Edexcel International GCSE Maths (4MA1)
Video lessons · IGCSE Maths revision notes · IGCSE Maths past papers
Every topic of Edexcel International GCSE Maths (4MA1) in short video lessons with worked exam examples, clear revision notes and all past papers with mark schemes. Higher and Foundation, linear and modular.
The first 5 lessons of every chapter are free.
1 Fractions, decimals and rounding
- Directed numbers
- Equivalent fractions and simplifying
- Mixed numbers and improper fractions
- Adding and subtracting fractions
- A fraction of a quantity
- Multiplying and dividing fractions
- Ordering decimals
- Fractions, decimals and percentages
- Recurring decimals to fractions
- Mixed recurring decimals
- Rounding to decimal places and significant figures
- Estimating by rounding
- Finding upper and lower bounds
- Calculating with bounds
2 Ratios and percentages
- Ratio and fraction links
- Sharing in a ratio
- Changing ratios
- Ratio word problems
- Percentage of an amount
- Writing one number as a percentage of another
- Percentage increase and decrease
- Repeated percentage change
- Compound interest
- Depreciation and decay
- Reverse percentage and compound interest problems
3 Powers and roots
- Squares, cubes and their roots
- Evaluating fractional powers
- Index laws with negative and zero powers
- Evaluating negative powers
- Index laws with whole-number powers
- Standard form arithmetic
- Solving problems in standard form
- Factors, multiples and primes
- Prime factor decomposition
- HCF and LCM
4 Working with algebra
- Order of operations
- Collecting like terms
- Substituting into expressions and formulae
- Index laws with algebraic terms
- Fractional indices
- Expanding a single bracket
- Expanding double brackets
- Expanding triple brackets
- Factorising with a common factor
- Factorising quadratics of the form x squared plus bx plus c
- Factorising with a coefficient
- Difference of two squares
- Writing and deriving a formula
- Changing the subject of a formula
- When the subject has a power on it
5 Algebraic equations
- Expressions, equations and identities
- Solving linear equations
- Setting up an equation from a problem
- Equations with brackets
- Equations with fractions
6 Graphs of straight lines
- Coordinates in all four quadrants
- The midpoint of a line segment
- Drawing a straight line from a table of values
- y = mx + c and the shape of the line
- Gradient from two points
- Equation of a line through two points
- Parallel lines
- Perpendicular lines
7 Simultaneous equations
- Simultaneous equations by inspection
- Simultaneous equations by elimination
- Simultaneous equations by substitution
- Simultaneous equations from a graph
- Setting up simultaneous equations from a problem
8 Inequalities
- Whole-number solutions to an inequality
- Solving linear inequalities
- Inequality symbols and the number line
- Regions defined by linear inequalities
9 Sequences and series
- Number sequences and term-to-term rules
- Finding a rule for a sequence
- Arithmetic sequences, a and d
- The nth term of an arithmetic sequence
- Using the nth term formula in reverse
- Finding a and d from two terms
- The sum of an arithmetic series
- Arithmetic series problem solving
10 Travel and other graphs
- Reading a distance-time graph
- Conversion graphs and reading information from graphs
- Modelling with graphs
11 Working with shape and space
- Angles at a point and on a line
- Angles in parallel lines
- Angle sum of a triangle
- Exterior angle of a triangle
- Angles in special triangles
- Angle sum of a quadrilateral
- Properties of quadrilaterals
- Writing geometrical reasons
- Angle sum of a polygon
- Interior and exterior angles of regular polygons
- Finding the number of sides from an angle
- Irregular polygon angle problems
- Perimeter and area of rectangles and triangles
- Area of a parallelogram
- Area of a trapezium
- Names of solids: faces, edges and vertices
- Surface area of a cuboid
- Surface area of a triangular prism
- Volume of a prism
- Compound prisms and volume units
- Time intervals, money and currency
- Converting units of length, area and volume
12 Circles, cylinders, cones and spheres
- Circumference of a circle
- Area of a circle
- Semicircles: perimeter and area
- Compound area with circles
- Arc length of a sector
- Area of a sector
- Perimeter of a sector
- Reverse sector problems
- Reverse circle problems
- Volume of a cylinder
- Surface area of a cylinder
- Leaving an answer in terms of pi
- Volume of a cone
- Surface area of a cone
- Volume of a sphere
- Surface area of a sphere
- Hemispheres and compound solids
- Frustums and truncated cones
- Reverse volume and surface area problems
13 Geometric constructions
- Constructing triangles with compasses
- Constructing the perpendicular bisector of a line segment
- Constructing the bisector of an angle
- Three-figure bearings
- Back bearings and return journeys
- Scale drawings and bearings
14 Transformation and similarity
- Lines of symmetry and rotational symmetry
- Equations of common mirror lines
- Reflecting a shape in a line
- Reflecting in y = x and y = -x
- Finding the mirror line from object and image
- What defines a rotation
- Rotating a shape about a point
- Positive and negative rotation angles
- Rotating about a point not on the shape
- What defines a translation
- Translating a shape
- Column vectors in translations
- Congruence under transformations
- Describing a single transformation fully
- Combining two transformations
- What defines an enlargement
- Similarity under enlargement
- Enlarging from a given centre
- Fractional scale factor enlargements
- Finding the centre of enlargement
- Conditions for congruent triangles
- Proving triangles are congruent
- Similar shapes: corresponding lengths
- Area scale factor
- Volume scale factor
- Similar solids, mass and capacity
- Similar shapes problem solving
15 Pythagoras theorem
- Introducing Pythagoras theorem
- Pythagoras: finding the hypotenuse
- Pythagoras: finding a shorter side
- Pythagoras in isosceles and composite shapes
- Pythagoras in three dimensions
- The space diagonal of a cuboid
- Pythagoras on a coordinate grid
16 Introducing trigonometry
- The sine ratio
- The cosine ratio
- The tangent ratio
- Labelling sides and choosing the trig ratio
- Finding a missing side with trigonometry
- Missing side when the unknown is in the denominator
- Finding a missing angle with inverse trig
- Combining Pythagoras and trigonometry
- Two-step right-angled triangle problems
- Right-angled trigonometry with bearings
- Angles of elevation and depression
17 Circle theorems
- Parts of a circle and cyclic quadrilaterals
- Tangent and radius, and two tangents from a point
- The angle at the centre is twice the angle at the circumference
- The angle in a semicircle
- Angles in the same segment
- Opposite angles of a cyclic quadrilateral
- The alternate segment theorem
- Using the alternate segment theorem in a reasoning chain
- Reasoning chains with circle theorems
- Multi-step circle theorem problems
- Intersecting chords inside a circle
- Intersecting chords from a point outside the circle
18 Sets
- Subsets and set notation
- Sets defined algebraically
- Counting elements in sets
- Venn diagrams with two sets
- Venn diagrams with three sets
- Set problems in context
19 Working with data
- Bar charts, pie charts and pictograms
- Two-way tables and reading statistical diagrams
- Mean from a frequency table
- Estimated mean and modal class for grouped data
- Frequency density
- Drawing a histogram
- Reading frequencies from a histogram
- Completing a histogram from a part drawn graph
- Estimating a frequency within a class
- Building a cumulative frequency table
- Plotting a cumulative frequency diagram
- Reading values from a cumulative frequency graph
- Estimating how many are above or below a value
- Estimating the median from a cumulative frequency diagram
- Estimating the interquartile range from a cumulative frequency diagram
- Comparing two cumulative frequency distributions
- Mean, median, mode and range
- Quartiles and the interquartile range for discrete data
- What a measure of spread tells you
- Using the interquartile range to compare distributions
20 Probability
- The language of probability and the probability scale
- Listing outcomes systematically
- Theoretical probability and sample space
- Relative frequency and mutually exclusive events
- Expected frequency and relative frequency
- Multiplying independent probabilities
- At least one, and the complement
- Tree diagrams with replacement
- Tree diagrams without replacement
- Three stage tree diagrams
- Probability problem solving
- Conditional probability from a two way table
- Conditional probability from a Venn diagram
- Conditional probability without replacement
- Forming an equation from a probability
21 Direct and inverse proportion
- Direct proportion
- Inverse proportion
- Graphs of direct and inverse proportion
- Speed, distance and time
- Density, mass and volume
- Pressure, force and area
- Average speed over a multi-stage journey
22 Quadratic equations, curves and inequalities
- Solving quadratics by factorising
- Completing the square
- Completing the square with a negative coefficient
- Solving quadratics by completing the square
- The quadratic formula
- Forming quadratics from a context
- Drawing a quadratic curve
- Reading roots and the turning point from a curve
- Quadratic inequalities
23 Advanced algebra
- Simplifying surds
- Expanding brackets with surds
- Rationalising a denominator
- Rationalising with conjugates
- Adding algebraic fractions
- Simplifying algebraic fractions
- Simultaneous equations, one linear and one quadratic
- When the subject appears twice
- Algebraic proof
24 Functions and function notation
- What is a function
- Function notation and evaluation
- Solving equations written in function notation
- Domain and range
- Excluded values from a domain
- Inverse functions
- Composite functions
- Solving composite and inverse function equations
25 Further trigonometry
- The sine rule: finding a missing side
- The sine rule: finding a missing angle
- The ambiguous case of the sine rule
- The cosine rule: finding a missing side
- The cosine rule: finding a missing angle
- Choosing between the sine rule and the cosine rule
- Area of a triangle using half ab sin C
- Finding a side or an angle from a given area
- Area of a segment
- The angle between a line and a plane
- Trigonometry in pyramids and cones
- Problem solving in three dimensions
26 Graphs and transformations
- Drawing cubic graphs
- Graphs with reciprocal terms
- Solving equations graphically
- Finding the line to draw
- Sine, cosine and tangent graphs
- Trig ratios of obtuse angles
- Graph translations
- Graph stretches
- Transforming trigonometric graphs
- Writing transformed functions algebraically
27 Vectors
- What is a vector
- Column vector notation
- Directed line segment notation
- Magnitude of a vector
- Adding and subtracting column vectors
- Resultant of two or more vectors
- Subtracting vectors in a diagram
- Multiplying a vector by a scalar
- Finding a route through a vector diagram
- Vectors with ratios on a line
- Proving two vectors are parallel
- Proving points are collinear
- Vector proofs with midpoints and medians