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BREAKING -  revise this maths topics before the commencement of your jamb exam

#1
TOPICS/CONTENTS/NOTES
OBJECTIVES
 
 
SECTION I: NUMBER AND NUMERATION
 
 
1. Number bases:
(a) operations in different number bases from 2 to 10;
(b) conversion from one base to another including fractional parts.
Candidates should be able to:
i. perform four basic operations (x,+,-,÷)
ii. convert one base to another.
 
 
2. Fractions, Decimals, Approximations and Percentages:
(a) fractions and decimals;
(b) significant figures;
© 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).
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.
 
 
3. Indices, Logarithms and Surds:
(a) laws of indices;
(b) standard form;
© 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.
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.
 
 
4. Sets:
(a) types of sets
(b) algebra of sets
© venn diagrams and their applications.
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.
 
 
SECTION II: ALGEBRA.
 
 
1. Polynomials:
(a) change of subject of formula
(b) factor and remainder theorems
© 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.
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 quadratic;
vi. interpret graphs of polynomials including applications to maximum and minimum values.
 
 
2. Variation:
(a) direct
(b) inverse
© joint
(d) partial
(e) percentage increase and decrease.
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.
 
 
3. Inequalities:
(a) analytical and graphical solutions of linear inequalities;
(b) quadratic inequalities with integral roots only.
Candidates should be able to:
i. solve problems on linear and quadratic
inequalities;
ii. interprete graphs of inequalities.
 
 
4. Progression:
(a) nth term of a progression
(b) sum of A. P. and G. P.
Candidates should be able to:
i. determine the nth term of a progression;
ii. compute the sum of A. P. and G.P;
iii. sum to infinity of a given G.P.
 
 
5. Binary Operations:
(a) properties of closure, commutativity, associativity and distributivity;
(b) identity and inverse elements (simple cases only).
Candidates should be able to:
i. solve problems involving closure, commutativity, associativity and distributivity;
ii. solve problems involving identity and inverse elements.
 
 
6. Matrices and Determinants:
(a) algebra of matrices not exceeding 3 x 3;
(b) determinants of matrices not exceeding 3 x 3;
© inverses of 2 x 2 matrices
[excluding quadratic and higher degree equations].
Candidates should be able to:
i. perform basic operations (x,+,-,÷) on matrices;
ii. calculate determinants;
iii. compute inverses of 2 x 2 matrices.
 
 
SECTION III: GEOMETRY AND TRIGONOMETRY
 
 
1. Euclidean Geometry:
(a) Properties of angles and lines
(b) Polygons: triangles, quadrilaterals and general polygons;
© Circles: angle properties, cyclic quadrilaterals and intersecting chords;
(d) construction.
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. 30°, 45°, 60°, 75°, 90° etc.
 
 
2. Mensuration:
(a) lengths and areas of plane geometrical figures;
(b) lengths of arcs and chords of a circle;
© 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.
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 earth's surface.
 
 
3. Loci:
locus in 2 dimensions based on geometric
principles relating to lines and curves.
Candidates should be able to:
identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles.
 
 
4. Coordinate Geometry:
(a) midpoint and gradient of a line segment;
(b) distance between two points;
© parallel and perpendicular lines;
(d) equations of straight lines.
Candidates should be able to:
i. determine the midpoint and gradient of a line segment;
ii. find the distance between two points;
iii. identify conditions for parallelism and perpendicularity;
iv. find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form.
 
 
5.Trigonometry:
(a) trigonometrical ratios of angels;
(b) angles of elevation and depression;
© bearings;
(d) areas and solutions of triangle;
(e) graphs of sine and cosine;
(f) sine and cosine formulae.
Candidates should be able to:
i. calculate the sine, cosine and tangent of angles between - 360°  θ  360°;
ii. apply these special angles, e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135° to solve simple problems in trigonometry;
iii. solve problems involving angles of elevation and depression;
iv. solve problems involving bearings;
v. apply trigonometric formulae to find areas of triangles;
vi. solve problems involving sine and cosine graphs.
 
 
SECTION IV: CALCULUS
 
 
I. Differentiation:
(a) limit of a function
(b) differentiation of explicit
algebraic and simple
trigonometrical functions -
sine, cosine and tangent.
Candidates should be able to:
i. find the limit of a function
ii. differentiate explicit algebraic and simple trigonometrical functions.
 
 
2. Application of differentiation:
(a) rate of change;
(b) maxima and minima.
Candidates should be able to:
solve problems involving applications of rate of change, maxima and minima.
 
 
3. Integration:
(a) integration of explicit
algebraic and simple
trigonometrical functions;
(b) area under the curve.
Candidates should be able to:
i. solve problems of integration involving algebraic and simple trigonometric functions;
ii. calculate area under the curve (simple cases only).
 
 
SECTION V: STATISTICS
 
 
1. Representation of data:
(a) frequency distribution;
(b) histogram, bar chart and pie chart.
Candidates should be able to:
i. identify and interpret frequency distribution tables;
ii. interpret information on histogram, bar chat and pie chart
 
 
2. Measures of Location:
(a) mean, mode and median of ungrouped and grouped data - (simple cases only);
(b) cumulative frequency.
Candidates should be able to:
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.
 
 
3. Measures of Dispersion:
range, mean deviation, variance and standard deviation.
Candidates should be able to:
calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data.
 
 
4. Permutation and Combination:
(a) Linear and circular arrangements;
(b) Arrangements involving repeated objects.
Candidates should be able to:
solve simple problems involving permutation and combination.
 
 
5. Probability:
(a) experimental probability (tossing of coin,
throwing of a dice etc);
(b) Addition and multiplication of probabilities
(mutual and independent cases).
Candidates should be able to:
solve simple problems in probability (including addition and multiplication).
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