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Hi there! Are you a science or commercial student who will be writing Further Mathematics in the upcoming WAEC examinations? Then you should see this.

This syllabus is a must-read for you as it exposes you to all the topics you should focus more on in Further Mathematics so you can have an A or B in your exams.

The syllabus will test you on your understanding of this subject which is a bridge between Elementary Mathematics and Higher Mathematics.

It will also test your ability to analyze data and draw valid conclusions.

If you’ll be writing Further Mathematics in WAEC, then do yourself a favour; download and study this syllabus. Get yourself a past questions booklet and practice daily for guaranteed success.

There will be two papers, Papers 1 and 2, both of which must be taken.

**PAPER 1:**

This first paper will consist of forty multiple-choice objective questions covering the entire syllabus.

Candidates will be required to answer all questions in 1 hour for 40 marks. The questions will be drawn from the sections of the syllabus as follows:

- Pure Mathematics – 30 questions
- Statistics and probability – 4 questions
- Vectors and Mechanics – 6 questions

**PAPER 2:**

Paper 2 will consist of two sections, Sections A and B, to be answered in 2 hours for 100 marks.

Section A will consist of eight compulsory questions that are elementary in type for 48 marks. The questions shall be distributed as follows:

- Pure Mathematics 4 questions
- Statistics and Probability – 2 questions
- Vectors and Mechanics – 2 questions

Section B will consist of seven questions of greater length and difficulty put into three parts: parts I, II, and III as follows:

- Part I: Pure Mathematics – 3 questions
- Part II: Statistics and Probability – 2 questions
- Part III: Vectors and Mechanics – 2 questions

WAEC Further Mathematics Syllabus | ||

SN | TOPICS | OBJECTIVES |

PAPER 1: PURE MATHEMATICS | ||

1 | SETS | (i) Idea of a set defined by a property, Set notations and their meanings. (ii) Disjoint sets, Universal set and complement of set (iii) Venn diagrams, Use of sets And Venn diagrams to solve problems. (iv) Commutative and Associative laws, Distributive properties over union and intersection. |

2 | SURDS | Surds of the form a/√b , a√b and a+b√n where a is rational, b is a positive integer and n is not a perfect square. |

3 | BINARY OPERATION | Properties: Closure, Commutativity, Associativity and Distributivity, Identity elements and inverses. |

4 | LOGICAL REASONING | (i) Rule of syntax: true or false statements, rule of logic applied to arguments, implications and deductions. (ii) The truth table |

5 | FUNCTIONS | (i) Domain and co-domain of a function. (ii) One-to-one, onto, identity and constant mapping; (iii) Inverse of a function. (iv) Composite of functions |

6 | POLYNOMIAL FUNCTIONS | (i) Linear Functions, Equations and Inequality (ii) Quadratic Functions, Equations and Inequalities (iii) Cubic Functions and Equations |

7 | RATIONAL FUNCTIONS | (i) Rational functions of the form (ii) Resolution of rational functions into partial fractions. |

8 | INDICES AND LOGARITHMIC FUNCTIONS | (i) Indices (ii) Logarithms |

9 | PERMUTATIONS AND COMBINATIONS | (i) Simple cases of arrangements (ii) Simple cases of selection of objects |

10 | BINOMIAL THEOREM | Expansion of (a + b)n . Use of (1+x)n ≈1+nx for any rational n, where x is sufficiently small |

11 | SEQUENCES AND SERIES | Expansion of (a + b)n . Use of (1+x)n ≈1+nx for any rational n, where x is sufficiently small |

12 | MATRICES AND LINEAR TRANSFORMATION | (i) Matrices (ii) Determinants (iii) Inverse of 2 x 2 Matrices (iv) Linear Transformation |

13 | TRIGONOMETRY | (i) Trigonometric Ratios and Rules (ii) Compound and Multiple Angles. (iii) Trigonometric Functions and Equations |

14 | CO-ORDINATE GEOMETRY | (i) Straight Lines (ii) Conic Sections |

15 | DIFFERENTIATION | (i) The idea of a limit (ii) The derivative of a function (iii)Differentiation of polynomials (iv) Differentiation of trigonometric Functions (v) Product and quotient rules. Differentiation of implicit functions such as ax2 + by2 = c ** (vi) Differentiation of Transcendental Functions (vii) Second order derivatives and Rates of change and small changes (∆x), Concept of Maxima and Minima |

16 | INTERGRATION | (i) Indefinite Integral (ii) Definite Integral (iii) Applications of the Definite Integral |

PAPER II: STATISTICS AND PROBABILITY | ||

17 | STATISTICS | (i) Tabulation and Graphical representation of data (ii) Measures of location (iii) Measures of Dispersion (iv)Correlation |

18 | PROBABILITY | (i) Meaning of probability. (ii) Relative frequency. (iii) Calculation of Probability using simple sample spaces. (iv) Addition and multiplication of probabilities. (v) Probability distributions. |

PAPER III: VECTORS AND MECHANICS | ||

19 | VECTORS | (i) Definitions of scalar and vector Quantities. (ii) Representation of Vectors. (iii) Algebra of Vectors. (iv) Commutative, Associative and Distributive Properties. (v) Unit vectors. (vi) Position Vectors. (vii) Resolution and Composition of Vectors. (viii) Scalar (dot) product and its application. **(ix) Vector (cross) product and its application. |

20 | STATICS | (i) Definition of a force. (ii) Representation of forces. (iii) Composition and resolution of coplanar forces acting at a point. (iv) Composition and resolution of general coplanar forces on rigid bodies. (v) Equilibrium of Bodies. (vi) Determination of Resultant. (vii) Moments of forces. (viii) Friction. |

21 | DYNAMICS | (i) The concepts of motion (ii) Equations of Motion (iii) The impulse and momentum equations: **(iv) Projectiles. |

- T.R Moses Spectrum New Further Further-mathematics (Scholastic Series).
- Tuttuh Adegun M.R. et al Bounty Press LTD. New Further Further-mathematics Project. 1 – 3
- Ivowi et-al. Further mathematics (NERDC)

How long is the WAEC Further Mathematics exam?

The duration of the WAEC Further Mathematics exam is usually three hours. You will have to write papers 1 and 2 within the stipulated time.

What type of questions can I expect in the exam?

The exam includes multiple-choice objective questions and theory questions that will test your understanding of the subject and your ability to apply them.

Are calculators allowed in the exam?

Yes, you will be given an official calculator by the West African Examination Council(WAEC). This is the only calculator you are expected to use during the exam.

How should I manage my time during the exam?

Time management is a very important skill for every exam. To manage time well, ensure you do not spend so much time on a particular question. Once you’re not sure of a question, leave it and answer others then come back to review and cross-check your work

How can I prepare for the WAEC Further Mathematics exam?

Practice, practice, practice. Study the syllabus, recommended textbooks, notes, and past questions together. You can also ask your teacher or tutor questions on topics you don’t understand

How can a candidate collect his/her certificate?

School candidates are to collect their certificate from the school where they write the exam.

Private candidates are to obtain their certificates from WAEC directly.

Are there any specific topics that are heavily tested in the exam?

All the topics in the syllabus above are important and you will be tested on them.

How should I manage my time during the exam?

Time management is a very important skill for every exam. To manage time well, ensure you do not spend so much time on a particular question. Once you’re not sure of a question, leave it and answer others then come back to review and cross-check your work

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