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