## Description

These lesson notes cover the following topics for SS2 First, Second and Third Term Further Mathematics:

**FIRST TERM**

WEEK |
TOPIC |

1 | Finding quadratic equation with given sum and product of roots, conditions for equal roots, real roots and no root |

2 | Tangents and Normals to Curves |

3 | Polynomials ;definition, basic operations + , x , – , ;– |

4 | Polynomials ( Continued) factorization |

5 | Cubic Equation , roots of cubic equations |

6 | Review and Test |

7 | Logical Reasoning ; fundamental issues and definitions and theorem proving |

8 | Trigonometric Function , six trig functions of angles of any magnitude ( sine, cosine,tangent,secant, cosecant, cotangent) |

9 | Relationship between graph of trigonometric ratios such as sin x and sin 2x, graphs of y= a sin (bx) + c , y = a cos (bx) + c , y = a tan (bx) + c |

10 | Graphs of inverse by ratio and equation of simpletrgonometric identities |

11 | Revision |

** **

**REFERENCES**

- Further Mathematics Project 1 by TuttuhAdegun
- Further Mathematics Project 2 by TuttuhAdegun
- Additional Mathematics by Godman

**SECOND TERM**

1. Differentiation: Limits of Function and First Principle, Differentiation of Polynomial

2. Differentiation (Continued): Rules of Differentiation

3. Differentiation of Transcendents: Derivative of Trigonometric Functions and Exponential Functions.

4. Application of Differentiation: Rate of Change, Equation of Motion, Maximum and Minimum Points and Values of Functions.

5. Conic Sections: Equation of Circles, General Equation of Circles, Finding Centre and Radius, Equation and Length of Tangents to a Circle.

6. Conic Sections: The Parabola, Hyperbola and Ellipse

7. Review of First Half Term

8. Statistics Probability: Sample Space, Event Space, Combination of Events, Independents and Dependent Events.

9. Permutation and Combination

10. Dynamics: Newton’s Laws of Motion

11. Work, Energy, Power, Impulse and Momentum

12. Revision and Examination.

REFERENCES

Further Mathematics Project 2 and 3.

**THIRD TERM**

1. Revision of Second Term Examination Questions.

2. Projectile: Trajectory of Projectile, Greatest Height Reached, Time of Flight, Range, and Projectile along Inclined Plane.

3. Binomial Expansion: Pascal Triangle Binomial Theorem of Negative, Positive and Fractional Power

4. Mechanics: Vectors in Two and Three Dimension. Scalar Product of Vectors inThree Dimension.

5 Vector or Cross Product on Three Dimension.Application of Cross Product Cross Product of Two Vectors.

6 Review of the Half Term Work.

7. Integration: Indefinite Integrals Concept, Different Methods of Integration.e.g (Algebraic and Trigonometric Substitution by Parts and Partial Fractions.

8. Integration Continued: Definite Integral, Area Under Curve.

9. Integration Continued: Application of Integration to Kinematics Volumes of Solids at Revolution and Trapezium Rule.

10. Correlation and Regression: Concept, Scatter Diagram, Regression Line, Coefficient of Regression, Rank Correlation and Product Moment Correlation Coefficient.

11. Revision.

REFERENCES

Further Mathematics Project 2 and 3.

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