## JAMB MATHEMATICS SYLLABUS

### JAMB MATHEMATICS SYLLABUS

JAMB MATHEMATICS SYLLABUS

The jamb syllabus is made available for students to serve as a study guide to follow while preparing for the jamb examination. The syllabus contains all the topics expected for candidates to cover be writing the examination.

The 2019 JAMB Mathematics syllabus is divided into five main sections, in which, under each sections, there are topic to be covered and what is expected of student to know from the topics

(i)ALGEBRA

(ii)CALCULUS

(iii) GEOMETRY AND TRIGONOMETRY

(iv) NUMBER AND NUMERATION

(v) STATISTICS

TOPIC 1: ALGEBRA

SUB TOPIC 1: POLYNOMIALS

CONTENT

(a) Change of subject of formula.

(b) Factor and remainder theorems.

(c ) Factorization of polynomials of degree not exceeding 3.

(d) Multiplication and division of polynomials.

(e) Roots of polynomials not exceeding degree 3.

(f) Simultaneous equations including one linear one quadratic.

(g) 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.

ii. apply factor and remainder theorem to factorize a given expression.

iii. multiply and divide polynomials of degree not more than 3.

iv. factorize by regrouping difference of two squares, perfect squares and cubic expressions, etc.

v. solve simultaneous equations one linear, one quadrant.

vi. interpret graphs of polynomials including applications to maximum and minimum values.

SUB TOPIC 2 : INEQUALITIES

OBJECTIVES

Candidates should be able to:

i. solve problems on linear and quadratic inequalities.

ii. interprete graphs of inequalities.

CONTENT

(a) Analytical and graphical solutions of linear inequalities.

(b) Quadratic inequalities with integral roots only.

SUB TOPIC 3 : MATRICES AND DETERMINANTS

OBJECTIVES

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on matrices.

ii. calculate determinants.

iii. compute inverses of 2 x 2 matrices.

CONTENT

(a) Algebra of matrices not exceeding 3 x 3.

(b) Determinants of matrices not exceeding 3 x 3.

(c ) Inverses of 2 x 2 matrices [excluding quadratic and higher degree equations].

SUB TOPIC 4: PROGRESSION

OBJECTIVES

Candidates should be able to:

i. determine th nth term of a progression.

ii. compute the sum of A. P. and G.P.

iii. sum to infinity of a given G.P.

CONTENT

(a) nth term of a progression.

(b) Sum of A. P. and G. P.

SUB TOPIC 5: VARIATION

OBJECTIVES

Candidates should be able to:

i. solve problems involving direct, inverse, joint and partial variations.

ii. Solve problems on percentage increase and decrease in variation.

CONTENT

(a) Direct.

(b) Inverse.

(c) Joint.

(d) Partial.

(e) Percentage increase and decrease.

SUB TOPIC 6: BINARY OPERATIONS

OBJECTIVES

Candidates should be able to:

i. solve problems involving closure, commutativity, associativity and distributivity.

ii. solve problems involving identity and inverse elements.

CONTENT

(a) Properties of closure, commutativity, associativity and distributivity.

(b) Identity and inverse elements (simple cases only).

TOPIC 2: CALCULUS

SUB TOPIC 1: DIFFERENTIATION

OBJECTIVES

Candidates should be able to:

i. find the limit of a function.

ii. differentiate explicit algebraic and simple trigonometrical functions.

CONTENT

(a) Limit of a function.

(b) Differentiation of explicit algebraic and simple trigonometrical functions sine, cosine and tangent.

SUB TOPIC 2 : INTEGRATION

OBJECTIVES

Candidates should be able to:

i. solve problems of integration involving algebraic and simple trigonometrical functions.

ii. calculate area under the curve (simple cases only).

CONTENT

(a) Integration of explicit algebraic and simple trigonometrical functions.

(b) Area under the curve.

SUB TOPIC3 : APPLICATION OF DIFFERENTIATION

OBJECTIVES

Candidates should be able to:

(i) solve problems involving applications of rate of change, maxima and minima.

CONTENT

(a) Rate of change.

(b) Maxima and minima.

TOPIC 3 : GEOMETRY AND TRIGONOMETRY

SUB TOPIC 1 : COORDINATE GEOMETRY

OBJECTIVES

Candidates should be able to:

i. Calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures.

ii. Find the length of an arc, a chord, perimeters and areas of sectors and segments of circles.

iii. Calculate total surface areas and volumes of cuboids, cylinders. Cones, pyramids, prisms, spheres and composite figures.

iv. Determine the distance between two points on the earths surface.

CONTENT

(a) Midpoint and gradient of a line segment.

(b) Distance between two points.

(c) Parallel and perpendicular lines.

(d) Equations of straight lines.

SUB TOPIC 2 : EUCLIDEAN GEOMETRY

OBJECTIVES

Candidates should be able to:

i. identify various types of lines and angles.

ii. solve problems involving polygons.

iii. calculate angles using circle theorems.

iv. Identify construction procedures of special angles, e.g. 30º, 45º, 60º, 75º, 90º etc.

CONTENT

(a) Properties of angles and lines.

(b) Polygons: triangles, quadrilaterals and generl polygons.

(c) Circles: angle properties, cyclicquadrilaterals and intersecng chords.

(d) Construction

SUB TOPIC 3: LOCI

OBJECTIVES

Candidates should be able to:

(i) identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles.

CONTENT

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

SUB TOPIC 4: TRIGONOMETRY

OBJECTIVES

Candidates should be able to:

i. calculate the sine, cosine and tangent of angles between - 360º = O = 6º.

ii. apply these special angles, e.g. 30º, 45º, 60º, 75º, 90º, 1050, 135º to solve simple problems in trigonometry.

iii. solve problems involving angles of elevation and depression.

iv. solve problems involvig bearings.

v. apply trigonometric formulae to find areaof triangles.

vi. solve problems involving sine and cosine graphs.

CONTENT

(a) Trigonometrical ratios of angles.

(b) Angles of elevation and depression.

(c) Bearings.

(d) Areas and solutions of triangle.

(e) Graphs of sine and cosine.

(f) Sine and cosine formulae.

SUB TOPIC 5: MENSURATION

OBJECTIVES

Candidates should be able to:

i. calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures.

ii. find the length of an arc, a chord, perimeters and areas of sectors and segments of circles.

iii. calculate total surface areas and volumes of cuboids, cylinders. cones, pyramids, prisms, spheres and composite figures.

iv. Determine the distance between two points on the earths surface.

CONTENT

(a) Lengths and areas of plane geometrical figures.

(b) Lengths of arcs and chords of a circles.

(c) Perimeters and areas of sectors and segments of circles.

(d) Surface areas and volumes of simple solids and composite figures.

(e) The earth as a sphere:- longitudes and latitudes.

TOPIC 5 :NUMBER AND NUMERATION

SUB TOPIC 1: FRACTIONS, DECIMALS, APPROXIMATION AND PERCENTAGES

OBJECTIVES

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on fractions and decimals.

ii. express to specified number of significant figures and decimal places.

iii. calculate simple interest, profit and loss percent; ratio proportion and rate.

iv. solve problems involving share and VAT.

CONTENT

(a) Fractions and demals.

(b) Significanfigures.

(c ) Decimal places.

(d) Percentage errors.

(e) Simple interest.

(f) Profit and loss percent.

(g) Ratio, proportion and rate.

(h) Shares and valued added tax (VAT).

SUB TOPIC 2: INDICES, LOGARITHMS AND SURDS

OBJECTIVES

Candidates should be able to:

i. apply the laws of indices in calculation.

ii. establish the relationship between indices and logarithms in solving problems.

iii. solve problems in different bases in logarithms.

iv. simplify and rationalize surds.

v. perform basic operations on surds.

CONTENT

(a) Laws of indices.

(b) Standard form.

(c ) Laws of logarithm.

(d) Logarithm of any positive number to a given base.

(e) Change of bases in logarithm and application.

(f) Relationship between indices and logarithm.

(g) Surds.

SUB TOPIC 3: SETS

OBJECTIVES

Candidates should be able to:

i. identify types of sets, i.e empty, universal, complements, subsets, finite, infinite and disjoint sets.

ii. solve problems involving cardinality of sets.

iii. solve set problems using symbol.

iv. use venn diagrams to solve problems involving not more than 3 sets.

CONTENT

(a) Types of sets.

(b) Algebra of sets.

(c ) Venn diagrams and their applications.

SUB TOPIC 4:NUMBER BASES

OBJECTIVES

candidates should be able to:

i. perform four basic operations (x,+,-,÷).

ii. convert one base to another.

CONTENT

(a) Operations in different number bases from 2 to 10.

(b)Conversion from one base to another including fractional parts.

TOPIC 5: STATISTICS

SUB TOPIC 1: MEASURES OF DISPERSION

OBJECTIVES

Candidates should be able to:

calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

CONTENT

Range, mean deviation, variance and standard deviation.

SUB TOPIC 2: MEASURES OF LOCATION

OBJECTIVES

i. calculate the mean, mode and median of ungrouped and grouped data (simple cases only).

ii. use ogive to find the median, quartiles and percentiles.

CONTENT

(a) Mean, mode and median of ungrouped and grouped data (simple cases only).

(b) Cumulative frequency.

SUB TOPIC 3: PERMUTATION AND COMBINATION

OBJECTIVES

Candidates should be able to:

solve simple problems involving permutation and combination.

CONTENT

(a) Linear and circular arrangements.

(b) Arrangements involving repeated objects.

SUB TOPIC 4: PROBABILITY

OBJECTIVES

Candidates should be able to:

(i)solve simple problems in probability (including addition and multiplication).

CONTENT

(a) Experimental probability (tossing of coin,throwing of a dice etc).

(b) Addition and multiplication of probabilities (mutual and independent cases).

SUB TOPIC 5: REPRESENTATION OF DATA

OBJECTIVES

Candidates should be able to:

i. identify and interpret frequency distribution tables.

ii. interpret information on histogram, bar chat and pie chart.

CONTENT

(a) Frequency distribution.

(b) Histogram, bar chart and pie chart.

JAMB RECOMMENDED MATHEMATICS TEXTBOOKS

1. Adelodun A. A (2000) Distinction in Mathematics: Comprehensive Revision Text, (3rd Edition) Ado Ekiti: FNPL.

2. Anyebe, J. A. B (1998) Basic Mathematics for Senior Secondary Schools and Remedial Students in Higher/ institutions, Lagos: Kenny Moore.

3. Channon, J. B. Smith, A. M (2001) New General Mathematics for West Africa SSS 1 to 3, Lagos: Longman.

4. David Osuagwu, M. et al (2000) New School Mathematics for Senior Secondary Schools, Onitsha: Africana - FIRST Publishers.

5. Egbe. E et al (2000) Further Mathematics, Onitsha: Africana FIRST Publishers.

6. Ibude, S. O. et al (2003) Agebra and Calculus for Schools and Colleges: LINCEL Publishers.

7. Tuttuh Adegun M. R. et al (1997), Further Mathematics Project Books 1 to 3, Ibadan: NPS Educational.

8. Wisdomline Pass at Once JAMB.

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