A ‘Teach Further Maths’ Resource 37 slides Lesson Objectives: To understand what is meant by an ‘imaginary number’. To be able to calculate with powers of i. To understand what is meant by a ‘complex number’. To be able to solve any quadratic equation. To know the condition for a quadratic equation to have complex conjugate solutions. To understand what is meant by an ‘Argand Diagram’. To be able to perform simple arithmetic with complex numbers. To be able to equate real and imaginary parts to solve some problems involving complex numbers.

A ‘Teach Further Maths’ Resource 18 Slides To write a complex number in exponential form. To multiply and divide complex numbers in exponential form.

A ‘Teach Further Maths’ Resource 45 Slides To recall the concept of a ‘limit’. To be able to use MacLaurin’s series expansions to find certain limits. To know and use two special limits

A ‘Teach Further Maths’ Resource 35 Slides To recall the derivatives of hyperbolic functions. To be able to integrate hyperbolic functions. To recognise integrals which integrate to inverse hyperbolic functions.

A ‘Teach Further Maths’ Resource 17 Slides To understand the Method of Differences. To be able to use the Method of Differences to prove results for the summation of certain series.

A ‘Teach Further Maths’ Resource 38 Slides To understand the chain rule when using first and second order derivatives. Use a substitution in conjunction with the chain rule to solve certain second order differential equations.

A ‘Teach Further Maths’ Resource 49 Slides To understand the method of Mathematical Induction. To use Induction to prove results for summation of series. To use Induction to prove results from other areas.

A ‘Teach Further Maths’ Resource 31 Slides To understand what is meant by hyperbolic functions. To be able to sketch graphs of hyperbolic functions. To be able to establish hyperbolic identities. To understand Osborn’s Rule.

A ‘Teach Further Maths’ Resource 22 Slides To find the area of surface of revolution for curves given in Cartesian form. To find the area of surface of revolution for curves given in Parametric form.

A ‘Teach Further Maths’ Resource 47 Slides To understand and use Sigma notation. To be able to derive and use the formula for ∑r. To be able to use the formulae for ∑r2 and ∑r3. To be able to solve series questions requiring algebraic manipulation.

A ‘Teach Further Maths’ Resource To be able to model certain situations using 1st order differential equations. To be able to model certain situations using coupled 1st order differential equations. (64 Slides)

A ‘Teach Further Maths’ Resource To be able to model simple harmonic motion using 2nd order differential equations. To be able to model damped (and forced) oscillations using 2nd order differential equations. (38 Slides)

A ‘Teach Further Maths’ Resource To be able to model certain situations using 1st order differential equations. To be able to model certain situations using coupled 1st order differential equations. (64 Slides)

A ‘Teach Further Maths’ Resource To be able to model simple harmonic motion using 2nd order differential equations. To be able to model damped (and forced) oscillations using 2nd order differential equations. (38 Slides)

A ‘Teach Further Maths’ Resource To be able to consider determinants of 2x2 matrices and 3x3 matrices geometrically. (30 Slides)

A ‘Teach Further Maths’ Resource To recall previously encountered partial fractions methods (i.e. linear denominators and repeated linear denominators) To be able to find partial fractions when there is a quadratic term in the denominator. To be able to integrate expression using partial fractions. (47 Slides)

A ‘Teach Further Maths’ Resource To understand and use the Mean Value Theorem for integration. To understand the term ‘Root Mean Square Value’ and know how to calculate it for certain functions. (37 Slides)