UTME syllabus
JAMB Mathematics syllabus
Every topic JAMB can set Mathematics questions on, with what you should be able to do for each. Open a topic to see its contents and objectives.
What the syllabus aims to do
It prepares candidates to:
- acquire computational and manipulative skills
- develop precise, logical and formal reasoning skills
- develop deductive skills in interpretation of graphs, diagrams and data
- apply mathematical concepts to resolve issues in daily living
Section I: Number and Numeration
Number bases/Modular Arithmetic
Contents
- operations in different number bases from 2 to 10
- conversion from one base to another including fractional parts
- modular arithmetic
Objectives: candidates should be able to
- perform four basic operations (×, +, −, ÷)
- convert one base to another
- perform operations in modulo arithmetic
Fractions, Decimals, Approximations and Percentages
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
- perform basic operations (×, +, −, ÷) on fractions and decimals
- express to specified number of significant figures and decimal places
- calculate simple interest, profit and loss per cent; ratio proportion, rate and percentage error
- solve problems involving share and VAT
Indices, Logarithms and Surds
Contents
- laws of indices
- equations involving 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
- apply the laws of indices in calculation
- establish the relationship between indices and logarithms in solving problems
- solve equations involving indices
- solve problems in different bases in logarithms
- simplify and rationalize surds
- perform basic operations on surds
Sets
Contents
- types of sets
- algebra of sets
- Venn diagrams and their applications
Objectives: candidates should be able to
- identify types of sets, i.e. empty, universal, complements, subsets, finite, infinite and disjoint sets
- solve problems involving cardinality of sets
- solve set problems using symbols
- use Venn diagrams to solve problems involving not more than 3 sets
Section II: Algebra
Polynomials
Contents
- change of subject of formula
- addition, subtraction, multiplication and division of polynomials
- factorization of polynomials of degree not exceeding 3
- roots of polynomials not exceeding degree 3
- factor and remainder theorems
- simultaneous equations including one linear one quadratic
- graphs of polynomials of degree not greater than 3
Objectives: candidates should be able to
- find the subject of the formula of a given equation
- apply factor and remainder theorem to factorize a given expression
- multiply, divide polynomials of degree not more than 3 and determine values of defined and undefined expression
- factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc.
- solve simultaneous equations – one linear, one quadratic
- interpret graphs of polynomials including applications to maximum and minimum values
Variation
Contents
- direct
- inverse
- joint
- partial
- percentage increase and decrease
Objectives: candidates should be able to
- solve problems involving direct, inverse, joint and partial variations
- solve problems on percentage increase and decrease in variation
Inequalities
Contents
- analytical and graphical solutions of linear inequalities
- quadratic inequalities with integral roots only
Objectives: candidates should be able to
- solve problems on linear and quadratic inequalities
- interpret graphs of inequalities
Progression
Contents
- nth term of a progression
- sum of A. P. and G. P.
Objectives: candidates should be able to
- determine the nth term of a progression
- compute the sum of A. P. and G.P
- sum to infinity of a given G.P.
Binary Operations
Contents
- properties of closure, commutativity, associativity and distributivity
- identity and inverse elements (simple cases only)
Objectives: candidates should be able to
- solve problems involving closure, commutativity, associativity and distributivity
- solve problems involving identity and inverse elements
Matrices and Determinants
Contents
- algebra of matrices not exceeding 3 x 3
- determinants of matrices not exceeding 3 x 3
- inverses of 2 x 2 matrices [excluding quadratic and higher degree equations]
Objectives: candidates should be able to
- perform basic operations (×, +, −, ÷) on matrices
- calculate determinants
- compute inverses of 2 x 2 matrices
Section III: Geometry and Trigonometry
Euclidean Geometry
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
- identify various types of lines and angles
- solve problems involving polygons
- calculate angles using circle theorems
- identify construction procedures of special angles, e.g. 30º, 45º, 60º, 75º, 90º etc.
Mensuration
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
- calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures
- find the length of an arc, a chord, perimeters and areas of sectors and segments of circles
- calculate total surface areas and volumes of cuboids, cylinders, cones, pyramids, prisms, spheres and composite figures
- determine the distance between two points on the earth’s surface
Loci
Contents
- locus in 2 dimensions based on geometric principles relating to lines and curves
Objectives: candidates should be able to
- identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles
Coordinate Geometry
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
- determine the midpoint and gradient of a line segment
- find the distance between two points
- identify conditions for parallelism and perpendicularity
- find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form
Trigonometry
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
- calculate the sine, cosine and tangent of angles between −360º ≤ θ ≤ 360º
- apply these special angles, e.g. 30º, 45º, 60º, 75º, 90º, 105º, 135º to solve simple problems in trigonometry
- solve problems involving angles of elevation and depression
- solve problems involving bearings
- apply trigonometric formulae to find areas of triangles
- solve problems involving sine and cosine graphs
Section IV: Calculus
Differentiation
Contents
- limit of a function
- differentiation of explicit algebraic and simple trigonometrical functions – sine, cosine and tangent
Objectives: candidates should be able to
- find the limit of a function
- differentiate explicit algebraic and simple trigonometrical functions
Application of differentiation
Contents
- rate of change
- maxima and minima
Objectives: candidates should be able to
- solve problems involving applications of rate of change, maxima and minima
Integration
Contents
- integration of explicit algebraic and simple trigonometrical functions
- area under the curve
Objectives: candidates should be able to
- solve problems of integration involving algebraic and simple trigonometric functions
- calculate area under the curve (simple cases only)
Section V: Statistics
Representation of data
Contents
- frequency distribution
- histogram, bar chart and pie chart
Objectives: candidates should be able to
- identify and interpret frequency distribution tables
- interpret information on histogram, bar chart and pie chart
Measures of Location
Contents
- mean, mode and median of ungrouped and grouped data – (simple cases only)
- cumulative frequency
Objectives: candidates should be able to
- calculate the mean, mode and median of ungrouped and grouped data (simple cases only)
- use Ogive to find the median, quartiles and percentiles
Measures of Dispersion
Contents
- range, mean deviation, variance and standard deviation
Objectives: candidates should be able to
- calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data
Permutation and Combination
Contents
- Linear and circular arrangements
- Arrangements involving repeated objects
Objectives: candidates should be able to
- solve simple problems involving permutation and combination
Probability
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
- solve simple problems in probability (including addition and multiplication)
Practise every Mathematics topic
JambCBT sorts its Mathematics past questions by these syllabus topics, so you can practise one topic at a time and see which ones need more work.
2 free practice quizzes. No card needed.