L4th Summer Examination Revision Notes

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.

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.

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.

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.

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.

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).

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. $\text{Percentage change} = \frac{\text{New value - Original value}}{\text{Original value}} \times 100 \%$ .

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).