JAMB

JAMB Mathematics Syllabus

General Objectives

  • 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

1. Number and Numeration

Number bases

Content:

  • •Operations in different number bases from 2 to 10
  • •Conversion from one base to another including fractional parts

Learning Objectives:

  • Perform four basic operations (+, -, ×, ÷)
  • Convert one base to another

Fractions, Decimals, Approximations and Percentages

Content:

  • •Fractions and decimals
  • •Significant figures
  • •Decimal places
  • •Percentage errors
  • •Simple interest
  • •Profit and loss percent
  • •Ratio, proportion and rate
  • •Shares and valued added tax (VAT)

Learning Objectives:

  • Perform basic operations (+, -, ×, ÷) on fractions and decimals
  • Express to specified number of significant figures and decimal places
  • Calculate simple interest, profit and loss percent; ratio, proportion and rate
  • Solve problems involving share and VAT

Indices, Logarithms and Surds

Content:

  • •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

Learning Objectives:

  • Apply the laws of indices in calculation
  • Establish the relationship between indices and logarithms in solving problems
  • Solve problems in different bases in logarithms
  • Simplify and rationalize surds
  • Perform basic operations on surds

Sets

Content:

  • •Types of sets
  • •Algebra of sets
  • •Venn diagrams and their applications

Learning Objectives:

  • 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

2. Algebra

Polynomials

Content:

  • •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

Learning Objectives:

  • Find the subject of the formula of a given equation
  • Apply factor and remainder theorem to factorize a given expression
  • Multiply and divide polynomials of degree not more than 3
  • 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

Content:

  • •Direct
  • •Inverse
  • •Joint
  • •Partial
  • •Percentage increase and decrease

Learning Objectives:

  • Solve problems involving direct, inverse, joint and partial variations
  • Solve problems on percentage increase and decrease in variation

Inequalities

Content:

  • •Analytical and graphical solutions of linear inequalities
  • •Quadratic inequalities with integral roots only

Learning Objectives:

  • Solve problems on linear and quadratic inequalities
  • Interpret graphs of inequalities

Progression

Content:

  • •nth term of a progression
  • •Sum of A.P. and G.P.
  • •Sum to infinity of a given G.P.

Learning Objectives:

  • 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

Content:

  • •Properties of closure, commutativity, associativity and distributivity
  • •Identity and inverse elements (simple cases only)

Learning Objectives:

  • Solve problems involving closure, commutativity, associativity and distributivity
  • Solve problems involving identity and inverse elements

Matrices and Determinants

Content:

  • •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]

Learning Objectives:

  • Perform basic operations (+, -, ×, ÷) on matrices
  • Calculate determinants
  • Compute inverses of 2 x 2 matrices

3. Geometry and Trigonometry

Euclidean Geometry

Content:

  • •Properties of angles and lines
  • •Polygons: triangles, quadrilaterals and general polygons
  • •Circles: angle properties, cyclic quadrilaterals and intersecting chords
  • •Construction

Learning Objectives:

  • Identify various types of lines and angles
  • Solve problems involving polygons
  • Calculate angles using circle theorems
  • Identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90°, etc.

Mensuration

Content:

  • •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

Learning Objectives:

  • 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

Content:

  • •Locus in 2 dimensions based on geometric principles relating to lines and curves

Learning Objectives:

  • Identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles

Coordinate Geometry

Content:

  • •Midpoint and gradient of a line segment
  • •Distance between two points
  • •Parallel and perpendicular lines
  • •Equations of straight lines

Learning Objectives:

  • 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

Content:

  • •Trigonometric ratios of angles
  • •Angles of elevation and depression
  • •Bearings
  • •Areas and solutions of triangle
  • •Graphs of sine and cosine
  • •Sine and cosine formulae

Learning Objectives:

  • Calculate the sine, cosine and tangent of angles between –360° ≤ θ ≤ 360°
  • Apply special angles (e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135°) 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

4. Calculus

Differentiation

Content:

  • •Limit of a function
  • •Differentiation of explicit algebraic and simple trigonometric functions—sine, cosine and tangent

Learning Objectives:

  • Find the limit of a function
  • Differentiate explicit algebraic and simple trigonometric functions

Application of differentiation

Content:

  • •Rate of change
  • •Maxima and minima

Learning Objectives:

  • Solve problems involving applications of rate of change, maxima and minima

Integration

Content:

  • •Integration of explicit algebraic and simple trigonometric functions
  • •Area under the curve

Learning Objectives:

  • Solve problems of integration involving algebraic and simple trigonometric functions
  • Calculate area under the curve (simple cases only)

5. Statistics

Representation of data

Content:

  • •Frequency distribution
  • •Histogram, bar chart and pie chart

Learning Objectives:

  • Identify and interpret frequency distribution tables
  • Interpret information on histogram, bar chart and pie chart

Measures of Location

Content:

  • •Mean, mode and median of ungrouped and grouped data (simple cases only)
  • •Cumulative frequency

Learning Objectives:

  • 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

Content:

  • •Range
  • •Mean deviation
  • •Variance
  • •Standard deviation

Learning Objectives:

  • Calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data

Permutation and Combination

Content:

  • •Linear and circular arrangements
  • •Arrangements involving repeated objects

Learning Objectives:

  • Solve simple problems involving permutation and combination

Probability

Content:

  • •Experimental probability (tossing of coin, throwing of a dice etc)
  • •Addition and multiplication of probabilities (mutual and independent cases)

Learning Objectives:

  • Solve simple problems in probability (including addition and multiplication)

Recommended Textbooks

  • Adelodun A. A (2000) Distinction in Mathematics: Comprehensive Revision Text, (3rd Edition) Ado -Ekiti: FNPL.
  • Anyebe, J. A. B (1998) Basic Mathematics for Senior Secondary Schools and Remedial Students in Higher/ institutions, Lagos: Kenny Moore.
  • Channon, J. B. Smith, A. M (2001) New General Mathematics for West Africa SSS 1 to 3, Lagos: Longman.
  • David -Osuagwu, M. et al (2000) New School Mathematics for Senior Secondary Schools, Onitsha: Africana – FIRST Publishers.
  • Egbe. E et al (2000) Further Mathematics, Onitsha: Africana – FIRST Publishers
  • Ibude, S. O. et al (2003) Algebra and Calculus for Schools and Colleges: LINCEL Publishers.
  • Tuttuh – Adegun M. R. et al (1997), Further Mathematics Project Books 1 to 3, Ibadan: NPS Educational

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