Please explain this jamb syllabus on math with questions 10 each with respect to jamb 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. 2. Fractions, Decimals, Approximations and Percentages: (a) fractions and decimals; (b) significant figures; (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). 3. Indices, Logarithms and Surds: (a) laws of indices; (b) equations involving indices; (c) standard form; (d) laws of logarithm; Candidates should be able to: i. perform four basic operations (x, +, -, ÷); ii. convert one base to another; iii. perform operations in modulo arithmetic. 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 per cent; ratio proportion, rate and percentage error; iv. solve problems involving share and VAT. 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 equations involving indices; iv. solve problems in different bases in logarithms; TOPICS/CONTENTS/NOTES OBJECTIVES (e) logarithm of any positive number to a given base; (f) change of bases in logarithm and application; (g) relationship between indices and logarithm; (h) Surds. 4. Sets: (a) types of sets (b) algebra of sets (c) Venn diagrams and their applications. SECTION II: ALGEBRA 1. Polynomials: (a) change of subject of formula; (b) multiplication and division of polynomials; (c) factorization of polynomials of degree not exceeding 3; (d) roots of polynomials not exceeding degree 3; (e) factor and remainder theorems; (f) simultaneous equations including one linear one quadratic; (g) graphs of polynomials of degree not greater than 3. 2. Variation: (a) direct; (b) inverse; (c) joint; (d) partial; (e) percentage increase and decrease. 3. Inequalities: (a) analytical and graphical solutions of linear inequalities; (b) quadratic inequalities with integral roots only. 4. Progression: (a) nth term of a progression (b) sum of A. P. and G. P. v. simplify and rationalize surds; vi. perform basic operations on surds. 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; iv. iii. solve set problems using symbols; v. iv. use Venn diagrams to solve problems involving not more than 3 sets. 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, divide polynomials of degree not more than 3 and determine values of defined and undefined expression; 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. 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. Candidates should be able to: i. solve problems on linear and quadratic inequalities; ii. interpret graphs of inequalities. 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. TOPICS/CONTENTS/NOTES OBJECTIVES 5. Binary Operations: (a) properties of closure, commutativity, associativity and distributivity; (b) identity and inverse elements (simple cases only). 6. Matrices and Determinants: (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]. SECTION III: GEOMETRY AND TRIGONOMETRY 1. Euclidean Geometry: (a) Properties of angles and lines (b) Polygons: triangles, quadrilaterals and general polygons; (c) Circles: angle properties, cyclic quadrilaterals and intersecting chords; (d) construction. 2. Mensuration: (a) lengths and areas of plane geometrical figures; (b) lengths of arcs and chords of a circle; (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. 3. Loci: locus in 2 dimensions based on geometric principles relating to lines and curves. 4. Coordinate Geometry: (a) midpoint and gradient of a line segment; (b) distance between two points; (c) parallel and perpendicular lines; (d) equations of straight lines. Candidates should be able to: i. solve problems involving closure, commutativity, associativity and distributivity; ii. solve problems involving identity and inverse elements. Candidates should be able to: i. perform basic operations (x, +, -, ÷) on matrices; ii. calculate determinants; iii. compute inverses of 2 x 2 matrices. 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. 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. Candidates should be able to: identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles. Candidates should be able to: i. determine the midpoint and gradient of a line segment; ii. find the distance between two points; TOPICS/CONTENTS/NOTES OBJECTIVES 5.Trigonometry: (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. SECTION IV: CALCULUS 1. Differentiation: (a) limit of a function (b) differentiation of explicit algebraic and simple trigonometrical functions – sine, cosine and tangent. 2. Application of differentiation: (a) rate of change; (b) maxima and minima. 3. Integration: (a) integration of explicit algebraic and simple trigonometrical functions; (b) area under the curve. SECTION V: STATISTICS 1. Representation of data: (a) frequency distribution; (b) histogram, bar chart and pie chart. 2. Measures of Location: (a) mean, mode and median of ungrouped and grouped data – (simple cases only); (b) cumulative frequency. 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. Candidates should be able to: i. calculate the sine, cosine and tangent of angles between - 360º ≤ Ɵ ≤ 360º; 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 involving bearings; v. apply trigonometric formulae to find areas of triangles; vi. solve problems involving sine and cosine graphs. Candidates should be able to: i. find the limit of a function ii. differentiate explicit algebraic and simple trigonometrical functions. Candidates should be able to: solve problems involving applications of rate of change, maxima and minima. 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). Candidates should be able to: i. identify and interpret frequency distribution tables; ii. interpret information on histogram, bar chat and pie chart. Candidates should be able to: i. calculate the mean, mode and median of ungrouped and grouped data (simple cases only); TOPICS/CONTENTS/NOTES OBJECTIVES 3. Measures of Dispersion: range, mean deviation, variance and standard deviation. 4. Permutation and Combination: (a) Linear and circular arrangements; (b) Arrangements involving repeated objects. 5.Probability: (a) experimental probability (tossing of coin, throwing of a dice etc); (b) Addition and multiplication of probabilities (mutual and independent cases). ii. use ogive to find the median, quartiles and percentiles. Candidates should be able to: calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data. Candidates should be able to: solve simple problems involving permutation and combination. Candidates should be able to: solve simple problems in probability (including addition and multiplication).