L4th Summer Examination Revision Notes

Probability

• Probability Scale: Understanding the range of probability values, typically from 0 to 1, where 0 indicates impossibility and 1 indicates certainty.
• Calculate Probability of Events: Determining the likelihood of specific events occurring, expressed as a fraction, decimal, or percentage. Calculating P(event) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}.
• Possibility Space Diagram: A visual tool used to represent all possible outcomes of an event, often used for two-way events (e.g., rolling two dice).
• Frequency of Events: Analyzing how often an event occurs within a set of observations or trials. Relative frequency is calculated as \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}.
• Venn Diagrams & Set Notation: Using Venn diagrams to represent sets, intersections, unions, and complements. Applying set notation. (e.g., A \cup B, A \cap B, A')
• Probability Trees: Diagram used to represent sequential events and calculate probabilities along different branches. Multiplying probabilities along the branches gives the probability of the combined event.

Numbers

• Factors, Multiples, Primes: Identifying factors of a number, multiples of a number, and prime numbers (numbers with exactly two distinct factors: 1 and itself).
• Negative Numbers: Understanding and performing operations with negative numbers, including addition, subtraction, multiplication, and division.
• Written Methods (+ - × ÷): Proficiency in performing arithmetic operations using standard written methods.
• BIDMAS: Order of operations (Brackets, Indices, Division, Multiplication, Addition, Subtraction) to ensure consistent evaluation of expressions.
• Squares and Cubes: Calculating squares (number multiplied by itself) and cubes (number multiplied by itself twice).
• Rules of Indices: Applying laws of exponents (e.g., a^m \times a^n = a^{m+n}, \frac{a^m}{a^n} = a^{m-n}, (a^m)^n = a^{mn}).
• Standard Form: Expressing numbers in the form A \times 10^n, where 1 \le A < 10 and n is an integer.
• Rounding: Approximating numbers to a specified degree of accuracy (e.g., to the nearest whole number, decimal place, or significant figure).
• Estimation: Making reasonable approximations to assess the magnitude of a calculation or quantity.

Scatter Graphs

• Drawing: Constructing scatter graphs to plot pairs of data points and visually represent the relationship between two variables.
• Interpreting: Analyzing scatter graphs to identify patterns, trends, and relationships between variables.
• Correlation: Describing the strength and direction of the linear relationship between two variables (positive, negative, or no correlation).
• Line of Best Fit: Drawing a line that best represents the trend in a scatter graph, used for making predictions.

Area and Perimeter

• Square: Area = side^2, Perimeter = 4 \times side
• Rectangle: Area = length \times width, Perimeter = 2(length + width)
• Triangle: Area = \frac{1}{2} \times base \times height
• Parallelogram: Area = base \times height
• Trapezium: Area = \frac{1}{2} \times (sum of parallel sides) \times height
• Compound Shapes: Calculating area and perimeter by dividing the shape into simpler shapes.

Circles

• Naming Parts of a Circle: Identifying the radius, diameter, circumference, chord, tangent, and sector of a circle.
• Area: Calculating the area of a circle using the formula Area = \pi r^2, where r is the radius.
• Circumference: Calculating the circumference of a circle using the formula Circumference = 2 \pi r = \pi d, where r is the radius and d is the diameter.
• Sectors: Calculating the area and arc length of a sector of a circle. \text{Area of sector} = \frac{\theta}{360} \times \pi r^2, where \theta is the angle in degrees.

Volume & 3D Shapes

• Nets: Understanding how 2D nets fold to form 3D shapes.
• Volume of Prisms: Calculating the volume of prisms using the formula Volume = Area of cross-section \times length
• Surface Area of Prisms: Calculating the total surface area of prisms by summing the areas of all faces.
• Changing Units of Area/Volume: Converting between different units of area (e.g., cm² to m²) and volume (e.g., cm³ to m³).

Fractions & Percentages

• Equivalent Fractions: Recognizing and generating fractions that represent the same value.
• Comparing Fractions: Determining which of two or more fractions is larger or smaller.
• Simplifying Fractions: Reducing fractions to their simplest form by dividing the numerator and denominator by their greatest common divisor.
• Fractions of Amounts: Calculating a fraction of a given quantity.
• Adding and Subtracting: Adding and subtracting fractions with common denominators. Converting to common denominators when necessary.
• Multiplying and Dividing: Multiplying fractions by multiplying numerators and denominators. Dividing fractions by multiplying by the reciprocal of the divisor.
• Mixed Numbers: Converting between mixed numbers and improper fractions.
• Fraction/Decimal/Percentage Equivalence: Converting between fractions, decimals, and percentages.
• Percentage of Amount: Calculating a percentage of a given quantity.
• Percentage Increase & Decrease: Calculating percentage increases and decreases. \text{Percentage change} = \frac{\text{New value - Original value}}{\text{Original value}} \times 100 \%.

Algebra

• Collecting Like Terms: Simplifying algebraic expressions by combining terms with the same variable and exponent.
• Expanding Brackets: Removing brackets by multiplying each term inside the bracket by the term outside the bracket. Using distributive property.
• Simplifying Expressions: Combining like terms and expanding brackets to write an expression in its simplest form.
• Substitution: Replacing variables with given numerical values to evaluate an expression.
• Indices: Applying laws of exponents to simplify algebraic expressions.
• Solving Equations: Finding the value(s) of the variable(s) that make the equation true. Using inverse operations.
• Sequences and the nth Term: Identifying patterns in sequences and finding the nth term (a formula for the general term of the sequence).

Transformations

• Reflection: Reflecting a shape over a given line.
• Rotation: Rotating a shape about a given point by a given angle.
• Translation: Translating a shape by a given vector.