Summary of High School Mathematical Literacy Exam
High School Mathematical Literacy Exam: Full Study Guide
Introduction
Mathematical literacy helps you use mathematics in everyday life: reading graphs, comparing costs, calculating repayments, interpreting tables and making decisions using numbers. This guide focuses on the core skills needed to solve real-world problems similar to those in the supplied exam material: reading graphs, working with percentages, interpreting tables, building cost formulas, and calculating loan costs.
Definition: Mathematical literacy is the ability to apply mathematical reasoning and techniques to solve everyday problems and to interpret numerical information presented in texts, tables and graphs.
1. Reading and interpreting graphs
Types of common graphs
- Line graph: shows change over time using points connected by lines. Useful for trends.
- Bar graph/histogram: compares categories using bars. Useful for comparing votes or counts.
- Pie chart: shows parts of a whole as slices.
Definition: A line graph displays data points connected by straight lines, showing how a quantity changes over time.
Example (election votes): Given vote percentages for three parties across three years, a line graph makes it easy to see which party rose or fell and which had the highest percentage in a given year.
How to answer typical questions
- Identify the graph type: look at axes and continuity of data points.
- Most votes in a year: find the highest point among the parties for that year.
- Difference between two values: subtract the smaller percentage from the larger one.
Practical tip: Always read the axis labels and legend first.
2. Working with percentages and differences
- Percentage difference between two values $A$ and $B$ (absolute difference): $|A - B|$.
- When comparing percentages across years, use the given percentage points (not percentage change) unless asked otherwise.
Example: If Party X had $65%$ in 2014 and $55%$ in 2024, the difference in percentage points is $|65 - 55| = 10$ percentage points.
Definition: Percentage point is the arithmetic difference between two percentages.
3. Understanding income and loan basics (excluding income tax and salaries details)
Key terms
- Gross monthly income: total monthly earnings before deductions such as tax, retirement or other withholdings.
Definition: Gross income is the total income earned before any deductions are taken out.
- Deposit (down payment): an initial lump sum paid towards the purchase price; reduces the borrowed amount.
- Initiation fee: one-off fee charged when a loan starts; not part of monthly repayments unless specified.
- Monthly repayment: the fixed amount paid each month that usually includes interest and sometimes fees.
Practical example (home loan): The loan calculator gives:
- Gross monthly income $R75,000$ (used to estimate affordability),
- Deposit $R250,000$,
- Loan amount after deposit $R2,076,207$,
- Monthly repayment $R22,500$,
- Initiation fee $R1,207.50$,
- Monthly service fee $R69$ (already included in the monthly repayment).
Converting years to months
- Repayment period in months = number of years $\times 12$. Example: $20$ years $= 20 \times 12 = 240$ months.
Definition: Repayment period in months is the total number of monthly instalments: $\text{years} \times 12$.
4. Calculating real cost of a loan
Use the formula: $$\text{Real cost of loan} = \text{Monthly repayment} \times \text{Loan period in months} + \text{initiation fee}$$ Step-by-step:
- Find loan period in months: $20$ years $= 240$ months.
- Multiply monthly repayment by months: $R22,500 \times 240$.
- Add the initiation fee $R1,207.50$.
Example calculation (carry out as practice): $$R22,500 \times 240 = R5,400,000$$ Add initiation fee: $$R5,400,000 + R1,207.50 = R5,401,207.50$$ This gives the total amount paid over the life of the loan (real cost), including the one-of
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Mathematical Literacy Essentials
Klíčová slova: Income tax, Mathematical literacy, School finance, Growth percentiles, Salaries
Klíčové pojmy: Mathematical literacy applies math to everyday contexts like loans, bills and graphs., Identify graph types first: line for trends, bar for category comparisons, pie for parts of a whole., Percentage point difference is $|A-B|$ between two percentages., Convert years to months using $\text{months}=\text{years}\times 12$., Real cost of loan: $\text{monthly repayment}\times\text{months} + \text{initiation fee}$., Loan principal formula: $\text{Loan}=M\times\dfrac{1-(1+i)^{-n}}{i}$ with $i$ monthly rate., Contract phone cost is piecewise: $450$ if $m\le100$, $450+1.40(m-100)$ if $m>100$., Prepaid cost is linear: $2.25\times m$., Find break-even by equating cost formulas and solving for $m$., Show units and steps in calculations; check whether fees are included in monthly repayments.