ms faruq maths

Probability scale

  • A scale showing the likelihood of an event, ranging from 0 (impossible) to 1 (certain).
    Calculate probability of events

  • Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
    Possibility space diagram

  • A diagram showing all possible outcomes of two events.
    Frequency of events

  • How often an event occurs.
    Venn diagrams & set notation

  • Visual representation of sets and their relationships using overlapping circles; includes unions, intersections, and complements.
    Probability trees

  • Diagrams showing probabilities of sequential events.

Numbers

  • Various types of numbers and their properties.
    Factors, multiples, primes

  • Factors: numbers that divide evenly into a given number.

  • Multiples: numbers obtained by multiplying a given number by an integer.

  • Primes: numbers divisible only by 1 and themselves.
    Negative numbers

  • Numbers less than zero.
    Written methods

  • Standard algorithms for addition, subtraction, multiplication, and division.
    BIDMAS

  • Order of operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction.
    Squares and cubes

  • Square: a number multiplied by itself.

  • Cube: a number multiplied by itself twice.
    Rules of indices

  • a^m \times a^n = a^{m+n}, \frac{a^m}{a^n} = a^{m-n}, (a^m)^n = a^{mn}, a^0 = 1
    Standard form

  • Writing numbers in the form A \times 10^n, where 1 ≤ |A| < 10.
    Rounding

  • Approximating a number to a specified degree of accuracy.
    Estimation

  • Approximating values to make calculations easier.

Scatter graphs

  • A graph showing the relationship between two variables.
    Drawing

  • Plotting points on a scatter graph.
    Interpreting

  • Identifying patterns and trends in a scatter graph.
    Correlation

  • Measure of the strength and direction of a linear relationship between two variables.
    Line of best fit

  • A line drawn on a scatter graph that best represents the trend in the data.

Area and perimeter

  • Area: the amount of space inside a 2D shape.

  • Perimeter: the distance around the outside of a 2D shape.
    Square

  • Area = side^2, Perimeter = 4 × side
    Rectangle

  • Area = length × width, Perimeter = 2 × (length + width)
    Triangle

  • Area = \frac{1}{2} × base × height
    Parallelogram

  • Area = base × height
    Trapezium

  • Area = \frac{1}{2} × (sum of parallel sides) × height
    Compound shapes

  • Shapes made up of two or more simpler shapes.

Circles

  • A round plane figure whose boundary consists of points equidistant from the center.
    Naming parts of a circle

  • Radius, diameter, circumference, chord, tangent, sector, segment.
    Area

  • Area = πr^2
    Circumference

  • Circumference = 2πr
    Sectors

  • A region bounded by two radii and an arc of a circle.

Volume & 3D shapes

  • The amount of space occupied by a 3D object.
    Nets

  • A 2D shape that can be folded to form a 3D shape.
    Volume of prisms

  • Volume = area of cross-section × length
    Surface area of prisms

  • The total area of all the faces of a prism.
    Changing units of area/volume

  • Converting between different units of area and volume (e.g., cm² to m², cm³ to m³).

Fractions & percentages

  • Ways of representing parts of a whole.
    Equivalent fractions

  • Fractions that represent the same value.
    Comparing fractions

  • Determining which of two or more fractions is larger or smaller.
    Simplifying fractions

  • Reducing a fraction to its simplest form.
    Fractions of amounts

  • Finding a fraction of a given quantity.
    Adding and subtracting

  • Combining or finding the difference between fractions.
    Multiplying and dividing

  • Performing multiplication or division with fractions.
    Mixed numbers

  • Numbers consisting of a whole number and a fraction.
    Fraction/Decimal/Percentage equivalence

  • Converting between fractions, decimals, and percentages.
    Percentage of amount

  • Finding a percentage of a given quantity.
    Percentage increase & decrease

  • Calculating the increase or decrease in a quantity as a percentage.

Algebra

  • Using letters and symbols to represent numbers and quantities in formulas and equations.
    Collecting like terms

  • Simplifying an expression by combining terms with the same variable and exponent.
    Expanding brackets

  • Multiplying each term inside a bracket