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Read this article till the end because we have provided you with a very easy-to-read and understandable syllabus as well as textbooks you can use to study.
With this syllabus, you are one step ahead of your lecturers and your fellow students. Isn’t that amazing?
Having a pass in your JUPEB Mathematics exam, you can get admitted into 200 level to study any engineering, computer, or social science course.
COURSE CODE | COURSE TITLE | CREDIT LOAD |
MAT001 | Advanced Pure Mathematics | 3 Units |
MAT002 | Calculus | 3 Units |
| JUPEB MATHEMATICS SYLLABUS | ||
| SN | TOPICS | OBJECTIVES |
| FIRST SEMESTER | ||
| MAT001: ADVANCED PURE MATHEMATICS | ||
| 1 | REAL NUMBERS | i. Integers, ii. Rational and irrational numbers, iii. Mathematical induction, iv. Real sequence and series (AP and GP), v. Sum to infinity of Geometric Progression and its convergence, and vi. Binary operations |
| 2 | ALGEBRA | i. Set Theory a) Elementary set theory, b) Subset, union, c) Intersection, d) Complements, e) Venn diagram and its applications to word problems. ii. Mapping a) Compositions of mapping b) Domain c) Range d) One-to-one e) Onto mapping f) Inverse Functions g) Composite Functions iii. Theory of Quadratics a) The roots of quadratic (completing the square, using the discriminant to determine the roots), b) Theory of quadratic equations. iv. Polynomials a) Polynomial as an equation up to degree 3, b) The Factor theorem and c) The Remainder theorem, d) Partial fractions. v. Binomial theorem, a) Binomial Theorem b) Pascal triangle. vi. Logarithm a) The relationship between logarithm and Indices, change of base, and the natural logarithm. vii. Matrices and Determinants a)Matrices and Determinants of not more than 3 x 3, inverse, addition, subtraction, multiplication and its applications to system of equations up to three unknowns. viii. Inequality a) Linear, quadratic, Simultaneous (one linear, one quadratic) and graphical solution. b) Absolute value and intervals. |
| 3 | COMPLEX NUMBERS | i. Basic complex numbers, ii. Algebra of complex numbers, iii. The Argand diagram, iv. Complex numbers in polar form, v. De- Moivre’s theorem with Proof (nth root of unity) and vi. Loci problems |
| 4 | TRIGONOMETRY | i. Circular Measure a) Radians and Degrees conversion, b) Length of an arc, c) Area of a sector, d) Area of the segment of a circle. ii. Trigonometric Function a) Magnitude simple trigonometricy equations, b) Graphs of trigonometric functions (Sine, Cosine, and Tangent). c) Inverse of trigonometric functions. trigonometric identities. d) Use of trigonometric function |
| 5 | COORDINATE GEOMETRY | i. Straight Line a) Length, gradient and mid-point of sta line. b) Equation of straight line (coordin of two points and one point, and the gradients). c) Association between the gradients of parallel and perpendicular lines. ii. Other Conic Equation a) Circles, b) Parabola, c) Ellipse, d) Hyperbola and e) Their properties (eg tangents and normal) |
| MAT002: CALCULUS | ||
| 6 | DIFFERENTIATION | i. Differentiation Functions of a real variable, graphs, limits and notion of continuity, differentiation from first principle, differentiation of: algebraic functions and trigonometric functions. Composite functions: chain rule, product rule, and quotient rule. Derivatives of implicit and parametric functions. Higher order derivatives ii. Application of derivation a) Rectilinear motion b) Tangent and normal to a curve c) Maximum and minimum d) Rate of change and curve sketching e) Maclaurin and Taylor series |
| 7 | EXPONENTIAL FUNCTIONS | i. The graph of exponential function (a”), ii. Limit and derivative of the function (a). iii. The exponential function (e), iv. The graph, limit and derivative of the exponential functions (e”). |
| 8 | LOGARITHM FUNCTION | i. The relationship between logarithmic and exponential functions, ii. the graph, limit and derivative of the logarithmic function (log, x). |
| 9 | INTEGRATION | i. Integration a) Standard integrals, b) Integration as inverse of differentiation, c) Definite integrals, d) Techniques of integration (substitution method, inverse frigonometric function, e) Integration by parts, f) Use of partial fraction and reduction formula). ii. Application of integration a) Areas, b) Volumes, c) Numerical methods of integration: Trapezoidal and Simpson rules. |
| 10 | SECOND ORDER DIFFERENTIATION EQUATIONS | i. Second Order Differential Equations a) Homogeneous second order differential equations with constant coefficients. ii. Geometric Application a) The exponential growth and decay problems. |
COURSE CODE | COURSE TITLE | CREDIT LOAD |
MAT003 | Applied Mathematics | 3 Units |
MAT004 | Statistics | 3 Units |
| SECOND SEMESTER | ||
| MAT003: APPLIED MATHEMATICS | ||
| 11 | VECTORS | i. Vector a) Scalar and vector quantities, b) Types of vectors, c) Representation and naming of vectors ii. Algebra of Vectors a) Addition, subtraction and scalar multiplication, b) Commutativity and associativity, c) Linear dependence and co-linearity of vectors, d) Perpendicularity of vectors and the angles between two vectors iii. Vectors Equations a) Vector equation of lines and planes, b) Application to geometry, c) Vectors in three dimensions, and d) The rectangular unit vectors i, j, and k. e) Representation of vectors in terms of rectangular coordinates, f) Scalar and vector functions. iv. Vector Function a) Differentiation of vector functions, b) Integration of vector functions (one integral and differential operators of at most order 3). |
| 12 | KINEMATICS OF MOTION IN A STRAIGHT LINE | i. Motion in a straight line a) Unit vectors, position vectors, speed, velocity, acceleration and displacement in simple cases. b) Area under a velocity-time graph representing displacement, and c) Gradient of velocity-time graph representing acceleration. d) Gradient of a displacement-time graph representing velocity ii. Rectilinear Motion a) Rectilinear motion with uniform acceleration, b) Motion under gravity, and c) Graphical method. iii. Motion in a plane a) Rectangular components of velocity and acceleration, b) Resultant velocity, c) Relative velocity and d) Relative path. |
| 13 | NEWTONIAN MECHANICS | i. Newtonian Mechanics a) Energy, work and power (simple cases) ii. Force and Motion a) Force and motion b) Momentum c) Newton’s Laws of motion d) Different types of forces (gravitational reactions, tension and thrust) e) Motion of connected particles f) The At’wood machine (simple cases) g) Motion of a particle on an inclined plane |
| 14 | FORCES AND EQUILIBRIUM | i. Forces and equilibrium a) Forces acting at various points of a rigid body b) Parallel Forces c) Couple d) Moment and application of vectors in a static (simple cases) ii. Frictional forces and centre of a mass a) Friction b) Smooth bodies c) Tension and thrust d) Bodies in equilibrium (rough, horizontal and inclined planes) e) Centre of gravity (simple cases) |
| 15 | EQUILIBRIUM OF A RIGID BODY | i. Moment of Inertia ii. Ratio of gyration iii. Parallel and perpendicular axes theorem iv. Kinetic energy of a body rotating about a fixed axis (simple cases) |
| MAT004: STATISTICS | ||
| 16 | DESCRIPTION OF A DATA SET | i. Data set a) Population and sample b) Random variables and graphical representation of data (histogram, bar chart, pie chart, Ogive and frequency polygon) c) Measure of central tendency for grouped and ungrouped data (mean, median and mode) d) Measure of dispersion for grouped and ungrouped data ( mean deviation, standard deviation and variance) e) Skewness and Kurtosis |
| 17 | MATHEMATICS OF COUNTING | i. Permutation and combination ii. Fundamental principles of of probability theory iii. Discrete and continuous random variables |
| 18 | RANDOM VARIABLES | i. Probability a) Probability density function b) Probability distribution function ii. Discrete random variables a) Find the mean and variance from a probability distribution table and the linear properties of expectation and variance iii. Discrete probability variables a) Expectation and variance of the following: Bernoulli, Binomial iv. Density, function, expectation and variance a) Geometric and poisson. Use of the Binomial and Poisson tables. |
| 19 | NORMAL RANDOM VARIABLES | i. Normal table a) Use of standard normal table b) Normal distribution as a model for data and it’s applications to real life problems ii. Significance testing a) Test of hypothesis b) Errors in hypothesis testing c) Significant tests using normal distribution and student i-distribution c) Chi-square test (goodness of fit test and contingency table) d) One sample mean test e) Difference of mean f) One sample proportion test |
| 20 | REGRESSION AND CORRELATION | i. Simple regression and correlation a) Types of correlation b) Simple correlation c) Simple Linear regression |
| 21 | BASIC SAMPLING TECHNIQUES | i. Types of sampling techniques a) Simple sampling techniques b) Finite and infinite sampling sizes |
1. Adamu Muminu, (2006). Understanding Basic Statistics, Lagos, Nile Ventures.
2. Barnett, R. (2011). College Algebra with Trigonometry, New York, McGraw.
3. Bunday M. (2014). Pure Mathematics for Advanced Level University of Lagos, Department of Mathematics (2014). Course in Statistics, Lagos, Nile Ventures.
4. University of Lagos, Department of Mathematics (2014). Mathematics, Lagos, Tonniichristo Concepts.
5. University of Lagos, Department of Mathematics (2014). Introduction Calculus, Lagos, Nile Ventures.
6. Department of Mathematics (2014). Introduction Mechanics, Lagos, Tonniichristo Concepts.
7. Dugopolski, M. (2011). College Algebra, Addison-Wesley.
8. Goetz, B.S. S. and Tobey, J. (2011). Basic Mathematics, Pearson, Boston.
9. Graham, A. (2003). Statistics, London, Hodder Education.
10. Humphrew and Topping (1980). Intermediate Mathematics, London, Longman group.
11. Nwagbogwu D.C. and Akinfenwa O.A. (2012). Fundamentals of Mathematics, Lagos, S. S. Stephen’s Nig. Ltd.. Okunuga,
12. S.A., (2009) WIM Publication. Elementary Mathematical Methods, Lagos,
13. Okunuga, S.A., (2006) Understanding Calculus, Lagos, WIM Publication
14. Riley, K.F., Hobson M.P and Bence, S.J., (2016). Mathematical Methods for Physics and Engineering.
15. Stroud K. A., (2006). Advanced Engineering Mathematics, New York, Palgrave Macmillan.
16. Young, C. Y. (2010). Algebra and Trigonometry, New Jersey, John Wiley and Sons.
NOTE: Candidates are required to write 3 subjects in the qualifying examination)
JUPEB currently offers examinations in the following nineteen (19) subjects as detailed in its syllabuses. The subjects can be classified into 3 categories: Arts & Humanities, Management & Social Science and Sciences
There is no official pass mark, but scores above 50 are considered good. However, you should try to score as high as you can because the higher you score, the better your chances of admission to your chosen course and institution.
The objective and theory exam takes 3 hours.
The JUPEB Mathematics exam will cover all the topics listed in the syllabus above. Go through them and study.
If you are interested in pursuing careers in the medical or engineering field, you will have to write Mathematics in JUPEB.
You will be required to answer 50 multiple-choice and 4 essay questions based on the syllabus listed above.
Here are a few tips for you:
-Start studying early enough. Do not do last-minute reading. You should also try practicing your time management skills.
Another tip is to study past questions regularly and ensure you get a good night’s rest a day before your exam.
Good luck!
Here are a few tips for you:
-Start studying early enough. Do not do last-minute reading. You should also attend classes as often as you can and join study groups.
Another tip is to study past questions regularly and ensure you get a good night’s rest a day before your exam.
Good luck!
