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).

Here is an explanation of Section I of the JAMB Mathematics syllabus, along with 10 JAMB-style questions for each sub-topic. --- SECTION I: NUMBER AND NUMERATION 1. Number Bases Explanation: This topic covers different ways of representing numbers using various bases (radix systems), from base 2 (binary) to base 10 (decimal). Key skills include converting numbers between any two bases, including those with fractional parts, and performing basic arithmetic operations (addition, subtraction, multiplication, division) directly within a given non-decimal base. Modulo arithmetic, which deals with remainders after division, is also included. Questions: 1. Convert 11011_2 to base 10. A. 25 B. 27 C. 29 D. 31 2. Convert 47_10 to base 3. A. 1201_3 B. 1202_3 C. 1211_3 D. 1212_3 3. Convert 234_5 to base 8. A. 74_8 B. 75_8 C. 76_8 D. 77_8 4. Evaluate 101_2 + 11_2. A. 110_2 B. 111_2 C. 1000_2 D. 1010_2 5. Subtract 12_3 from 21_3. A. 2_3 B. 10_3 C. 11_3 D. 12_3 6. Multiply 13_4 by 2_4. A. 30_4 B. 31_4 C. 32_4 D. 33_4 7. Divide 1011_2 by 11_2. A. 11_2 B. 101_2 C. 110_2 D. 111_2 8. If 23_x = 17_10, find x. A. 5 B. 6 C. 7 D. 8 9. Convert 0.625_10 to base 2. A. 0.101_2 B. 0.110_2 C. 0.111_2 D. 0.011_2 10. Evaluate (15 × 3) 7. A. 1 B. 2 C. 3 D. 4 --- 2. Fractions, Decimals, Approximations and Percentages Explanation: This section covers fundamental arithmetic operations with fractions and decimals, along with methods for rounding numbers to a specified number of significant figures or decimal places. It also includes practical applications of percentages such as calculating percentage error, simple interest, profit/loss, and problems involving ratios, proportions, rates, shares, and Value Added Tax (VAT). Questions: 1. Simplify (3)/(4) + (1)/(3) - (1)/(2). A. (5)/(12) B. (7)/(12) C. (1)/(2) D. (2)/(3) 2. Express 0.00567 to 2 significant figures. A. 0.0056 B. 0.0057 C. 0.006 D. 0.01 3. Round 2.3456 to 3 decimal places. A. 2.345 B. 2.346 C. 2.35 D. 2.34 4. A student measured the length of a line as 12.5 cm. If the actual length is 12.0 cm, calculate the percentage error. A. 0.5\% B. 4.0\% C. 4.17\% D. 4.2\% 5. Calculate the simple interest on N5000 for 3 years at 4\% per annum. A. N200 B. N400 C. N600 D. N800 6. A trader bought an item for N800 and sold it for N1000. Calculate the percentage profit. A. 20\% B. 25\% C. 30\% D. 40\% 7. The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there? A. 30 B. 35 C. 40 D. 45 8. A car travels 180 km in 2 hours. What is its average speed in km/h? A. 60 km/h B. 75 km/h C. 90 km/h D. 100 km/h 9. A company's profit is shared among three partners in the ratio 2:3:5. If the largest share is N150,000, what is the total profit? A. N250,000 B. N300,000 C. N450,000 D. N500,000 10. An item costs N2500 before VAT. If VAT is 7.5\%, what is the total cost of the item? A. N2687.50 B. N2700.00 C. N2750.00 D. N2812.50 --- 3. Indices, Logarithms and Surds Explanation: This topic focuses on powers (indices), their inverse operations (logarithms), and irrational numbers involving roots (surds). It requires understanding and applying the laws of indices and logarithms to simplify expressions and solve equations. Standard form (scientific notation) is also covered. For surds, the key skills are simplification, rationalization of denominators, and performing basic arithmetic operations. Questions: 1. Simplify (2^3 × 3^2)^2. A. 2^5 × 3^4 B. 2^6 × 3^4 C. 2^6 × 3^2 D. 2^5 × 3^2 2. Solve for x in 2^x+1 = 16. A. 2 B. 3 C. 4 D. 5 3. Express 0.0000045 in standard form. A. 4.5 × 10^-5 B. 4.5 × 10^-6 C. 4.5 × 10^5 D. 4.5 × 10^6 4. Simplify _2 8 + _2 4. A. _2 12 B. _2 32 C. 5 D. 6 5. Evaluate _3 81. A. 2 B. 3 C. 4 D. 5 6. Given _10 2 = 0.3010 and _10 3 = 0.4771, find _10 12. A. 0.7781 B. 1.0791 C. 1.0000 D. 1.2041 7. If y = 10^x, express x in terms of y. A. x = _10 y B. x = _y 10 C. x = 10y D. x = (y)/(10) 8. Simplify $72