--- title: "WAEC General Mathematics Syllabus 2027/2028 PDF Download" url: https://examloaded.com/waec-mathematics-syllabus-questions/ date: 2026-07-17 modified: 2026-10-16 lang: en author: "Rabiu Francis" description: "Download the WAEC General Mathematics Syllabus 2027/2028 PDF and see the complete topics, exam structure, algebra, geometry, trigonometry, calculus, statistics and probability. The WAEC General Mathematics Syllabus 2027/2028 contains the..." categories: - "2027 Official WAEC Exam Insights: Practice Questions, and Syllabus" tags: - "WAEC Syllabus 2027" image: https://examloaded.com/wp-content/uploads/2026/07/WAEC-General-Mathematics-Syllabus-2027-2028-PDF-Download.webp word_count: 5693 --- # WAEC General Mathematics Syllabus 2027/2028 PDF Download Download the WAEC General Mathematics Syllabus 2027/2028 PDF and see the complete topics, exam structure, algebra, geometry, trigonometry, calculus, statistics and probability. The **WAEC General Mathematics Syllabus 2027/2028** contains the mathematical concepts, calculations and problem-solving skills you need to prepare for General Mathematics in the West African Senior School Certificate Examination. [![WAEC General Mathematics Syllabus 2027/2028 PDF Download](https://examloaded.com/wp-content/uploads/2026/07/WAEC-General-Mathematics-Syllabus-2027-2028-PDF-Download-300x203.webp)](https://examloaded.com/waec-mathematics-syllabus-questions/waec-general-mathematics-syllabus-2027-2028-pdf-download/)WAEC General Mathematics Syllabus 2027/2028 PDF Download The subject is also presented in the syllabus as **General Mathematics/Mathematics (Core)**. It is designed to test your mathematical competence, computational skills, understanding of mathematical concepts, ability to translate practical problems into mathematical language and ability to solve them using appropriate methods. It also develops logical, abstract and precise thinking. **READ:** [Access 2027 WAEC Questions and Answers in all Subjects – Free Study Guide](/waec-questions-and-answers/) **ALSO READ:** [WAEC Specimens 2027](/waec-specimens-practicals/) The major areas covered are: - Number and Numeration - Algebraic Processes - Mensuration - Plane Geometry - Coordinate Geometry of Straight Lines - Trigonometry - Introductory Calculus - Statistics and Probability - Vectors and Transformation You should prepare General Mathematics by solving questions regularly. Reading formulas and worked examples is useful, but you need repeated practice before you can confidently identify the correct method during the examination. **READ ALSO:** [WAEC Syllabus 2027/2028 PDF Download for All Subjects](/waec-syllabus-for-all-subjects-pdf-download/) ## Download WAEC General Mathematics Syllabus 2027/2028 PDF You can download the complete **WAEC General Mathematics Syllabus 2027/2028 PDF** and keep it on your phone, tablet or computer for revision. The syllabus covers: - Number Bases - Modular Arithmetic - Fractions - Decimals - Approximations - Significant Figures - Indices - Standard Form - Logarithms - Sequences and Series - Arithmetic Progression - Geometric Progression - Sets - Venn Diagrams - Logical Reasoning - Rational Numbers - Surds - Matrices - Determinants - Ratio - Proportion - Rates - Percentages - Simple Interest - Compound Interest - Profit and Loss - Hire Purchase - Financial Arithmetic - Depreciation - Amortization - Annuities - Shares and Stocks - Bonds and Debentures - Variation - Algebraic Expressions - Factorization - Binary Operations - Linear Equations - Simultaneous Equations - Change of Subject of Formula - Quadratic Equations - Linear and Quadratic Graphs - Linear Inequalities - Algebraic Fractions - Functions and Relations - Pythagoras’ Theorem - Sine and Cosine Rules - Arc Lengths - Sectors - Segments - Latitude and Longitude - Areas - Surface Areas - Volumes - Angles - Parallel Lines - Triangles - Polygons - Circle Theorems - Construction - Loci - Coordinate Geometry - Trigonometric Ratios - Elevation and Depression - Bearings - Differentiation - Integration - Frequency Distribution - Pie Charts - Bar Charts - Histograms - Frequency Polygons - Mean - Median - Mode - Ogive - Range - Variance - Standard Deviation - Probability - Vectors - Reflection - Rotation - Translation - Enlargement [**DOWNLOAD WAEC GENERAL MATHEMATICS SYLLABUS 2027/2028 PDF**](https://examloaded.com/wp-content/uploads/2026/10/GENERAL-MATHEMATICS.pdf) Use the complete syllabus as your study checklist. Mark each topic after you have studied it and solved enough questions to understand how it works. ## WAEC General Mathematics Examination Structure The examination consists of **two papers: Paper 1 and Paper 2**, and both papers must be taken. ### WAEC General Mathematics Paper 1 Paper 1 contains **50 multiple-choice objective questions** drawn from the common areas of the syllabus. You are required to answer all the questions within **1 hour 30 minutes**. The paper carries **50 marks**. Since Paper 1 can test different parts of the syllabus, you should not concentrate only on Algebra or Mensuration while leaving other areas. ### WAEC General Mathematics Paper 2 Paper 2 contains **13 essay questions** divided into: - Section A - Section B The paper lasts **2 hours 30 minutes** and carries **100 marks**. You are required to answer **10 questions altogether**. ### General Mathematics Paper 2 Section A Section A contains **five compulsory questions**. All five questions must be answered. The section carries a total of **40 marks** and the questions are drawn from the common areas of the syllabus. ### General Mathematics Paper 2 Section B Section B contains **eight questions** of greater length and difficulty. You are required to answer **five questions**. The section carries **60 marks**. The syllabus also notes that this section can contain a maximum of two questions drawn from syllabus areas that may not be peculiar to candidates’ home countries. ## Complete WAEC General Mathematics Syllabus 2027/2028 The detailed syllabus is organised into nine main sections: - Number and Numeration - Algebraic Processes - Mensuration - Plane Geometry - Coordinate Geometry of Straight Lines - Trigonometry - Introductory Calculus - Statistics and Probability - Vectors and Transformation ## Number and Numeration Number and Numeration is a broad section containing many of the arithmetic concepts you will use throughout Mathematics. The major topics include: - Number Bases - Modular Arithmetic - Fractions and Decimals - Approximations - Indices - Standard Form - Logarithms - Sequences and Series - Sets - Logical Reasoning - Rational Numbers - Surds - Matrices and Determinants - Ratio and Proportion - Rates - Percentages - Financial Arithmetic - Variation ## Number Bases Study: - Conversion from one base to another - Conversion from another base to base 10 - Conversion from base 10 to another base - Addition in different number bases - Subtraction in different number bases - Multiplication in different number bases ### Converting Number Bases You should be able to convert numbers: - From base 2 to base 10 - From base 10 to base 2 - From one non-decimal base to another Practise the method rather than memorising individual conversions. ### Operations in Number Bases You should also practise: - Addition - Subtraction - Multiplication while keeping the base in mind. ## Modular Arithmetic The syllabus covers: - Concept of Modulo Arithmetic - Addition in Modular Arithmetic - Subtraction in Modular Arithmetic - Multiplication in Modular Arithmetic - Applications to Daily Life Examples in the syllabus include expressions such as: `6 + 4 = k (mod 7)` and applications involving: - Market Days - Clocks - Shift Duty ## Fractions and Decimals Study the four basic operations involving: - Fractions - Decimals You should be comfortable with: - Addition - Subtraction - Multiplication - Division without depending completely on a calculator. ## Approximations and Significant Figures Study: - Decimal Places - Significant Figures - Appropriate Levels of Accuracy The syllabus emphasises that approximations should be realistic for the quantity being measured. For example, different situations may require different degrees of accuracy. ## Indices Study the Laws of Indices. These include rules involving: - Multiplication - Division - Powers of Powers - Zero Indices - Negative Indices - Fractional Indices The syllabus includes simple examples involving negative and fractional indices. ## Standard Form You should be able to express very large and very small numbers in **scientific notation or standard form**. Examples include forms such as: `3.753 × 10⁸` or: `3.5 × 10⁻⁷` Practise: - Converting ordinary numbers to standard form - Converting standard form to ordinary numbers - Performing calculations involving standard form ## Logarithms The syllabus covers: - Relationship Between Indices and Logarithms - Laws of Logarithms - Logarithm Tables - Antilogarithm Tables ### Laws of Logarithms Study rules involving: - Products - Quotients - Powers You should understand how logarithms can be used in calculations involving: - Multiplication - Division - Powers - Roots ## Sequences and Series Study: - Patterns of Sequences - Arithmetic Progression - Geometric Progression ### Finding Terms of a Sequence You should be able to identify a pattern and determine a required term. The notation: `Uₙ` may be used for the nth term. ### Arithmetic Progression Study: - First Term - Common Difference - nth Term - Sum of an Arithmetic Progression The syllabus includes simple word problems. ### Geometric Progression Study: - First Term - Common Ratio - nth Term The syllabus includes simple G.P. cases but excludes the sum of a G.P. in this section. ## Sets Study: - Universal Sets - Finite Sets - Infinite Sets - Subsets - Empty Sets - Disjoint Sets - Union - Intersection - Complement ## Venn Diagrams You should be able to use Venn diagrams to solve classification problems. The syllabus restricts these questions to **at most three sets**. Practise: - Two-Set Problems - Three-Set Problems - Complements - Intersections - Unions ## Logical Reasoning The syllabus includes: - Simple Statements - True Statements - False Statements - Negation - Implications You should understand mathematical statements and use the logical symbols provided in your course correctly. ## Positive and Negative Integers and Rational Numbers Study: - Positive Integers - Negative Integers - Rational Numbers - Number Line Practise the four basic operations involving rational numbers. You should also recognise standard notation for: - Natural Numbers - Integers - Rational Numbers ## Surds Study: - Simplification of Surds - Rationalisation - Addition - Subtraction - Multiplication - Division The syllabus limits the work to simple surd forms. Do not convert every surd into a decimal unless the question requires it. ## Matrices and Determinants The syllabus includes: - Order of a Matrix - Matrix Notation - Types of Matrices - Addition - Subtraction - Scalar Multiplication - Matrix Multiplication - Determinants - Application to Simultaneous Equations ### Order of a Matrix You should understand the meaning of: - Rows - Columns - Matrix Order ### Matrix Operations Practise: - Addition - Subtraction - Multiplication by a Scalar - Matrix Multiplication Check whether matrices have compatible orders before carrying out an operation. ### Determinants The detailed syllabus restricts the determinant application for simultaneous linear equations to **2 × 2 matrices**. ## Ratio Proportion and Rates Study: - Ratios - Proportions - Financial Partnerships - Rates of Work - Costs - Taxes - Foreign Exchange - Population Density - Mass - Distance - Time - Speed The syllabus expects these ideas to be related to practical situations. ## Rates Practise calculations involving: - Distance and Time - Speed - Work Rates - Population Density - Exchange Rates Also pay attention to average rates. ## Taxes The syllabus includes practical tax calculations, with examples such as: - VAT - Withholding Tax Read each question carefully because the percentage may apply to a particular part of the amount. ## Percentages Study percentage applications involving: - Simple Interest - Commission - Discount - Depreciation - Profit and Loss - Compound Interest - Hire Purchase - Percentage Error ## Simple Interest Understand how interest depends on: - Principal - Rate - Time Practise both finding interest and finding the final amount. ## Profit and Loss Study: - Cost Price - Selling Price - Profit - Loss - Percentage Profit - Percentage Loss ## Discount and Commission Practise questions where percentages are applied to selling prices, marked prices or transaction values. ## Compound Interest The syllabus limits compound-interest problems in this section to a maximum of **three years**. ## Hire Purchase Understand the relationship among: - Cash Price - Deposit - Instalments - Hire-Purchase Price ## Percentage Error Study how to calculate percentage error from an approximate and actual value. ## Financial Arithmetic The syllabus includes: - Depreciation - Amortization - Annuities - Capital Market Instruments ## Depreciation and Amortization Study the meaning and calculations involving depreciation of fixed assets and amortization of capitalised assets. ## Annuities Understand the meaning of an annuity and solve the simple problems required by the syllabus. ## Shares Stocks Bonds and Debentures The syllabus includes: - Shares - Stocks - Debentures - Bonds - Interest on Bonds - Interest on Debentures ## Variation Study: - Direct Variation - Inverse Variation - Partial Variation - Joint Variation You should be able to: - Translate the relationship into mathematical symbols. - Determine the constant of variation. - Form an equation. - Solve practical problems. ## Algebraic Processes Algebra is one of the most important areas in General Mathematics. The syllabus covers: - Algebraic Expressions - Expansion - Factorization - Binary Operations - Linear Equations - Simultaneous Equations - Change of Subject of Formula - Quadratic Equations - Graphs - Linear Inequalities - Algebraic Fractions - Functions and Relations ## Algebraic Expressions You should be able to translate practical statements into algebraic expressions. For example, a question may describe prices, quantities or measurements and require you to represent them using variables. You should also be able to substitute values and evaluate an expression. ## Expansion Practise expanding expressions such as products of binomials. Take care with: - Signs - Like Terms - Brackets ## Factorization Study factorization involving: - Common Factors - Grouping - Difference of Two Squares - Quadratic Expressions Factorization is particularly important because it is used again when solving quadratic equations. ## Binary Operations The syllabus includes binary operations on real numbers. A question may define an operation such as: `a * b = 2a + b - ab` and ask you to calculate a particular value. Always use the definition supplied in the question. ## Linear Equations Study linear equations in one variable. Practise: - Removing Brackets - Collecting Like Terms - Working With Fractions - Solving Word Problems ## Simultaneous Linear Equations You should be able to solve two simultaneous equations using: - Elimination - Substitution - Graphical Method Practise word problems that require you to first form the equations. ## Change of Subject of Formula Study how to rearrange a formula so that a particular variable becomes the subject. For example, you may be required to make one variable the subject of a relationship containing several others. ## Substitution After changing the subject, you may also be asked to substitute numerical values. Watch carefully for: - Powers - Roots - Fractions - Negative Values ## Quadratic Equations Study solving quadratic equations using: - Factorization - Completing the Square - Quadratic Formula ## Forming Quadratic Equations From Roots You should also be able to form a quadratic equation when its roots are given. If the roots are `α` and `β`, the structure: `(x - α)(x - β) = 0` can be used before expanding. ## Applications of Quadratic Equations Practise word problems that lead to quadratic equations. Do not assume every algebra word problem is linear. ## Graphs of Linear and Quadratic Functions Study: - Tables of Values - Coordinates - Plotting Points - Quadratic Curves - Roots From Graphs - Maximum and Minimum Points - Intercepts - Axis of Symmetry ## Solving Equations Graphically The syllabus includes graphical solutions involving equations such as: `y = ax² + bx + c` and: `y = mx + k` You should be able to identify the coordinates of intersection. ## Gradient of a Curve The syllabus also includes drawing a tangent to a curve and using it to estimate the gradient at a point. Draw a sufficiently large gradient triangle to reduce reading errors. ## Linear Inequalities Study: - Inequalities in One Variable - Number-Line Representation - Inequalities in Two Variables - Simultaneous Inequalities - Maximum and Minimum Values - Linear Programming ## Inequalities on a Number Line Be careful when multiplying or dividing an inequality by a negative number because the inequality sign changes direction. ## Graphical Inequalities You should be able to: - Draw the boundary line. - Determine the required region. - Shade correctly. - Identify the feasible region. ## Linear Programming The syllabus connects simultaneous inequalities with practical situations involving: - Minimum Cost - Maximum Profit ## Algebraic Fractions Study operations involving algebraic fractions with: - Monomial Denominators - Binomial Denominators Pay attention to values for which a denominator becomes zero. These values are excluded from the domain of the expression. ## Functions and Relations Study: - One-to-One - One-to-Many - Many-to-One - Many-to-Many - Mapping - Determining the Rule of a Function or Relation You should understand the relationship between input values and output values. ## Mensuration Mensuration covers measurement of: - Length - Perimeter - Area - Surface Area - Volume It also includes applications involving Pythagoras’ Theorem, Sine and Cosine Rules, arcs, sectors, latitude and longitude. ## Lengths and Perimeters Study: - Pythagoras’ Theorem - Sine Rule - Cosine Rule - Arc Length - Perimeter of Sectors - Perimeter of Segments - Latitude and Longitude ## Pythagoras’ Theorem Be able to identify the hypotenuse correctly before applying: `a² + b² = c²` The theorem is frequently used with: - Right-Angled Triangles - Distance Problems - Three-Dimensional Shapes ## Sine and Cosine Rules The syllabus allows these rules to be used for determining lengths and distances. Know when the available information suggests: - Sine Rule - Cosine Rule ## Arc Length Understand how the length of an arc relates to: - Radius - Central Angle - Circumference ## Sectors and Segments Study perimeters and areas involving sectors and segments of circles. Take care not to confuse: - Arc Length - Sector Area - Segment Area ## Latitude and Longitude The syllabus includes distances along: - Latitudes - Longitudes and their corresponding angles. Practise interpreting diagrams of the Earth carefully. ## Areas Study areas of: - Triangles - Rectangles - Parallelograms - Trapeziums - Circles - Sectors - Segments - Compound Shapes ## Area of a Triangle Know formulas such as: `Area = ½ × base × height` and: `Area = ½ab sin C` where applicable. ## Similar Figures The syllabus includes areas of similar figures. Understand how the scale factor for lengths relates to the scale factor for areas. ## Surface Areas Study surface areas of: - Cubes - Cuboids - Cylinders - Pyramids - Right Triangular Prisms - Cones - Spheres ## Cone and Sector Relationship The syllabus specifically connects the sector of a circle with the curved surface of a cone. Understand how a sector can form the curved surface when folded. ## Volumes Study volumes of: - Cubes - Cuboids - Cylinders - Cones - Right Pyramids - Spheres - Compound Solids ## Similar Solids Understand how the linear scale factor relates to the volume scale factor. ## Plane Geometry Plane Geometry includes: - Angles - Parallel Lines - Triangles - Polygons - Circles - Construction - Loci ## Angles Know basic angle relationships such as: - Angles at a Point Sum to 360° - Angles on a Straight Line Sum to 180° - Vertically Opposite Angles Are Equal Also recognise: - Acute Angles - Obtuse Angles - Reflex Angles - Right Angles ## Angles on Parallel Lines Study: - Alternate Angles - Corresponding Angles - Interior Angles The syllabus also includes the Intercept Theorem. ## Triangles Study: - Sum of Angles of a Triangle - Exterior Angle Property - Congruent Triangles - Isosceles Triangles - Equilateral Triangles - Right-Angled Triangles - Similar Triangles ## Congruent Triangles Know conditions such as: - SSS - SAS and other conditions covered in your course. The syllabus notes that the conditions should be known even where formal proofs are not required. ## Similar Triangles Understand: - Corresponding Angles - Corresponding Sides - Ratios of Sides - Ratios of Areas ## Quadrilaterals Study properties of: - Parallelograms - Rhombuses - Squares - Rectangles - Trapeziums ## Polygons Study: - Interior Angles - Exterior Angles - Sum of Interior Angles The syllabus gives: `(n - 2) × 180°` for the sum of the interior angles of an n-sided polygon. ## Circle Geometry Important circle properties include: - Chords - Angles at the Centre - Angles at the Circumference - Angles in a Semicircle - Angles in the Same Segment - Opposite Angles of Cyclic Quadrilaterals - Tangent and Radius - Alternate Segment Theorem ## Chords Understand properties involving: - Chords - Perpendicular Bisectors - Centre of the Circle ## Angle at the Centre The angle subtended by an arc at the centre is twice the angle subtended by the same arc at the circumference. ## Angle in a Semicircle An angle subtended at the circumference by a diameter is a right angle. ## Angles in the Same Segment Angles in the same segment are equal. ## Opposite Angles in a Cyclic Quadrilateral Opposite angles are supplementary. ## Tangent and Radius A tangent is perpendicular to the radius at the point of contact. ## Alternate Segment Theorem Study the relationship between the angle made by a tangent and chord and the angle in the alternate segment. ## Geometrical Construction Study construction of: - Angle Bisectors - Perpendicular Bisectors - Parallel Lines - Perpendicular Lines - 90° Angles - 60° Angles - 45° Angles - 30° Angles - Triangles - Quadrilaterals The syllabus also includes combinations producing angles such as: - 75° - 105° - 135° ## Loci Study loci involving: - Points at a Given Distance From a Point - Points Equidistant From Two Points - Points Equidistant From Two Straight Lines - Points at a Given Distance From a Straight Line - Intersections of Loci Practise drawing the required construction rather than describing it only in words. ## Coordinate Geometry of Straight Lines The syllabus covers the x-y plane and coordinates of points. Important areas include: - Midpoint - Distance Between Two Points - Gradient - Equation of a Straight Line ## Midpoint For points: `P(x₁, y₁)` and `Q(x₂, y₂)` you should be able to find their midpoint. ## Distance Between Two Points Study the distance formula: `PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]` ## Gradient of a Straight Line For two points, study: `m = (y₂ - y₁)/(x₂ - x₁)` where `m` is the gradient. ## Equation of a Straight Line The syllabus includes forms such as: `y = mx + c` and: `y - y₁ = m(x - x₁)` You should be able to form the equation from: - A Gradient and a Point - Two Points - A Graph ## Trigonometry The Trigonometry section includes: - Sine - Cosine - Tangent - Special Angles - Angles From 0° to 360° - Trigonometric Graphs - Angles of Elevation and Depression - Bearings ## Sine Cosine and Tangent Understand the trigonometric ratios in a right-angled triangle. You should know how to identify: - Opposite Side - Adjacent Side - Hypotenuse relative to a specified angle. ## Special Angles The syllabus requires the trigonometric ratios of: - 30° - 45° - 60° without using tables. Learn their exact values. ## Angles From 0° to 360° Study sine, cosine and tangent for general angles in this range. The syllabus relates these ratios to the unit circle. ## Trigonometric Graphs Study graphs of: - Sine - Cosine - Other Trigonometric Ratios The syllabus includes examples such as: `y = a sin x` and: `y = b cos x` ## Angles of Elevation and Depression Study simple problems involving: - Heights - Distances - Angles of Elevation - Angles of Depression Draw a diagram before attempting the calculation. ## Bearings Study: - Three-Figure Bearings - Directional Bearings - Distances - Angles The syllabus gives notations such as: `035°` and: `N35°E` A diagram is particularly useful in bearing questions. ## Introductory Calculus The syllabus introduces: - Differentiation - Integration ## Differentiation Study the meaning of differentiation and its relationship to the gradient of a curve at a point. For example, if: `y = x²` then: `dy/dx = 2x` ## Applications of Differentiation The syllabus includes applications such as: - Maximum Values - Minimum Values - Rates of Change - Velocity For example, where displacement is expressed as a function of time, differentiation can be used to obtain velocity. ## Integration Study the meaning of integration and the evaluation of simple definite integrals of algebraic functions. Understand integration as closely related to the reverse process of differentiation. ## Statistics and Probability This section is divided into: - Statistics - Probability ## Statistics The syllabus covers: - Frequency Distribution - Pie Charts - Bar Charts - Histograms - Frequency Polygons - Mean - Median - Mode - Cumulative Frequency Curves - Range - Interquartile Range - Variance - Mean Deviation - Standard Deviation ## Frequency Distribution Study: - Frequency Tables - Class Intervals - Class Marks - Class Boundaries You should be able to construct and interpret a frequency distribution table. ## Pie Charts Practise converting frequencies into angles and interpreting data represented in a pie chart. ## Bar Charts Understand how categorical or discrete data can be represented and interpreted. ## Histograms The syllabus includes histograms and specifically excludes unequal class intervals. Be able to: - Draw Histograms - Read Values - Interpret Information ## Frequency Polygons Study how a frequency polygon can be constructed from grouped data. ## Mean Practise calculating mean for: - Discrete Data - Grouped Data The use of an assumed mean is accepted but not required. ## Median For grouped data, the syllabus expects median estimation from the cumulative frequency curve. ## Mode For grouped data, the mode should be estimated from the histogram. ## Cumulative Frequency Curve The cumulative frequency curve is also called an **Ogive**. You should be able to estimate: - Median - Quartiles - Percentiles from the curve. ## Measures of Dispersion Study: - Range - Interquartile Range - Semi-Interquartile Range - Variance - Mean Deviation - Standard Deviation ## Range Calculate the difference between the highest and lowest values. ## Interquartile Range Understand: `IQR = Q₃ - Q₁` and how quartiles may be read from an Ogive. ## Mean Deviation The syllabus describes Mean Deviation as the mean of the absolute deviations from the mean. ## Variance and Standard Deviation Study both concepts and their relationship. The syllabus notes that variance is the square of the standard deviation. ## Probability The syllabus covers: - Experimental Probability - Theoretical Probability - Mutually Exclusive Events - Independent Events - Addition of Probabilities - Multiplication of Probabilities - With Replacement - Without Replacement ## Experimental Probability Understand probability based on actual observed outcomes. ## Theoretical Probability Study probability based on equally likely outcomes, such as: - Tossing a Fair Coin - Throwing a Fair Die ## Addition of Probabilities Pay attention to whether events are mutually exclusive or otherwise as required by the question. ## Multiplication of Probabilities Study multiplication involving independent events. The syllabus also expects you to interpret the words: - **and** - **or** correctly in probability problems. ## With and Without Replacement Understand how replacing an item after selection affects the probability of later selections. ## Vectors and Transformation The final major section covers: - Vectors in a Plane - Transformations in the Cartesian Plane ## Vectors in a Plane Study: - Vectors as Directed Line Segments - Cartesian Components - Magnitude - Equal Vectors - Addition - Subtraction - Zero Vector - Parallel Vectors - Multiplication by a Scalar ## Magnitude of a Vector You should be able to calculate the magnitude of a vector from its Cartesian components. ## Vector Addition and Subtraction Practise both: - Algebraic Representation - Graphical Representation The syllabus requires knowledge of graphical representation. ## Transformation in the Cartesian Plane Study: - Reflection - Rotation - Translation - Enlargement ## Reflection The syllabus includes reflection of points and shapes in: - The x-axis - The y-axis - Lines of the form `x = k` - `y = x` - `y = k` - Other specified lines within the stated limits You should also be able to determine mirror lines or lines of symmetry. ## Rotation Study rotation: - About the Origin - About a Point Other Than the Origin The syllabus restricts angles of rotation to the range from **-180° to 180°**. ## Translation Study translation using a translation vector. You should be able to determine the new coordinates of a point or shape. ## Enlargement Study enlargement using: - Centre of Enlargement - Scale Factor You should also be able to enlarge or reduce plane figures using a given scale. ## Units You Should Know The syllabus requires familiarity with common units and their symbols. These include units of: - Length - Area - Capacity - Mass - Currency ## Length Units Know: - 1000 millimetres = 100 centimetres = 1 metre - 1000 metres = 1 kilometre ## Area Units Know: - 10,000 square metres = 1 hectare ## Capacity Units Know: - 1000 cubic centimetres = 1 litre ## Mass Units Know: - 1000 milligrammes = 1 gramme - 1000 grammes = 1 kilogramme - 1000 kilogrammes = 1 tonne ## Currency Calculations The syllabus contains currency units for different WAEC countries and some major international currencies. Your preparation should include calculations involving: - Exchange Rates - Conversion From One Currency to Another - Practical Financial Problems ## 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 accuracy is that obtainable from the mathematical tables. ## Use of Calculators The syllabus permits: - Non-Programmable Calculators - Silent Calculators - Cordless Calculators The calculator must not be able to: - Print - Receive Information - Send Information Phones with or without calculator functions are not allowed. The syllabus also states that individual questions may prohibit the use of tables or calculators. ## Mathematical Instruments to Bring Candidates should bring the mathematical instruments required for the examination, including items such as: - Ruler - Pair of Compasses - Protractor - Set Squares You should not depend on borrowing instruments from another candidate during the examination. Graph paper will be provided where required. ## Important General Mathematics Formulas to Know Create a formula notebook covering areas such as: - Percentages - Simple Interest - Compound Interest - Variation - Quadratic Formula - Pythagoras’ Theorem - Areas - Surface Areas - Volumes - Arc Length - Sector Area - Sine Rule - Cosine Rule - Coordinate Geometry - Trigonometric Ratios - Statistics Do not memorise a formula without understanding what each symbol represents. ## Important General Mathematics Calculations to Practise Give regular attention to: - Number Bases - Modular Arithmetic - Fractions - Standard Form - Logarithms - AP and GP - Sets - Matrices - Ratio - Rates - Percentages - Interest - Financial Arithmetic - Variation - Linear Equations - Quadratic Equations - Mensuration - Trigonometry - Statistics - Probability - Vectors ## Important Graphs to Practise You should be confident in: - Linear Graphs - Quadratic Graphs - Linear Inequality Graphs - Sine Graphs - Cosine Graphs - Bar Charts - Histograms - Frequency Polygons - Cumulative Frequency Curves For every graph: - Choose an appropriate scale. - Label both axes. - Plot points accurately. - Draw the required line or curve neatly. - Read required values carefully. ## Important Geometry Areas to Practise Give strong attention to: - Angle Properties - Parallel Lines - Similar Triangles - Congruent Triangles - Polygon Angles - Circle Theorems - Construction - Loci - Bearings Many Geometry questions require you to identify the appropriate theorem before beginning calculations. ## How to Use the WAEC General Mathematics Syllabus to Prepare ### Start With the Complete Syllabus Use the syllabus PDF as your main checklist. **READ ALSO:** [WAEC English Language Syllabus 2027/2028 PDF Download](/waec-english-syllabus-questions/) ### Identify Your Weak Areas Early Divide the syllabus into three groups: - Strong - Average - Weak Spend more time on weak topics while still revising the areas you already understand. ### Solve Mathematics Every Day You do not need to complete an entire paper every day. A useful daily target can be: - 10 Objective Questions - 2 or 3 Theory Questions - One Difficult Topic Review Consistency is more useful than waiting to practise only on weekends. ### Show Your Working For Paper 2, write your mathematical steps clearly. Do not jump from the question directly to an answer. Showing your method also makes it easier to find your own mistakes. ### Check Units Mensuration and practical problems can involve: - Metres - Centimetres - Square Units - Cubic Units - Litres - Kilogrammes - Time - Currency Convert units before performing calculations where necessary. ### Practise Without a Calculator Sometimes Although calculators are permitted subject to the syllabus conditions, you should still be comfortable with basic arithmetic without one. This helps you work faster and check whether a calculator answer is reasonable. ### Learn to Use Your Calculator Correctly Practise entering: - Powers - Roots - Fractions - Trigonometric Ratios correctly. A calculator will only give the correct answer if the expression is entered correctly. ### Draw Diagrams For questions involving: - Bearings - Elevation and Depression - Geometry - Vectors - Mensuration draw a clear diagram before calculating. ### Practise Past Questions by Topic After completing each topic, answer related WAEC questions. For example: After Number Bases → solve Number Base questions. After Quadratic Equations → solve both direct and word problems. After Circle Theorems → practise theorem questions. After Statistics → answer questions involving tables and graphs. After Probability → practise both “and” and “or” questions. ## Best Order to Study WAEC General Mathematics A practical revision order is to move from basic arithmetic into Algebra, Geometry and then Statistics. ### Stage 1 Number and Numeration Start with: - Fractions and Decimals - Approximation - Indices - Standard Form - Number Bases - Modular Arithmetic - Logarithms - Sequences - Sets - Surds ### Stage 2 Commercial and Financial Mathematics Study: - Ratio - Proportion - Rates - Percentages - Simple Interest - Compound Interest - Profit and Loss - Hire Purchase - Financial Arithmetic - Variation ### Stage 3 Algebra Study: - Algebraic Expressions - Expansion - Factorization - Linear Equations - Simultaneous Equations - Formulae - Quadratic Equations - Algebraic Fractions - Functions - Inequalities ### Stage 4 Graphs and Coordinate Geometry Study: - Tables of Values - Linear Graphs - Quadratic Graphs - Gradients - Straight-Line Equations - Graphical Solutions ### Stage 5 Mensuration and Geometry Study: - Pythagoras’ Theorem - Areas - Surface Areas - Volumes - Angle Properties - Triangles - Polygons - Circle Theorems - Construction - Loci ### Stage 6 Trigonometry and Calculus Study: - Sine - Cosine - Tangent - Bearings - Elevation and Depression - Trigonometric Graphs - Differentiation - Integration ### Stage 7 Statistics Probability and Transformation Finish the main cycle with: - Frequency Tables - Charts - Histograms - Mean - Median - Mode - Ogive - Measures of Dispersion - Probability - Vectors - Reflection - Rotation - Translation - Enlargement Continue solving questions from earlier topics as you move through the later stages. ## What Should You Focus on Most for WAEC General Mathematics You should cover the complete syllabus, but make sure you are particularly confident in: - Number Bases - Indices - Logarithms - Sequences - Sets - Ratio and Proportion - Percentages - Financial Arithmetic - Variation - Algebraic Expressions - Factorization - Linear Equations - Simultaneous Equations - Quadratic Equations - Graphs - Linear Inequalities - Mensuration - Plane Geometry - Circle Theorems - Coordinate Geometry - Trigonometry - Bearings - Introductory Calculus - Statistics - Probability - Vectors - Transformation For a more focused revision guide, use the [WAEC General Mathematics Areas of Concentration 2027/2028](/waec-general-mathematics-areas-of-concentration/). You can also use the [WAEC Areas of Concentration 2027/2028 for All Subjects](/waec-areas-of-concentration-for-all-subjects/) to access the other subject guides. ## Frequently Asked Questions ### What Is the WAEC General Mathematics Syllabus 2027/2028? The WAEC General Mathematics syllabus contains the mathematical topics, concepts and problem-solving skills you need to prepare for General Mathematics/Mathematics (Core) in WASSCE. ### Is General Mathematics the Same as Mathematics Core? The syllabus uses the title **General Mathematics/Mathematics (Core)**. ### How Many Papers Are in WAEC General Mathematics? There are two papers: - Paper 1 - Paper 2 Both papers must be taken. ### How Many Questions Are in General Mathematics Paper 1? Paper 1 contains **50 multiple-choice objective questions**. ### How Long Is General Mathematics Paper 1? Paper 1 lasts **1 hour 30 minutes** and carries 50 marks. ### How Many Questions Are in General Mathematics Paper 2? Paper 2 contains **13 essay questions** divided into Sections A and B. ### How Many Questions Do I Answer in Paper 2? You answer **10 questions altogether**: - All 5 questions in Section A - 5 questions from Section B ### How Long Is WAEC General Mathematics Paper 2? Paper 2 lasts **2 hours 30 minutes**. ### Is Algebra Important in WAEC General Mathematics? Yes. The syllabus covers: - Algebraic Expressions, - Factorization, - Linear Equations, - Simultaneous Equations, - Quadratic Equations, - Graphs, - Inequalities, - Algebraic Fractions and Functions. ### Are Number Bases Included? Yes. You should study conversion and basic operations involving different number bases. ### Is Modular Arithmetic Included? Yes. The syllabus covers the concept, operations and everyday applications of Modular Arithmetic. ### Are Logarithms Included? Yes. You should understand the relationship between indices and logarithms, logarithmic rules and the use of logarithm and antilogarithm tables. ### Are Matrices Included? Yes. The syllabus includes Matrix Order, Matrix Operations, Determinants and application to simultaneous equations. ### Is Financial Mathematics Included? Yes. The syllabus covers percentages, interest, commission, discount, depreciation, hire purchase, annuities, shares, stocks, bonds and debentures. ### Are Quadratic Equations Important? Yes. You should be able to solve quadratic equations through Factorization, Completing the Square and the Quadratic Formula, as well as form equations from given roots. ### Does WAEC General Mathematics Include Graphs? Yes. The syllabus includes linear and quadratic graphs, trigonometric graphs and statistical graphs. ### Is Linear Programming Included? Yes. The syllabus includes graphical simultaneous inequalities and applications involving maximum and minimum values. ### Is Mensuration Included? Yes. You should study lengths, perimeters, areas, surface areas and volumes. ### Are Circle Theorems Included? Yes. The syllabus includes chords, angles at the centre and circumference, cyclic quadrilateral properties, tangent-radius relationships and the Alternate Segment Theorem. ### Is Construction Included? Yes. The syllabus covers construction of angles, bisectors, parallel and perpendicular lines, triangles and quadrilaterals. ### Are Loci Included? Yes. You should study common two-dimensional loci and their intersections. ### Does General Mathematics Include Coordinate Geometry? Yes. The syllabus includes midpoint, distance between two points, gradient and equation of a straight line. ### Is Trigonometry Important? Yes. You should study Sine, Cosine, Tangent, special angles, trigonometric graphs, elevation and depression, and bearings. ### Does WAEC General Mathematics Include Calculus? Yes. The syllabus contains **Introductory Calculus**, including differentiation and simple integration. ### Is Statistics Included? Yes. The syllabus covers frequency distributions, charts, histograms, mean, median, mode, Ogives and measures of dispersion. ### Is Standard Deviation Included? Yes. Standard Deviation is included under Measures of Dispersion. ### Is Probability Included? Yes. You should study experimental and theoretical probability, addition and multiplication of probabilities, and questions involving replacement. ### Are Vectors Included? Yes. The syllabus covers vectors as directed line segments, Cartesian components, magnitudes and vector operations. ### Are Transformations Included? Yes. The syllabus includes: - Reflection - Rotation - Translation - Enlargement ### Can I Use a Calculator in WAEC General Mathematics? The syllabus allows non-programmable, silent and cordless calculators, subject to the stated restrictions. ### 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? You should bring the mathematical instruments required for the examination, including: - Ruler - Pair of Compasses - Protractor - Set Squares ### Where Can I Download the Complete General Mathematics Syllabus? Use the download button near the beginning of this article to save the complete WAEC General Mathematics Syllabus PDF to your device. ### Where Can I Find the WAEC General Mathematics Areas of Concentration? Use the [WAEC General Mathematics Areas of Concentration 2027/2028](/waec-general-mathematics-areas-of-concentration/) guide to organise your revision around the major topics and calculations. ## Conclusion The **[WAEC](https://www.waecnigeria.org/) General Mathematics Syllabus 2027/2028** gives you a complete guide to the mathematical concepts and problem-solving skills required for General Mathematics/Mathematics (Core). Your preparation should cover Number and Numeration, Algebraic Processes, Mensuration, Plane Geometry, Coordinate Geometry, Trigonometry, Introductory Calculus, Statistics, Probability, Vectors and Transformation. Give regular attention to arithmetic and algebra because they provide the foundation for many other topics. You should also practise graphs, Geometry, Mensuration, Trigonometry and Statistics rather than simply reading formulas. General Mathematics becomes easier when you solve questions consistently. Use the syllabus as your main checklist, study one topic at a time, solve related questions immediately and return to any area where you repeatedly make mistakes. As the examination approaches, combine topic-by-topic revision with complete timed Paper 1 and Paper 2 practice. **READ ALSO:** [WAEC General Mathematics Areas of Concentration 2027/2028](/waec-general-mathematics-areas-of-concentration/) **READ ALSO:** [WAEC Syllabus 2027/2028 PDF Download for All Subjects](/waec-syllabus-for-all-subjects-pdf-download/) **READ ALSO:** [WAEC Areas of Concentration 2027/2028 for All Subjects](/waec-areas-of-concentration-for-all-subjects/) **READ ALSO:** [WAEC Timetable 2027](/waec-timetable-for-science-art-and-commercial/)