Mathematical Literacy Study Notes
Unit 1: Review of Basic Skills
Basic Arithmetic Operations
Addition & Subtraction: Ensure you align numbers properly in
columns, particularly with decimals.
Multiplication & Division:
o Long multiplication and division methods.
o Division with remainders and decimals.
Order of Operations (BODMAS/BIDMAS):
o Brackets
o Orders (exponents, square roots)
o Division and Multiplication (from left to right)
o Addition and Subtraction (from left to right)
Fractions, Decimals, and Percentages
Conversions:
o Fraction → Decimal: Divide the numerator by the denominator.
o Decimal → Fraction: Count decimal places and convert
accordingly.
o Percentage → Decimal: Divide by 100.
o Decimal → Percentage: Multiply by 100.
Operations with Fractions:
o Common denominator required for addition/subtraction.
o Multiplication: Multiply numerators and denominators directly.
o Division: Invert (flip) the second fraction and multiply.
Ratios and Proportions
Definition: A ratio compares two or more values (e.g., 2:3 means 2
parts of one thing for every 3 parts of another).
Scaling Ratios: Multiply or divide all parts by the same number.
Proportional Problems: Use cross-multiplication to solve for
missing values.
, Estimation and Rounding
Rounding Rules:
o 0-4 → Round down
o 5-9 → Round up
Significant Figures: Rounding a number to a certain number of
significant digits (e.g., 1234 rounded to 2 significant figures is
1200).
Decimal Places: Keep only the required number of decimal places
(e.g., 3.14159 rounded to 2 decimal places is 3.14).
Unit 2: Patterns, Relationships, and Representations
Number Patterns
Arithmetic Sequences:
o Sequence where each term increases/decreases by a constant
difference.
o Formula: Tn=a+(n−1)dT_n = a + (n-1)d, where aa is the first
term, dd is the common difference.
Geometric Sequences:
o Each term is multiplied by a constant ratio.
o Formula: Tn=a×r(n−1)T_n = a \times r^{(n-1)}, where rr is
the common ratio.
Algebraic Representations
Substituting Values into formulas (e.g., calculating distance using
speed×time\text{speed} \times \text{time}).
Solving for Unknowns: Isolating the variable to solve for missing
values in equations.
Graphs and Tables
Types of Graphs:
o Line Graphs (show trends over time).
o Bar Graphs (compare different categories).
o Pie Charts (show parts of a whole).
Interpreting Graphs:
o Identify trends (increase, decrease, constant).
Unit 1: Review of Basic Skills
Basic Arithmetic Operations
Addition & Subtraction: Ensure you align numbers properly in
columns, particularly with decimals.
Multiplication & Division:
o Long multiplication and division methods.
o Division with remainders and decimals.
Order of Operations (BODMAS/BIDMAS):
o Brackets
o Orders (exponents, square roots)
o Division and Multiplication (from left to right)
o Addition and Subtraction (from left to right)
Fractions, Decimals, and Percentages
Conversions:
o Fraction → Decimal: Divide the numerator by the denominator.
o Decimal → Fraction: Count decimal places and convert
accordingly.
o Percentage → Decimal: Divide by 100.
o Decimal → Percentage: Multiply by 100.
Operations with Fractions:
o Common denominator required for addition/subtraction.
o Multiplication: Multiply numerators and denominators directly.
o Division: Invert (flip) the second fraction and multiply.
Ratios and Proportions
Definition: A ratio compares two or more values (e.g., 2:3 means 2
parts of one thing for every 3 parts of another).
Scaling Ratios: Multiply or divide all parts by the same number.
Proportional Problems: Use cross-multiplication to solve for
missing values.
, Estimation and Rounding
Rounding Rules:
o 0-4 → Round down
o 5-9 → Round up
Significant Figures: Rounding a number to a certain number of
significant digits (e.g., 1234 rounded to 2 significant figures is
1200).
Decimal Places: Keep only the required number of decimal places
(e.g., 3.14159 rounded to 2 decimal places is 3.14).
Unit 2: Patterns, Relationships, and Representations
Number Patterns
Arithmetic Sequences:
o Sequence where each term increases/decreases by a constant
difference.
o Formula: Tn=a+(n−1)dT_n = a + (n-1)d, where aa is the first
term, dd is the common difference.
Geometric Sequences:
o Each term is multiplied by a constant ratio.
o Formula: Tn=a×r(n−1)T_n = a \times r^{(n-1)}, where rr is
the common ratio.
Algebraic Representations
Substituting Values into formulas (e.g., calculating distance using
speed×time\text{speed} \times \text{time}).
Solving for Unknowns: Isolating the variable to solve for missing
values in equations.
Graphs and Tables
Types of Graphs:
o Line Graphs (show trends over time).
o Bar Graphs (compare different categories).
o Pie Charts (show parts of a whole).
Interpreting Graphs:
o Identify trends (increase, decrease, constant).
