WAEC Further Mathematics Syllabus 2027/2028 Questions PDF Download
By Rabiu Francis ✨ Last Updated: October 16, 2026Download the WAEC Further Mathematics Syllabus 2027/2028 PDF and see the complete topics in Pure Mathematics, Statistics, Probability, Vectors and Mechanics.
The WAEC Further Mathematics Syllabus 2027/2028 contains the topics, mathematical concepts and problem-solving skills you need to prepare for Further Mathematics in the West African Senior School Certificate Examination.
The subject is also presented in the syllabus as Further Mathematics/Mathematics (Elective). It is designed to develop mathematical skills beyond the level covered in General Mathematics and provide an intermediate foundation between elementary and higher Mathematics.
READ: Access 2027 WAEC Questions and Answers in all Subjects – Free Study Guide
ALSO READ: WAEC Specimens 2027
The syllabus aims to test your:
- Further conceptual and manipulative skills in Mathematics
- Understanding of mathematical concepts that bridge Elementary Mathematics and Higher Mathematics
- Knowledge of mathematical ideas useful to potential mathematicians, engineers, scientists and other professionals
- Ability to analyse data and draw valid conclusions
- Logical, abstract and precise reasoning skills
The syllabus is divided into three broad areas:
- Pure Mathematics
- Statistics and Probability
- Vectors and Mechanics
If Further Mathematics is one of your registered WAEC subjects, you should use the complete syllabus as your main study checklist and combine it with regular problem-solving and WAEC past-question practice.
READ ALSO: WAEC Syllabus 2027/2028 PDF Download for All Subjects
Download WAEC Further Mathematics Syllabus 2027/2028 PDF
You can download the complete WAEC Further Mathematics Syllabus 2027/2028 PDF and keep it on your phone, tablet or computer for easy reference.
The syllabus covers:
- Sets
- Surds
- Binary Operations
- Logical Reasoning
- Functions
- Linear Functions
- Quadratic Functions
- Cubic Functions
- Polynomial Functions
- Rational Functions
- Partial Fractions
- Indices
- Logarithms
- Permutations
- Combinations
- Binomial Theorem
- Sequences
- Series
- Arithmetic Progression
- Geometric Progression
- Recurrence Series
- Matrices
- Determinants
- Linear Transformations
- Trigonometric Ratios
- Compound Angles
- Multiple Angles
- Trigonometric Functions
- Trigonometric Equations
- Coordinate Geometry
- Straight Lines
- Circles
- Parabolas
- Differentiation
- Applications of Differentiation
- Integration
- Applications of Integration
- Statistics
- Measures of Location
- Measures of Dispersion
- Correlation
- Probability
- Probability Distributions
- Vectors
- Statics
- Dynamics
Use the syllabus as a checklist and mark each topic after you have studied it and solved enough questions to understand the methods involved.
WAEC Further Mathematics Examination Structure
The examination consists of two papers: Paper 1 and Paper 2, and both papers must be taken.
WAEC Further Mathematics Paper 1
Paper 1 consists of 40 multiple-choice objective questions covering the entire syllabus.
You are required to answer all the questions.
The questions are distributed as follows:
- Pure Mathematics — 30 questions
- Statistics and Probability — 4 questions
- Vectors and Mechanics — 6 questions
Paper 1 carries 40 marks.
This means Pure Mathematics forms the largest part of Paper 1, but you should not ignore Statistics, Probability, Vectors or Mechanics.
WAEC Further Mathematics Paper 2
Paper 2 is divided into:
- Section A
- Section B
The paper carries 100 marks.
Further Mathematics Paper 2 Section A
Section A contains eight compulsory questions.
The questions are distributed as follows:
- Pure Mathematics — 4 questions
- Statistics and Probability — 2 questions
- Vectors and Mechanics — 2 questions
Section A carries 48 marks.
You must attempt all eight questions.
Further Mathematics Paper 2 Section B
Section B contains seven longer and more difficult questions divided into three parts:
- Part I — Pure Mathematics — 3 questions
- Part II — Statistics and Probability — 2 questions
- Part III — Vectors and Mechanics — 2 questions
You are required to answer four questions, with at least one question selected from each of the three parts.
Section B carries 52 marks.
This makes it important to prepare all three broad areas of the syllabus because you cannot rely only on Pure Mathematics in Section B.
Country-Specific Topics in the Further Mathematics Syllabus
The syllabus uses special symbols to identify some country-specific topics:
*— Topics peculiar to Ghana only**— Topics peculiar to Nigeria only
You should therefore pay attention to the markings beside individual topics and prepare the content applicable to your examination.
Relationship With General Mathematics
The syllabus states that, in addition to the topics specifically listed under Further Mathematics, more challenging questions may also be set on topics in the General Mathematics/Mathematics (Core) syllabus.
This means your General Mathematics foundation should also be strong.
Topics such as algebra, graphs, geometry and basic trigonometry become even more important when you move into Further Mathematics.
Complete WAEC Further Mathematics Syllabus 2027/2028
The syllabus is divided into:
- Pure Mathematics
- Statistics and Probability
- Vectors and Mechanics
Pure Mathematics
Pure Mathematics forms the largest section of the syllabus.
The topics include:
- Sets
- Surds
- Binary Operations
- Logical Reasoning
- Functions
- Polynomial Functions
- Rational Functions
- Indices and Logarithmic Functions
- Permutations and Combinations
- Binomial Theorem
- Sequences and Series
- Matrices and Linear Transformation
- Trigonometry
- Coordinate Geometry
- Differentiation
- Integration
Sets
The Sets section covers:
- Definition of a set by a property
- Set notation
- Universal set
- Complement of a set
- Disjoint sets
- Venn diagrams
- Union and intersection
- Subsets
- De Morgan’s Laws
- Commutative Laws
- Associative Laws
- Distributive Properties
You should be able to solve both symbolic and word problems involving sets.
Set Notation
Learn the standard notation used for:
- Universal Set
- Complement
- Union
- Intersection
- Subset
- Empty Set
You should be able to interpret set expressions correctly.
Venn Diagrams
The syllabus includes the use of Venn diagrams to solve problems.
Give attention to:
- Two-Set Problems
- Three-Set Problems
- Complements
- Intersections
- Unions
Practise translating word problems into Venn diagrams.
De Morgan’s Laws
De Morgan’s Laws are specifically included in the Sets section.
You should understand how complements interact with:
- Union
- Intersection
Practise both symbolic manipulation and Venn-diagram interpretation.
Surds
The Surds section covers operations involving irrational expressions.
Study:
- Addition
- Subtraction
- Multiplication
- Division
- Simplification
- Rationalisation of Denominators
Rationalising Surds
You should be able to rationalise denominators containing simple surds and combinations involving surds.
Practise carefully because errors with signs and conjugates can affect the entire solution.
Binary Operations
Study the properties of binary operations, including:
- Closure
- Commutativity
- Associativity
- Distributivity
- Identity Elements
- Inverses
You should be able to determine whether a given operation satisfies these properties.
Closure
Understand whether applying a defined operation to elements of a set produces another element belonging to the same set.
Identity Elements
You should be able to determine an identity element under a given binary operation.
Inverses
Study how to determine the inverse of an element where an inverse exists.
Logical Reasoning
Logical Reasoning covers:
- True and False Statements
- Rules of Logic
- Arguments
- Implications
- Deductions
- Compound Statements
- Truth Tables
- Negation
Truth Tables
You should be able to construct and interpret truth tables for compound statements.
Practise:
- Negation
- Conjunction
- Disjunction
- Implication
and other logical connectives contained in your course.
Validity of Arguments
The syllabus expects you to use logical reasoning to determine whether conclusions follow from given statements.
Do not memorise truth tables without understanding what the logical statements mean.
Functions
The syllabus covers:
- Domain
- Co-domain
- Range
- One-to-One Functions
- Onto Functions
- Identity Functions
- Constant Functions
- Inverse Functions
- Composite Functions
Domain Co-domain and Range
Make sure you can distinguish between:
- Domain
- Co-domain
- Range
These concepts become important when working with inverse and composite functions.
One-to-One Functions
Understand the condition required for a function to have an inverse that is also a function.
Inverse Functions
You should be able to determine the inverse of simple algebraic functions.
Practise checking your answers by composition where appropriate.
Composite Functions
Understand notation such as:
fog(x) = f(g(x))
Practise evaluating composite functions and distinguishing fog from gof.
Polynomial Functions
Polynomial Functions form a broad part of the syllabus.
They include:
- Linear Functions
- Quadratic Functions
- Cubic Functions
Linear Functions Equations and Inequalities
Study:
- Linear Graphs
- Gradient
- Intercepts
- Equations of Straight Lines
- Parallel Lines
- Perpendicular Lines
- Linear Inequalities
- Graphical Representation of Inequalities
- Linear Programming
Linear Graphs
You should be able to recognise and sketch linear functions.
Study different forms of straight-line equations and understand how gradient and intercepts affect the graph.
Parallel and Perpendicular Lines
Understand the gradient conditions for:
- Parallel Lines
- Perpendicular Lines
These ideas also appear again in Coordinate Geometry.
Linear Inequalities
Practise solving inequalities and representing them graphically.
The syllabus also includes applications to Linear Programming.
Linear Programming
You should be able to:
- Translate conditions into inequalities
- Draw boundary lines
- Identify the feasible region
- Apply the objective function
where required.
Quadratic Functions Equations and Inequalities
The syllabus includes:
- Graphs of Quadratic Functions
- Vertex
- Axis of Symmetry
- Maximum and Minimum
- Increasing and Decreasing Portions
- Quadratic Equations
- Simultaneous Linear and Quadratic Equations
- Completing the Square
- Nature of Roots
- Sum and Product of Roots
- Quadratic Inequalities
Graphs of Quadratic Functions
You should be able to identify:
- Vertex
- Axis of Symmetry
- Maximum or Minimum Point
- Regions where the function is positive or negative
Completing the Square
Practise expressing a quadratic expression in completed-square form.
This is useful for:
- Solving Equations
- Determining Maximum or Minimum Values
- Sketching Graphs
Nature of Roots
Study the discriminant and understand how it determines whether the roots of a quadratic equation are:
- Equal
- Real and Unequal
- Non-Real
Sum and Product of Roots
You should be able to use the relationship between the roots and coefficients of a quadratic equation.
Practise forming new quadratic equations from transformed roots.
Cubic Functions and Equations
The syllabus includes:
- Recognition of Cubic Functions
- Graphs of Cubic Functions
- Factorisation
- Solving Cubic Equations
- Sum and Difference of Cubes
- Polynomial Operations
- Remainder Theorem
- Factor Theorem
Factor Theorem
Understand how a zero of a polynomial relates to its factors.
Remainder Theorem
Practise determining the remainder when a polynomial is divided by a linear factor.
Rational Functions
Study rational functions in which both numerator and denominator are polynomials.
The syllabus includes:
- Basic Operations
- Zeros
- Domain
- Range
- Resolution into Partial Fractions
Partial Fractions
You should be able to resolve suitable rational expressions into partial fractions.
This skill is also useful later in more advanced Mathematics.
Practise different forms of denominators covered in your lessons.
Indices
Study:
- Laws of Indices
- Products
- Quotients
- Powers
- Roots
- Equations Involving Indices
Logarithms
The syllabus covers:
- Laws of Logarithms
- Products
- Quotients
- Powers
- Roots
- Change of Base
- Logarithmic Equations
- Reduction of Relations to Linear Form
- Logarithmic Graphs where applicable
Laws of Logarithms
Know how to apply logarithmic laws to simplify expressions and solve equations.
Change of Base
Practise converting logarithms from one base to another.
Linearisation Using Logarithms
The syllabus includes converting some nonlinear relationships into linear form through logarithms.
You should understand how this allows constants to be estimated from graphs.
Permutations and Combinations
The syllabus covers:
- Simple Arrangements
- Simple Selections
- Permutations
- Combinations
- Selection With or Without Replacement
Permutations
Use permutations where order matters.
Be familiar with the standard permutation notation and formula.
Combinations
Use combinations where order does not matter.
Practise identifying from the wording of a problem whether permutation or combination is required.
Binomial Theorem
Study the expansion of expressions of the form:
(a + b)^n
The syllabus restricts proof of the theorem and focuses on using it for expansion.
It also includes simple approximation using binomial expansion.
Sequences and Series
The syllabus covers:
- Finite Sequences
- Infinite Sequences
- Arithmetic Progression
- Geometric Progression
- Finite Series
- Infinite Series
- Sum of an Arithmetic Progression
- Sum of a Geometric Progression
- Sum to Infinity
- Recurrence Series where applicable
Arithmetic Progression
You should understand:
- First Term
- Common Difference
- General Term
- Sum of Terms
Practise both direct and word problems.
Geometric Progression
Study:
- First Term
- Common Ratio
- General Term
- Sum of Terms
- Sum to Infinity where applicable
Recurrence Series
For the relevant syllabus provision, you should be able to generate the terms of a recurrence series and determine an explicit form in suitable cases.
Matrices and Linear Transformation
This section covers:
- Matrices
- Matrix Order
- Types of Matrices
- Equality of Matrices
- Addition
- Subtraction
- Scalar Multiplication
- Matrix Multiplication
- Determinants
- Inverse Matrices
- Linear Transformations
Matrix Operations
Practise:
- Addition
- Subtraction
- Multiplication by a Scalar
- Multiplication of Matrices
The syllabus includes matrices up to the orders specified in the detailed notes.
Determinants
Study determinants and their applications.
The syllabus includes determinants of 2 × 2 matrices and country-specific provisions involving 3 × 3 matrices.
Inverse of a Matrix
You should be able to determine the inverse of a 2 × 2 matrix where the inverse exists.
Simultaneous Equations Using Matrices
Determinants can also be applied to solving simultaneous linear equations.
Practise the methods taught in your course.
Linear Transformations
Study:
- Images of Points
- Matrices of Transformations
- Inverse Transformations
- Composite Transformations
- Identity Transformation
The syllabus includes transformations such as:
- Reflection in the x-axis
- Reflection in the y-axis
- Reflection in the line y = x
- Rotation about the origin
- Reflection in a line through the origin
Trigonometry
Trigonometry forms a substantial part of the syllabus.
It includes:
- Trigonometric Ratios
- General Angles
- Special Angles
- Trigonometric Identities
- Radians
- Heights and Distances
- Bearings
- Sine Rule
- Cosine Rule
- Compound Angles
- Multiple Angles
- Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Equations
Trigonometric Ratios
Study:
- Sine
- Cosine
- Tangent
- Reciprocal Ratios
You should know the exact values of common special angles required by the syllabus.
Degrees and Radians
Be able to convert:
- Degrees to Radians
- Radians to Degrees
Heights and Distances
Practise real-life applications involving:
- Angles of Elevation
- Angles of Depression
- Heights
- Distances
Bearings
The syllabus includes bearing problems.
Draw diagrams carefully before attempting calculations.
Sine and Cosine Rules
Know when to apply:
- Sine Rule
- Cosine Rule
during the solution of triangles.
Compound Angles
Study expressions involving sums and differences of angles.
Practise using compound-angle identities to obtain exact trigonometric values.
Multiple Angles
The syllabus includes multiple-angle applications up to the specified limits.
Trigonometric Functions and Graphs
Study graphs involving:
- Sine
- Cosine
- Tangent
and related combinations.
You should be able to identify:
- Maximum Points
- Minimum Points
- Increasing Portions
- Decreasing Portions
where required.
Trigonometric Equations
Practise solving trigonometric equations over stated intervals.
Read the required range carefully before giving your answers.
Coordinate Geometry
Coordinate Geometry covers:
- Straight Lines
- Conic Sections
Straight Lines
Study:
- Midpoint of a Line Segment
- Division of a Line in a Given Ratio
- Distance Between Two Points
- Gradient
- Equation of a Line
- Intercept Form
- Gradient Form
- Parallel Lines
- Perpendicular Lines
- Angle Between Intersecting Lines
Midpoint
You should be able to calculate the coordinates of the midpoint of a line segment.
Section Formula
Study the coordinates of a point dividing a line segment in a given ratio.
Distance Between Points
Practise the coordinate formula for finding the distance between two points.
Gradient
Understand gradient geometrically and algebraically.
Equation of a Straight Line
Be familiar with the different forms of a straight-line equation included in the syllabus.
Angle Between Two Lines
You should be able to calculate the acute angle between two intersecting lines using their gradients.
Conic Sections
The syllabus includes:
- Loci
- Circles
- Parabolas
Equation of a Circle
Study equations of circles in:
- Centre-Radius Form
- General Form
You should be able to determine:
- Centre
- Radius
from the equation.
Tangents and Normals to Circles
Study the relationships involving:
- Radius
- Tangent
- Normal
at a point on a circle.
Parabolas
The syllabus covers the standard form of the parabola in rectangular Cartesian coordinates and includes:
- Parametric Representation
- Tangents
- Normals
- Axis of Symmetry where applicable
Differentiation
Differentiation introduces Calculus into the syllabus.
It includes:
- Limits
- Derivative From First Principles
- Differentiation of Polynomials
- Differentiation of Trigonometric Functions
- Product Rule
- Quotient Rule
- Implicit Differentiation
- Transcendental Functions where applicable
- Second Derivatives
- Rates of Change
- Small Changes
- Maxima and Minima
- Curve Sketching
- Linear Kinematics
Limits
Understand the intuitive idea of a limit and how it relates to the gradient of a curve.
Differentiation From First Principles
You should understand the meaning of a derivative and be able to differentiate simple functions from first principles as required by the syllabus.
Differentiation of Polynomials
Practise differentiating polynomial expressions accurately.
Differentiation of Trigonometric Functions
The syllabus includes differentiation involving simple trigonometric functions.
Product Rule
Use the Product Rule when differentiating a product of functions.
Quotient Rule
Use the Quotient Rule when differentiating a quotient of functions.
Implicit Differentiation
Practise differentiating equations where one variable is not written explicitly as a function of another.
Second Derivatives
Understand how to obtain and interpret a second derivative.
Maxima and Minima
Study:
- Turning Points
- Maximum Points
- Minimum Points
You should be able to apply differentiation to determine them.
Equation of a Tangent
You should be able to determine the equation of a tangent to a curve at a given point.
Rates of Change
Differentiation is also applied to rate-of-change problems.
Read the quantities and units carefully.
Small Changes
Study the application of differentiation to approximate small changes where required.
Integration
Integration covers:
- Indefinite Integrals
- Definite Integrals
- Integration of Polynomials
- Simple Substitution
- Trigonometric Integrals
- Applications of Definite Integration
Indefinite Integration
Practise reversing differentiation to obtain antiderivatives.
Remember the constant of integration where required.
Definite Integration
Understand how limits are applied to an integral.
Integration by Substitution
The syllabus includes simple problems involving substitution.
Integration of Trigonometric Functions
Practise the simple trigonometric forms specified in your course.
Applications of Integration
Applications include:
- Plane Areas
- Rates of Change
- Linear Kinematics
- Area Under a Curve
- Volume of Solids of Revolution
- Trapezium Rule Approximation
Area Under a Curve
You should understand how definite integration can represent an area.
Volume of a Solid of Revolution
Study the method covered in the syllabus.
Trapezium Rule
The syllabus includes approximation using the Trapezium Rule.
Practise setting out the numerical work carefully.
Statistics and Probability
The second major section contains:
- Statistics
- Probability
Statistics
Statistics covers:
- Tabulation of Data
- Graphical Representation
- Measures of Location
- Measures of Dispersion
- Correlation
Frequency Tables
You should be able to construct and interpret:
- Frequency Tables
- Cumulative Frequency Tables
Histograms
The syllabus includes histograms, including situations involving unequal class intervals.
Practise selecting the appropriate quantities for the axes.
Cumulative Frequency Curves
Study the construction and interpretation of the Ogive.
Measures of Location
The syllabus includes:
- Mean
- Median
- Mode
- Quartiles
- Percentiles
Mean
Practise calculating mean for:
- Ungrouped Data
- Grouped Data
The syllabus includes the use of an assumed mean for grouped data.
Median
Study how to determine the median from both raw and grouped data.
Mode
Understand how to determine:
- Mode
- Modal Group
including interpretation from a histogram.
Quartiles and Percentiles
Learn how to obtain quartiles and percentiles from suitable data representations.
Measures of Dispersion
Study:
- Range
- Interquartile Range
- Semi-Interquartile Range
- Mean Deviation
- Variance
- Standard Deviation
Range
Understand the simplest measure of spread.
Interquartile Range
Be able to obtain quartile-related measures from an Ogive where required.
Variance and Standard Deviation
Practise calculations for:
- Grouped Data
- Ungrouped Data
Correlation
The syllabus covers:
- Scatter Diagrams
- Positive Correlation
- Negative Correlation
- Zero Correlation
- Line of Best Fit
- Spearman’s Rank Correlation Coefficient
Scatter Diagrams
You should be able to interpret the relationship between two variables.
Line of Best Fit
Understand how a line of best fit can be used to estimate one variable from another.
Spearman’s Rank Correlation
Practise calculating Spearman’s Rank Coefficient for data without ties as specified by the syllabus.
Probability
The Probability section covers:
- Meaning of Probability
- Relative Frequency
- Sample Spaces
- Addition of Probabilities
- Multiplication of Probabilities
- Probability Distributions
Sample Spaces
Practise simple experiments involving situations such as:
- Tossing Dice
- Drawing Objects From a Box
- Selection With Replacement
- Selection Without Replacement
Types of Events
Study:
- Equally Likely Events
- Mutually Exclusive Events
- Independent Events
- Conditional Events
Addition of Probabilities
Understand when the Addition Rule should be used.
Multiplication of Probabilities
Understand when the Multiplication Rule should be used and how independence affects the calculation.
Probability Distributions
The syllabus includes:
- Binomial Distribution
- Poisson Distribution for the applicable country provision
Binomial Distribution
Study situations involving repeated trials with:
- Success
- Failure
- Constant Probability
- Fixed Number of Trials
Practise simple binomial probability problems.
Poisson Distribution
This is marked as a Nigeria-specific topic in the syllabus.
Study the simple applications required by the syllabus.
Vectors and Mechanics
The third broad area contains:
- Vectors
- Statics
- Dynamics
Vectors
The syllabus covers:
- Scalar Quantities
- Vector Quantities
- Vector Representation
- Vector Algebra
- Vector Properties
- Unit Vectors
- Position Vectors
- Resolution of Vectors
- Composition of Vectors
- Scalar Product
- Vector Product where applicable
Scalar and Vector Quantities
Understand the difference between quantities that have:
- Magnitude only
- Magnitude and direction
Be able to classify examples correctly.
Vector Representation
Study representation in component form using unit vectors.
Vector Algebra
Practise:
- Addition of Vectors
- Subtraction of Vectors
- Multiplication by Scalars
The syllabus also applies:
- Triangle Law
- Parallelogram Law
- Polygon Law
Unit Vectors
Understand the standard unit vectors along the coordinate axes.
You should also be able to determine a unit vector in the direction of a given vector.
Position Vectors
Study:
- Position Vector of a Point
- Midpoint Using Position Vectors
- Division of a Line Segment in a Given Ratio where applicable
Resolution of Vectors
Practise resolving vectors into perpendicular components.
This becomes particularly important in Mechanics.
Composition of Vectors
Use vector laws to find resultants.
The syllabus also applies vector composition to forces.
Scalar Product
Study the dot product and its applications.
You should be able to use it to determine the angle between two vectors.
Vector Product
The Vector or Cross Product is marked as a Nigeria-specific topic.
Prepare the applications required by the syllabus if you are taking the Nigerian examination.
Statics
Statics deals with forces acting on bodies in equilibrium.
The syllabus covers:
- Definition of Force
- Representation of Forces
- Composition of Forces
- Resolution of Forces
- Equilibrium
- Resultants
- Moments
- Friction
Forces
Understand force as a vector quantity.
You should be able to represent forces with:
- Magnitude
- Direction
Composition and Resolution of Forces
Practise resolving and combining coplanar forces.
Draw clear diagrams before calculating.
Equilibrium of Bodies
Understand the conditions required for a body to remain in equilibrium.
Resultant Forces
You should be able to determine the resultant of forces acting at a point.
Lami’s Theorem
The detailed syllabus includes the application of Lami’s Theorem to suitable problems.
Understand the conditions under which it can be used.
Moments of Forces
Study the Principle of Moments and apply it to equilibrium problems.
Friction
The syllabus covers:
- Smooth Planes
- Rough Planes
- Coefficient of Friction
Understand the distinction between smooth and rough surfaces.
Dynamics
Dynamics deals with motion and the forces that produce or affect motion.
The syllabus includes:
- Displacement
- Velocity
- Speed
- Acceleration
- Composition of Velocities
- Composition of Accelerations
- Rectilinear Motion
- Newton’s Laws of Motion
- Motion Along Inclined Planes
- Motion Under Gravity
- Equations of Motion
- Momentum
- Impulse
- Conservation of Linear Momentum
- Projectiles where applicable
Displacement Speed Velocity and Acceleration
Be able to distinguish clearly among these quantities.
In particular, remember the difference between:
- Speed and Velocity
- Distance and Displacement
Equations of Motion
The syllabus includes the standard equations for uniformly accelerated motion.
Practise selecting the correct equation from the information given in a problem.
Newton’s Laws of Motion
Study all the laws covered in your course and be able to apply them to numerical problems.
Motion Along an Inclined Plane
Practise resolving forces into components:
- Parallel to the Plane
- Perpendicular to the Plane
This is especially important where friction is involved.
Motion Under Gravity
The syllabus includes motion under gravity while ignoring air resistance.
Practise both upward and downward motion problems.
Momentum
Understand momentum and apply the principle of conservation of linear momentum to suitable problems.
Impulse
Know the difference between:
- Impulse
- Momentum
and understand their relationship.
Projectiles
Projectile motion is marked as a Nigeria-specific topic.
The syllabus describes objects projected at an angle to the horizontal.
Prepare this topic if it applies to your examination.
Units You Should Know
The syllabus provides units that candidates should be familiar with.
These include units of:
- Length
- Area
- Capacity
- Mass
- Currency
Length Units
You should know relationships involving:
- Millimetres
- Centimetres
- Metres
- Kilometres
Area Units
The syllabus includes the relationship between:
- Square Metres
- Hectares
Capacity Units
Be familiar with:
- Cubic Centimetres
- Litres
Mass Units
Know conversions involving:
- Milligrammes
- Grammes
- Kilogrammes
- Tonnes
Currency Units
The syllabus includes currencies used across different WAEC member countries and other common currencies.
You should be able to work with any conversion explicitly provided in a question.
Use of Mathematical and Statistical Tables
The syllabus states that Mathematical and Statistical Tables published or approved by WAEC may be used in the examination room.
Where a question does not specify the required degree of accuracy, the expected degree of accuracy is that obtainable from the mathematical tables.
Use of Calculators
The syllabus allows:
- Non-programmable calculators
- Silent calculators
- Cordless calculators
However, the calculator must not:
- Produce a paper printout
- Receive information
- Send information
Phones are not allowed as calculators.
The syllabus also notes that individual questions may prohibit the use of calculators or tables.
Other Materials Needed for Further Mathematics
Candidates should bring the mathematical instruments required for the examination, including:
- Ruler
- Pair of Compasses
- Protractor
- Set Squares
The syllabus states that candidates should not depend on borrowing these materials from other candidates during the examination.
Graph paper will be provided where required.
Important Further Mathematics Calculations to Practise
Further Mathematics is heavily problem-based.
Give particular attention to calculations involving:
- Sets
- Surds
- Binary Operations
- Functions
- Quadratic Equations
- Polynomial Equations
- Partial Fractions
- Indices
- Logarithms
- Permutations
- Combinations
- Sequences and Series
- Matrices
- Trigonometry
- Coordinate Geometry
- Differentiation
- Integration
- Statistics
- Probability
- Vectors
- Forces
- Motion
Important Graphs to Practise
You should be comfortable drawing and interpreting graphs involving:
- Linear Functions
- Quadratic Functions
- Cubic Functions
- Linear Inequalities
- Logarithmic Relationships where applicable
- Sine Functions
- Cosine Functions
- Tangent Functions
- Statistical Data
- Histograms
- Ogives
- Scatter Diagrams
- Parabolas
Important Formula Areas to Master
Rather than memorising one long formula sheet without understanding it, organise your formulae by topic.
Useful groups include:
- Quadratic Equations
- Permutations and Combinations
- Arithmetic Progression
- Geometric Progression
- Trigonometry
- Coordinate Geometry
- Differentiation
- Integration
- Statistics
- Probability
- Vectors
- Mechanics
For each formula, understand:
What it calculates → When it applies → Meaning of each symbol
How to Use the WAEC Further Mathematics Syllabus to Prepare
Start With the Complete Syllabus
Use the syllabus PDF as your main checklist.
READ ALSO: WAEC Further Mathematics Areas of Concentration 2027/2028
Strengthen Your General Mathematics Foundation
The Further Mathematics syllabus can include more challenging questions based on the General Mathematics syllabus.
Make sure you are already comfortable with:
- Algebra
- Basic Geometry
- Graphs
- Trigonometry
- Equations
- Basic Statistics
before moving deeply into the harder Further Mathematics topics.
Solve Questions Instead of Reading Solutions
Mathematics improves through problem-solving.
After studying a worked example:
- Close the solution.
- Try a similar problem yourself.
- Check your answer.
- Identify your mistake.
- Solve another question.
Show Your Working
For Paper 2, do not jump from a question directly to a final answer.
Write the important steps clearly.
This also makes it easier to identify errors before finishing the question.
Practise Without a Calculator Sometimes
Some questions may prohibit calculators.
Build enough number sense and algebraic skill to work without depending completely on a calculator.
Learn How to Use Your Calculator Properly
For questions where calculators are permitted, know how to perform:
- Powers
- Roots
- Trigonometric Calculations
- Logarithms
efficiently on your permitted calculator.
Practise Graphs Manually
Do not depend on a graphing device.
Practise:
- Constructing Tables
- Choosing Scales
- Plotting Points
- Drawing Curves
- Reading Values From Graphs
Practise Mathematics Under Time
Further Mathematics questions can take time.
As your examination approaches, solve complete papers under timed conditions.
Best Order to Study WAEC Further Mathematics
A practical order is to move from Algebra into Calculus, then Statistics and Mechanics.
Stage 1 Mathematical Foundations
Start with:
- Sets
- Surds
- Binary Operations
- Logical Reasoning
- Functions
Stage 2 Algebra
Continue with:
- Linear Functions
- Quadratic Functions
- Cubic Functions
- Rational Functions
- Partial Fractions
- Indices
- Logarithms
- Permutations and Combinations
- Binomial Theorem
- Sequences and Series
Stage 3 Matrices and Trigonometry
Study:
- Matrices
- Determinants
- Linear Transformations
- Trigonometric Ratios
- Compound Angles
- Trigonometric Functions
- Trigonometric Equations
Stage 4 Coordinate Geometry and Calculus
Study:
- Straight Lines
- Circles
- Parabolas
- Limits
- Differentiation
- Applications of Differentiation
- Integration
- Applications of Integration
Stage 5 Statistics and Probability
Study:
- Frequency Tables
- Histograms
- Ogives
- Measures of Location
- Measures of Dispersion
- Correlation
- Probability
- Probability Distributions
Stage 6 Vectors and Mechanics
Finish the main cycle with:
- Vectors
- Scalar Product
- Vector Product where applicable
- Forces
- Equilibrium
- Moments
- Friction
- Motion
- Newton’s Laws
- Momentum
- Impulse
- Projectiles where applicable
Continue revising earlier topics while moving through each stage.
What Should You Focus on Most for WAEC Further Mathematics
You should cover the complete syllabus, but make sure you are especially confident in:
- Functions
- Quadratic Equations
- Polynomial Functions
- Partial Fractions
- Indices and Logarithms
- Permutations and Combinations
- Sequences and Series
- Matrices
- Trigonometry
- Coordinate Geometry
- Differentiation
- Integration
- Statistical Graphs
- Mean, Median and Mode
- Variance and Standard Deviation
- Correlation
- Probability
- Probability Distributions
- Vectors
- Forces
- Equilibrium
- Moments
- Friction
- Motion
- Newton’s Laws
- Momentum
For a more focused revision guide, use the WAEC Further Mathematics Areas of Concentration 2027/2028.
You can also use the WAEC Areas of Concentration 2027/2028 for All Subjects to access the other subject guides.
Frequently Asked Questions
What Is the WAEC Further Mathematics Syllabus 2027/2028?
The WAEC Further Mathematics syllabus contains the Pure Mathematics, Statistics, Probability, Vectors and Mechanics topics you need to prepare for Further Mathematics/Mathematics (Elective) in WASSCE.
Is Further Mathematics the Same as Mathematics Elective?
The syllabus is titled Further Mathematics/Mathematics (Elective).
The wording accommodates the subject naming used within the WAEC examination system.
How Many Papers Are in WAEC Further Mathematics?
There are two papers:
- Paper 1
- Paper 2
Both must be taken.
How Many Questions Are in Further Mathematics Paper 1?
Paper 1 contains 40 multiple-choice questions.
They are distributed as:
- 30 Pure Mathematics questions
- 4 Statistics and Probability questions
- 6 Vectors and Mechanics questions
What Is in WAEC Further Mathematics Paper 2?
Paper 2 has two sections.
Section A contains eight compulsory questions.
Section B contains seven longer questions divided among Pure Mathematics, Statistics and Probability, and Vectors and Mechanics.
How Many Questions Do I Answer in Paper 2 Section B?
You answer four questions, with at least one selected from each of the three parts.
Is Pure Mathematics Important in Further Mathematics?
Yes.
Pure Mathematics forms the largest part of the syllabus and receives the highest number of questions in Paper 1.
Does Further Mathematics Include Calculus?
Yes.
The syllabus includes:
- Differentiation
- Integration
- Applications of Differentiation
- Applications of Integration
Does WAEC Further Mathematics Include Matrices?
Yes.
The syllabus includes matrices, determinants, inverse matrices and linear transformations.
Is Trigonometry Included?
Yes.
You should study trigonometric ratios, compound angles, multiple angles, functions, graphs and equations.
Is Coordinate Geometry Included?
Yes.
Coordinate Geometry includes straight lines, circles and parabolas.
Does the Syllabus Include Statistics?
Yes.
Statistics includes frequency tables, histograms, Ogives, measures of location, measures of dispersion and correlation.
Is Probability Included?
Yes.
The syllabus covers sample spaces, relative frequency, addition and multiplication rules and probability distributions.
Is Binomial Distribution Included?
Yes.
Binomial Distribution is part of the Probability section.
Is Poisson Distribution Included?
Yes, but the syllabus marks Poisson Distribution as a Nigeria-specific topic.
Are Vectors Included?
Yes.
The syllabus covers vector algebra, unit vectors, position vectors, resolution, composition and scalar products.
Is Vector Product Included?
The Vector or Cross Product is marked as a Nigeria-specific topic in the syllabus.
Does Further Mathematics Include Mechanics?
Yes.
Mechanics is divided into:
- Statics
- Dynamics
What Should I Study in Statics?
Study:
- Forces
- Resolution
- Composition
- Equilibrium
- Resultants
- Moments
- Friction
What Should I Study in Dynamics?
Study:
- Motion
- Displacement
- Velocity
- Acceleration
- Equations of Motion
- Newton’s Laws
- Momentum
- Impulse
and the applicable country-specific topics.
Is Projectile Motion Included?
Projectile Motion is marked as a Nigeria-specific topic.
Can WAEC Set General Mathematics Questions in Further Mathematics?
The syllabus states that more challenging questions may be set on topics contained in the General Mathematics/Mathematics (Core) syllabus.
Can I Use a Calculator in WAEC Further Mathematics?
The syllabus allows non-programmable, silent and cordless calculators, subject to the stated restrictions.
However, individual questions may prohibit calculator use.
Can I Use My Phone Calculator?
No.
The syllabus specifically states that phones with or without calculators are not allowed.
What Mathematical Instruments Should I Bring?
The syllabus states that candidates should bring instruments such as:
- Ruler
- Pair of Compasses
- Protractor
- Set Squares
as required for the examination.
Where Can I Download the Complete Further Mathematics Syllabus?
Use the download button near the beginning of this article to save the complete syllabus PDF to your phone, tablet or computer.
Where Can I Find the WAEC Further Mathematics Areas of Concentration?
Use the WAEC Further Mathematics Areas of Concentration 2027/2028 guide to organise your revision around the major topics and calculations.
Conclusion
The WAEC Further Mathematics Syllabus 2027/2028 gives you a complete guide to the mathematical topics and problem-solving skills required for Further Mathematics/Mathematics (Elective).
Your preparation should cover Pure Mathematics topics such as Functions, Polynomials, Logarithms, Sequences, Matrices, Trigonometry, Coordinate Geometry, Differentiation and Integration.
You should also prepare Statistics and Probability topics including data representation, measures of location, measures of dispersion, correlation and probability distributions.
For Vectors and Mechanics, give attention to vector operations, forces, equilibrium, moments, friction, equations of motion, Newton’s Laws, momentum and impulse.
Further Mathematics is best mastered through consistent problem-solving rather than reading notes alone.
Use the syllabus as your main checklist, solve questions after every topic and practise full WAEC papers under examination conditions as your preparation improves.
READ ALSO: WAEC Further Mathematics Areas of Concentration 2027/2028
READ ALSO: WAEC Syllabus 2027/2028 PDF Download for All Subjects
READ ALSO: WAEC Areas of Concentration 2027/2028 for All Subjects
READ ALSO: WAEC Timetable 2027
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