WAEC Further Mathematics / Mathematics (Elective) Syllabus
Every section, topic and candidate objective in the official WAEC Further Mathematics / Mathematics (Elective) outline — 3 sections, 6 topics and 6 objectives.
- Sections
- 3sections
- Topics
- 6topics
- Objectives
- 6objectives
- Category
- Sciencescategory
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Syllabus sections
3 sectionsTap a section to open it, then tap a topic to see its content and objectives.
1Section I: Pure Mathematics
4 topics · 4 objectives
1Sets, Surds, Binary Operations, and Logical Reasoning
1 content item · 1 objective
Content
Set properties, Venn diagrams, De Morgan's laws, surd operations, rationalization, binary operation properties, logic truth tables
Objective
Solve set problems involving union, intersection, complements, and Venn diagrams; simplify, manipulate, and rationalize surd denominators; apply closure, commutativity, associativity, identity, and inverse to binary operations; construct truth tables to evaluate compound logical statements and implications.
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2Functions, Polynomials, Rational Functions, Indices, and Logarithms
1 content item · 1 objective
Content
Mapping types, composite/inverse functions, linear/quadratic/cubic functions, quadratic inequalities, polynomial remainder/factor theorems, partial fractions, laws of indices and logarithms
Objective
Determine domains, ranges, inverse, and composite functions; sketch and solve linear, quadratic, and cubic functions/equations; apply factor and remainder theorems to polynomials; resolve rational functions into partial fractions; solve exponential and logarithmic equations including change of base and linear reduction ($y=ax^b$).
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3Permutations, Combinations, Binomial Theorem, Sequences & Series, Matrices, and Linear Transformations
1 content item · 1 objective
Content
Arrangements and selections ($^nP_r, ^nC_r$), binomial expansions, AP/GP sequences, infinite series, matrix operations, determinants, inverse matrices, linear transformations
Objective
Solve arrangement and combination problems; expand binomial expressions for positive integral indices; calculate terms and sums of AP, GP, recurrence, and infinite series; perform matrix operations, evaluate $2\times2$ and $3\times3$ determinants, find inverses, and apply matrices to linear transformations and geometry.
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4Trigonometry, Coordinate Geometry, Calculus (Differentiation & Integration)
1 content item · 1 objective
Content
Trigonometric ratios/identities, compound/multiple angles, graphs, coordinate geometry of lines and conic sections (circles, parabolas), differentiation rules, maxima/minima, indefinite/definite integrals, area/volume applications
Objective
Prove trigonometric identities and solve equations involving compound/multiple angles; analyze line gradients, midpoints, acute angles, perpendicular distances, circles, and parabola equations; differentiate polynomials, trigonometric, and transcendental functions using chain/product/quotient rules; determine turning points, tangents, normals, and kinematics; evaluate indefinite/definite integrals to compute plane areas, volumes of revolution, and trapezium rule approximations.
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2Section II: Statistics and Probability
1 topic · 1 objective
1Statistics and Probability Distributions
1 content item · 1 objective
Content
Data representation, measures of location and dispersion, scatter diagrams, correlation coefficients, regression lines, sample spaces, probability laws, binomial and Poisson distributions
Objective
Construct frequency tables, histograms, and cumulative frequency curves (Ogives); calculate mean, median, mode, variance, and standard deviation for grouped/ungrouped data; plot scatter diagrams, calculate Spearman's rank correlation, and find lines of best fit; compute classical, conditional, mutually exclusive, and independent probabilities; apply Binomial and Poisson probability distributions.
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3Section III: Vectors and Mechanics
1 topic · 1 objective
1Vectors, Statics, and Dynamics
1 content item · 1 objective
Content
Vector algebra, unit/position vectors, scalar (dot) products, coplanar forces, equilibrium, Lami's theorem, moments, friction, kinematics equations, Newton's laws, impulse, momentum, and projectiles
Objective
Perform vector addition, scalar multiplication, unit vector calculations, and scalar dot products; resolve coplanar forces, apply Lami's theorem, moments, and friction principles to bodies in equilibrium; solve rectilinear motion problems using equations of motion, Newton's laws, momentum conservation, and projectile trajectories.
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