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Mathematics — JAMB Syllabus
Below are the topics and areas you are expected to study for Mathematics in the UTME examination. Questions will be drawn from these topics.
Section I: Number and Numeration
1
Number Bases
Topics / Contents
- Operations in different number bases from 2 to 10
- Conversion from one base to another including fractional parts
Objectives — Candidates should be able to:
- i.Perform four basic operations (×, +, −, ÷)
- j.Convert one base to another
2
Fractions, Decimals, Approximations and Percentages
Topics / Contents
- Fractions and decimals
- Significant figures
- Decimal places
- Percentage errors
- Simple interest
- Profit and loss percent
- Ratio, proportion and rate
- Shares and Value Added Tax (VAT)
Objectives — Candidates should be able to:
- i.Perform basic operations (×, +, −, ÷) on fractions and decimals
- j.Express to specified number of significant figures and decimal places
- k.Calculate simple interest, profit and loss percent; ratio, proportion and rate
- l.Solve problems involving share and VAT
3
Indices, Logarithms and Surds
Topics / Contents
- Laws of indices
- Standard form
- Laws of logarithm
- Logarithm of any positive number to a given base
- Change of bases in logarithm and application
- Relationship between indices and logarithm
- Surds
Objectives — Candidates should be able to:
- i.Apply the laws of indices in calculation
- j.Establish the relationship between indices and logarithms in solving problems
- k.Solve problems in different bases in logarithms
- l.Simplify and rationalize surds
- m.Perform basic operations on surds
4
Sets
Topics / Contents
- Types of sets
- Algebra of sets
- Venn diagrams and their applications
Objectives — Candidates should be able to:
- i.Identify types of sets, i.e. empty, universal, complements, subsets, finite, infinite and disjoint sets
- j.Solve problems involving cardinality of sets
- k.Solve set problems using symbols
- l.Use Venn diagrams to solve problems involving not more than 3 sets
Section II: Algebra
1
Polynomials
Topics / Contents
- Change of subject of formula
- Factor and remainder theorems
- Factorization of polynomials of degree not exceeding 3
- Multiplication and division of polynomials
- Roots of polynomials not exceeding degree 3
- Simultaneous equations including one linear one quadratic
- Graphs of polynomials of degree not greater than 3
Objectives — Candidates should be able to:
- i.Find the subject of the formula of a given equation
- j.Apply factor and remainder theorem to factorize a given expression
- k.Multiply and divide polynomials of degree not more than 3
- l.Factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc.
- m.Solve simultaneous equations — one linear, one quadratic
- n.Interpret graphs of polynomials including applications to maximum and minimum values
2
Variation
Topics / Contents
- Direct
- Inverse
- Joint
- Partial
- Percentage increase and decrease
Objectives — Candidates should be able to:
- i.Solve problems involving direct, inverse, joint and partial variations
- j.Solve problems on percentage increase and decrease in variation
3
Inequalities
Topics / Contents
- Analytical and graphical solutions of linear inequalities
- Quadratic inequalities with integral roots only
Objectives — Candidates should be able to:
- i.Solve problems on linear and quadratic inequalities
- j.Interpret graphs of inequalities
4
Progression
Topics / Contents
- nth term of a progression
- Sum of A.P. and G.P.
Objectives — Candidates should be able to:
- i.Determine the nth term of a progression
- j.Compute the sum of A.P. and G.P.
- k.Sum to infinity of a given G.P.
5
Binary Operations
Topics / Contents
- Properties of closure, commutativity, associativity and distributivity
- Identity and inverse elements (simple cases only)
Objectives — Candidates should be able to:
- i.Solve problems involving closure, commutativity, associativity and distributivity
- j.Solve problems involving identity and inverse elements
6
Matrices and Determinants
Topics / Contents
- Algebra of matrices not exceeding 3 × 3
- Determinants of matrices not exceeding 3 × 3
- Inverses of 2 × 2 matrices (excluding quadratic and higher degree equations)
Objectives — Candidates should be able to:
- i.Perform basic operations (×, +, −, ÷) on matrices
- j.Calculate determinants
- k.Compute inverses of 2 × 2 matrices
Section III: Geometry and Trigonometry
1
Euclidean Geometry
Topics / Contents
- Properties of angles and lines
- Polygons: triangles, quadrilaterals and general polygons
- Circles: angle properties, cyclic quadrilaterals and intersecting chords
- Construction
Objectives — Candidates should be able to:
- i.Identify various types of lines and angles
- j.Solve problems involving polygons
- k.Calculate angles using circle theorems
- l.Identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90° etc.
2
Mensuration
Topics / Contents
- Lengths and areas of plane geometrical figures
- Lengths of arcs and chords of a circle
- Perimeters and areas of sectors and segments of circles
- Surface areas and volumes of simple solids and composite figures
- The earth as a sphere: longitudes and latitudes
Objectives — Candidates should be able to:
- i.Calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures
- j.Find the length of an arc, a chord, perimeters and areas of sectors and segments of circles
- k.Calculate total surface areas and volumes of cuboids, cylinders, cones, pyramids, prisms, spheres and composite figures
- l.Determine the distance between two points on the earth's surface
3
Loci
Topics / Contents
- Locus in 2 dimensions based on geometric principles relating to lines and curves
Objectives — Candidates should be able to:
- i.Identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles
4
Coordinate Geometry
Topics / Contents
- Midpoint and gradient of a line segment
- Distance between two points
- Parallel and perpendicular lines
- Equations of straight lines
Objectives — Candidates should be able to:
- i.Determine the midpoint and gradient of a line segment
- j.Find the distance between two points
- k.Identify conditions for parallelism and perpendicularity
- l.Find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form
5
Trigonometry
Topics / Contents
- Trigonometrical ratios of angles
- Angles of elevation and depression
- Bearings
- Areas and solutions of triangle
- Graphs of sine and cosine
- Sine and cosine formulae
Objectives — Candidates should be able to:
- i.Calculate the sine, cosine and tangent of angles between −360° ≤ θ ≤ 360°
- j.Apply these special angles, e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135° to solve simple problems in trigonometry
- k.Solve problems involving angles of elevation and depression
- l.Solve problems involving bearings
- m.Apply trigonometric formulae to find areas of triangles
- n.Solve problems involving sine and cosine graphs
Section IV: Calculus
1
Differentiation
Topics / Contents
- Limit of a function
- Differentiation of explicit algebraic and simple trigonometrical functions — sine, cosine and tangent
Objectives — Candidates should be able to:
- i.Find the limit of a function
- j.Differentiate explicit algebraic and simple trigonometrical functions
2
Application of Differentiation
Topics / Contents
- Rate of change
- Maxima and minima
Objectives — Candidates should be able to:
- i.Solve problems involving applications of rate of change, maxima and minima
3
Integration
Topics / Contents
- Integration of explicit algebraic and simple trigonometrical functions
- Area under the curve
Objectives — Candidates should be able to:
- i.Solve problems of integration involving algebraic and simple trigonometric functions
- j.Calculate area under the curve (simple cases only)
Section V: Statistics
1
Representation of Data
Topics / Contents
- Frequency distribution
- Histogram, bar chart and pie chart
Objectives — Candidates should be able to:
- i.Identify and interpret frequency distribution tables
- j.Interpret information on histogram, bar chart and pie chart
2
Measures of Location
Topics / Contents
- Mean, mode and median of ungrouped and grouped data (simple cases only)
- Cumulative frequency
Objectives — Candidates should be able to:
- i.Calculate the mean, mode and median of ungrouped and grouped data (simple cases only)
- j.Use ogive to find the median, quartiles and percentiles
3
Measures of Dispersion
Topics / Contents
- Range, mean deviation, variance and standard deviation
Objectives — Candidates should be able to:
- i.Calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data
4
Permutation and Combination
Topics / Contents
- Linear and circular arrangements
- Arrangements involving repeated objects
Objectives — Candidates should be able to:
- i.Solve simple problems involving permutation and combination
5
Probability
Topics / Contents
- Experimental probability (tossing of coin, throwing of a dice etc.)
- Addition and multiplication of probabilities (mutual and independent cases)
Objectives — Candidates should be able to:
- i.Solve simple problems in probability (including addition and multiplication)