of regular monthly deposits.
Formula Sheet: The Excel function =FV(rate, nper, pmt, [pv], [type]) is listed under Financial Functions. The sheet provides the mathematical formula for PMT based on FV, but not FV based on PMT.
Excel: Use the FV function: =FV(0.04/12, 2*12, -250, 0). (Rate=APR/n, Nper=Y*n, Pmt is negative as it's an outflow).
Desmos: Could calculate using the full FV of annuity formula if known: $ FV = PMT \times \frac{\left(1 + \frac{APR}{n}\right)^{(nY)} - 1}{\left(\frac{APR}{n}\right)} $.
14. Investment Returns:
Concept: Calculating total and annualized returns.
Formula Sheet: Financial Formulas -> Investment Returns -> Total Return: $ \frac{(A - P)}{P} \times 100\% $ (A - P) / P * 100% and Annual Return: $ \left(\frac{A}{P}\right)^{(1/Y)} - 1 $ (A / P)^(1/Y) - 1.
First calculate Initial Principal (P): 150 * 60 = 9000.
A = $12900$, Y = 4 years.
Excel/Desmos: Use for the calculations after finding P.
Total Return: ((12900 - 9000) / 9000) * 100
Annual Return: ((12900 / 9000)^(1/4) - 1) * 100
15. Loan Comparison:
Concept: Analyzing trade-offs between loan term, APR, monthly payment, and total interest paid.
Excel: Use the PMT function to calculate payments for both scenarios:
Scenario 1 (3yr, 5%): =PMT(0.05/12, 3*12, 100000)
Scenario 2 (5yr, 6%): =PMT(0.06/12, 5*12, 100000)
Compare payments and calculate total paid (PMT * term * 12) to compare total interest. Shorter term = higher payment, less total interest.
16. Mortgage Calculations:
Concept: Calculating mortgage payment, total cost, and interest/principal portions.
Formula Sheet:
a. Monthly Payment: Financial Formulas -> Savings/Loan Payments -> PMT based on PV formula (see Q15).
b. Total Paid: Basic arithmetic (Monthly Payment * n * Y).
c. Total Interest = Total Paid - Principal (PV). Calculate percentages using Relative Change formula if needed.
Excel:
a. =PMT(0.03/12, 15*12, 225000)
b. Result from (a) * 15 * 12
c. Principal Percentage: =225000 / Result from (b). Interest Percentage: =(Result from (b) - 225000) / Result from (b) or =1 - Principal Percentage. Format as percentage.
17. Statistics Concepts:
Concept: Definitions of Population, Sample, Population Parameters, and Sample Statistics.
Formula Sheet: Conceptual, no specific formulas.
18. Survey Bias:
Concept: Identifying biased questions (specifically, leading questions).
Formula Sheet: Conceptual, no specific formulas.
19. Data Types:
Concept: Distinguishing between Qualitative (categorical) and Quantitative (numerical) data.
Formula Sheet: Conceptual, no specific formulas.
20. Data Types:
Concept: Distinguishing between Qualitative and Quantitative data.
Formula Sheet: Conceptual, no specific formulas.
21. Graph Interpretation (Bar Chart):
Concept: Reading and comparing values from a double bar chart.
Formula Sheet: No formulas needed.
22. Graph Interpretation (Scatter Plot):
Concept: Identifying the type (positive/negative/none) and strength (strong/weak) of correlation shown in a scatter plot.
Formula Sheet: Conceptual, no specific formulas.
23. Graph Interpretation (Scatter Plot):
Concept: Identifying the type and strength of correlation.
Formula Sheet: Conceptual, no specific formulas.
24. Descriptive Statistics:
Concept: Calculating measures of central tendency.
Formula Sheet: Descriptive Statistics & Change -> Measures of Center -> Mean, Median, Mode definitions.
Excel: Enter the data into a column. Use =AVERAGE(range), =MEDIAN(range), =MODE.SNGL(range) or =MODE.MULT(range).
Desmos: Can calculate mean and median using `mean()` and `median()` functions on a list. Mode needs manual identification.
25. Descriptive Statistics:
Concept: Definition of Range.
Formula Sheet: Descriptive Statistics & Change -> Measures of Variation -> Range: $\text{Highest Value} - \text{Lowest Value}$ Range: Highest Value - Lowest Value.
26. Descriptive Statistics:
Concept: Calculating Mean and Median.
Formula Sheet: Descriptive Statistics & Change -> Measures of Center -> Mean, Median definitions.
Excel:=AVERAGE(range), =MEDIAN(range).
27. Normal Distribution Validity:
Concept: Understanding properties of normal distribution and standard deviation. A standard deviation (7 lbs) cannot be larger than the mean (6.8 lbs) for a variable like baby weight which must be non-negative. A value 1 standard deviation below the mean would be negative (6.8 - 7 = -0.2 lbs), which is impossible.
Formula Sheet: Conceptual understanding related to Distributions section.
28. Normal Distribution (Z-score & Percentiles):
Concept: Calculating z-scores and finding corresponding percentiles using a table.
Formula Sheet: Distributions -> Standard Score (z-score): $ z = \frac{(x - \mu)}{\sigma} $ z = (x - μ) / σ. Variable definitions use code tags: x (data value), μ (population mean), σ (population std dev). Use the Z-Table on the sheet or in the question.
Excel: Calculate z-score using the formula or =STANDARDIZE(x, mean, stdev). Find percentile using =NORM.S.DIST(z, TRUE).
Desmos: Calculate z-score using the formula: $(x - 62.6) / 2.5$.
29. Exponential Decay:
Concept: Modeling exponential decrease and calculating future value.
Formula Sheet: Growth Models -> Exponential Growth -> Formula (rate 'r'): $ Q = Q_0 \times (1 + r)^t $. Q = Q_0 * (1 + r)^t Note that for decay, 'r' is negative (r = -0.09).
Excel: Calculate directly: =120*(1-0.09)^3. Or use =FV( -0.09, 3, 0, -120) (treating decay rate like a negative interest rate).
Desmos: Calculate using the formula: $120*(1-0.09)^3$.
30. Linear Growth:
Concept: Modeling linear increase and calculating future value.
Formula Sheet: Growth Models -> Linear Growth (Basic): New Value = Initial Value + (Growth Rate × Time). Or Linear Modeling -> General Form. (Initial Value = 100000, Growth Rate = 1600, Time = 4).
Excel/Desmos: Calculate using the formula: $100000 + (1600 * 4)$.
31. Exponential Growth (Doubling Time):
Concept: Understanding doubling time and its relation to growth factor over multiple periods. If doubling time is $T_{dbl}$, then in time $t$, the factor of growth is $2^{(t/T_{dbl})}$.
Step 2: Calculate population for t = 2059-2020 = 39 years: $ 330 \times 2^{(39 / 116.67)} $.
Step 3: Calculate population for t = 2098-2020 = 78 years: $ 330 \times 2^{(78 / 116.67)} $.
Excel/Desmos: Use for calculations in steps 1, 2, and 3.
34. Function Relationships:
Concept: Describing the relationship between two variables as a function.
Formula Sheet: Conceptual, related to Linear Modeling/Growth Models definitions.
35. Function Representation (Table, Graph):
Concept: Identifying independent/dependent variables, domain/range from a table, and matching to a graph. Plotting points.
Formula Sheet: No formulas needed.
Desmos: Useful for plotting the points from the table `(speed, stopping distance)` to visualize the shape and verify the correct graph.
Excel: Can create a scatter plot from the data.
36. Linear Functions:
Concept: Definition of a linear function and its graphical representation (a straight line).
Formula Sheet: Conceptual, see Linear Modeling section definition.
37. Linear Functions (Graph Interpretation):
Concept: Describing the function shown in a graph and calculating its slope (rate of change).
Formula Sheet: Linear Modeling -> Slope (Rate of Change): $ m = \frac{y_2 - y_1}{x_2 - x_1} $. m = (y2 - y1) / (x2 - x1) Pick two points from the graph (e.g., (0,0) and (4,3)). Slope = $(3-0)/(4-0) = 3/4$.
Desmos: Can plot points and find the equation of the line passing through them.
38. Linear Modeling:
Concept: Finding a linear equation from two data points and using it for prediction.
Formula Sheet: Linear Modeling -> Slope ($ m = \frac{y_2 - y_1}{x_2 - x_1} $ m = (y2 - y1) / (x2 - x1)) and Equation of a Line ($ y = mx + b $ y = mx + b).