Edexcel IGCSE Maths Revision Guide - Specification A

Number

• Negative and fractional indices

• Surds and rationalising

• Standard form (harder applications)

• Bounds and error intervals

Algebra

• Quadratic expressions (expanding, factorising)

• Solving quadratics (common forms)

• Algebraic fractions (simplifying and basic solving)

• Simultaneous equations (including one linear + one non-linear)

• Inequalities (including graphical)

• Sequences including quadratic sequences

Graphs

• Quadratic graphs

• Cubic and reciprocal graphs

• Gradient/intersection problems

• Transformations of graphs

Geometry

• Circle theorems

• Complex angle reasoning

• Trigonometry in 2D (sine rule, cosine rule)

• Pythagoras’ theorem in problem contexts

• 3D shapes with surface area and volume

Statistics

• Histograms

• Cumulative frequency curves

• Box plots

• Comparing distributions

Probability

• Tree diagrams

• Probability from Venn diagrams (basic)

• ❓Question Types: 

📘 Foundation Tier – Typical Question Types

Paper 1F focuses on fundamental skills, heavily guided and usually avoids multi-stage algebra or geometry.

1. Basic Number Skills

• Straight arithmetic: adding, subtracting, multiplying, dividing integers and decimals

• Fractions: simple conversions, ordering, operations with straightforward denominators

• Percentages: finding %, percentage increase/decrease with easy numbers

• Estimation: rounding to nearest 10/100/whole number

• Basic ratio problems in simple contexts

2. Guided Algebra

• Simplifying expressions (e.g., collect like terms)

• Substitution into short formulas

• Solving simple 1-step or 2-step equations

• Expanding single brackets

• Recognising a linear sequence pattern

• Plotting a simple straight-line graph using a table

• Reading points from graphs

3. Basic Geometry / Measures

• Measuring or reading angles from diagrams

• Using angle rules in straightforward combinations

• Perimeter and area of simple shapes (rectangles, triangles)

• Units and conversions (mm–cm, cm–m, etc.)

• Basic symmetry questions

• Simple scale diagrams (no bearings complications)

• Transformations: reflection, rotation, translation

4. Straightforward Statistics

• Completing or reading tables

• Bar charts, pictograms, line graphs

• Finding mean, median, mode, range from small sets

• Interpreting a simple statistical diagram

5. Basic Probability

• Probability from a table or list

• One-event probability (e.g., rolling a dice)

• Very simple combined events (e.g., “one red, one blue”)

6. Typical Formats

• “Fill in the missing steps”

• Very guided multi-part questions (a → b → c)

• Little reading required; diagrams are easy

• Units and context are kept simple

🧩Higher Tier – Typical Question Types

Paper 1H contains mid-level difficulty and core Higher content, with a mix of procedural, applied and reasoning questions.




1. Higher Number Skills

• Fractional & negative indices

• Surds: simplifying, rationalising

• Standard form in real-life scientific contexts

• Upper/lower bounds problems with calculations

2. Higher Algebra

• Expanding and factorising quadratics

• Solving quadratics (factorisation or formula)

• Solving simultaneous equations (two linear, sometimes mixed)

• Algebraic fractions - simplifying, sometimes solving

• Rearranging complex formulas

• Quadratic & exponential sequences

3. Higher Graphs

• Sketching quadratic curves

• Identifying graph features (roots, turning point, symmetry)

• Reciprocal and cubic graph questions

• Using graphs to estimate solutions or gradients

• Distance–time and velocity–time graphs

4. Higher Geometry

• Circle theorem applications

• Similarity with area/volume scale factors

• More difficult Pythagoras and 2D trigonometry

• Sine rule / cosine rule questions

• Surface area/volume of combined 3D solids

5. Intermediate Statistics

• Histograms (read/interpret/find frequency density)

• Cumulative frequency curves

• Box plots

• Comparing distributions using median/IQR

6. Probability

• Multi-step probability using tree diagrams

• Venn diagram questions (without heavy conditional probability)

Formats

• “Show that …” questions

• Multi-part algebra/geometry reasoning

• Mostly unstructured, requiring method and clarity

More problem-solving: ratio, percentages, algebra, volume, graphs, scatter graphs, frequency trees

Number

• Ratio and proportion in real-life contexts

• More complex percentage problems (reverse percentage, repeated change)

• Bounds and estimation (simpler forms)

Algebra

• Harder linear equations

• Linear inequalities on a number line

• Simultaneous equations in simple contexts (often graphical)

• Simple quadratic recognition (not solving)

• Formula rearrangement with multiple steps (still basic)

Graphs

• Using straight lines to estimate values

• Graphical solutions to equations

• Real-life graphs with interpretation

Geometry

• Mensuration: area/volume of basic prisms

• Pythagoras’ theorem (by itself, no context tricks)

• Similar shapes (basic scale factors)

• Combined transformations

Statistics

• Frequency tables

• Pie charts

• Scatter graphs (including line of best fit)

Probability

• Two-way tables

• Frequency trees

• Combined events (but not conditional probability)

🧩Higher Tier

Hardest topics: functions, proofs, 3D trig, advanced probability, algebraic fractions, complex multi-step problems

Number

• Complex standard form problems

• Combined percentage and ratio questions

• Error intervals in multi-step context questions

Algebra

• Quadratic formula and completing the square

• Hard simultaneous equations

• Full algebraic manipulation and proof

• Functions:

  • composite functions

  • inverse functions

  • domain/range analysis

• More advanced algebraic fractions

• Problem-solving algebra (rate problems, proportionality, exponential relationships)

Graphs

• Graph transformations

• Trig graphs (sin/cos/tan basic forms)

• Non-linear solutions using graphs

• Gradient problems in context

Geometry & Trigonometry

• 3D trigonometry

• Further circle theorem proofs

• Complex loci questions

• Mensuration in mixed 3D shapes

Vectors

• Vector geometry

• Proofs using vectors

• Ratio division problems

Statistics & Probability

• Conditional probability

• Venn diagrams with complex intersections

• Using statistical diagrams in multi-step reasoning

• More challenging probability tree diagrams

• ❓Question Types: 

📘Foundation Tier - Typical Question Types

Paper 2F builds on Paper 1F but is more applied, with more reasoning and more compound steps.

1. Applied Number

• Reverse percentages

• Compound interest with simple figures

• Ratio in recipe, map and scale problems

• Bounds (simple upper/lower bounds)

• Speed–distance–time calculations

2. Extended Algebra

• Solving linear equations with letters on both sides

• Solving simple linear inequalities and representing them

• Forming equations from word problems

• Simultaneous equations (both linear, usually solved graphically)

• Generating the nth term of a linear sequence

3. Intermediate Geometry

• Area of compound shapes

• Volume of cuboids and simple prisms

• Constructions (bisectors, perpendiculars)

• Bearings questions

• More advanced transformations (combinations)

• Pythagoras’ theorem in simple contexts

4. More Developed Statistics

• Frequency tables

• Scatter diagrams with line of best fit

• Interpreting correlation

• Pie chart questions (both reading and creating)

5. Probability Beyond Basics

• Two-way tables

• Frequency trees

• Probability of combined independent events (but not conditional probability)

6. Typical Formats

• Multi-step real-life contexts (money, journeys, everyday tasks)

• Longer questions requiring step-by-step reasoning

• Some unstructured “show your method” problems

🧩Higher Tier - Typical Question Types

Paper 2H is designed to contain the hardest questions in the qualification.
It targets reasoning, problem-solving and the highest grades (7–9).

1. Advanced Algebra

• Quadratic formula in non-standard or disguised contexts

• Completing the square with reasoning

• Algebraic fractions with complex manipulation

• Hard simultaneous equations (non-linear: circle/line, quadratic/line)

• Algebraic proof problems (classic proof styles)

• Functions:

  • composite functions

  • inverse functions

  • domain and range

  • functional equations

2. Advanced Graphs

• Transformations of curves (f(x) → f(x−a), f(ax), etc.)

• Intersections between non-linear graphs

• Using derivatives-like reasoning (steepest gradient questions)

• Trigonometric graphs (sin, cos, tan basic forms)

3. Advanced Geometry / Trigonometry

• Circle theorem proofs

• 3D trigonometry (angles between lines/planes in simple contexts)

• Loci involving multiple conditions

• Complex geometry configurations requiring mixed skills

• Composite 3D shapes with tricky volume/surface reasoning

4. Vectors

• Vector geometry in 2D

• Proof using vectors (parallelism, ratios, midpoints)

• Vector equations and pathways

5. Higher Statistics & Probability

• Conditional probability in tree diagrams and Venn diagrams

• Probability of combined dependent events

• Expected values and reasoning (occasionally)

• Complex histogram interpretation

• Multi-step statistical reasoning combining graphs and tables

6. Real-Life Problem Solving

• Multi-stage modelling questions (speed/pressure/scale/decay)

• Problems that mix algebra, ratio, graphs and number

• “Show that the value is approximately…” requiring estimation and explanation

• Minimal scaffolding - student chooses strategy