A ‘Teach Further Maths’ Resource 36 Slides To be able to differentiate hyperbolic functions. To be able to sketch graphs of hyperbolic functions. To be able to differentiate inverse hyperbolic functions. To be able to sketch graphs of inverse hyperbolic functions. To write inverse hyperbolic functions in logarithmic form.

A ‘Teach Further Maths’ Resource 30 Slides To be able to solve certain first order differential equations using a complementary function and a particular integral. To use a change of variable to solve some first and second order differential equations.

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 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 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 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 be able to derive the formulae for volumes of revolution about the coordinates axes To be able to calculate volumes of revolution about the coordinates axes. To be able to calculate more complicated volumes of revolution about the coordinates axes. (69 Slides)

A ‘Teach Further Maths’ Resource To be able to find the vector product of two vectors. To understand various properties of the vector product. To be able to use the vector product to find perpendicular vectors. To be able to find certain areas and volumes using the vector product. (52 Slides)

A ‘Teach Further Maths’ Resource To know and use the basic rules for simplifying determinants. To be able to factorise determinants. (57 Slides)

A ‘Teach Further Maths’ Resource To be able to sum certain series using DeMoivre’s Theorem. (39 Slides)

A ‘Teach Further Maths’ Resource To be able to solve geometric problems using DeMoivre’s Theorem. (57 Slides)

A ‘Teach Further Maths’ Resource To be able to approximate the area under a curve using the Mid-Ordinate Rule. To be able to approximate the area under a curve using Simpson’s Rule. (51 Slides)

A ‘Teach Further Maths’ Resource To be able to derive and use reduction formulae for integration. (47 Slides)

A ‘Teach Further Maths’ Resource To be able to use L’Hôpital’s Rule to evaluate certain limits of indeterminate form. (36 Slides)

A ‘Teach Further Maths’ Resource: 50 Slides To be able to interpret geometrically the solution (and failure of solution) of 3 simultaneous linear equations: Students should be able to interpret, on analysis of the 3 equations, whether the 3 planes meet in a point meet in a line (forming a sheaf) form a prism are all parallel are such that 2 of the 3 planes are parallel. Students should be familiar with the terms ‘dependent‘, ‘consistent’ and ‘inconsistent’.

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 be able to apply the Rational Root Theorem to identify factors of polynomials. To be able to use Descartes’ Rule of Signs to identify the nature (signs) of roots of polynomials. To be able to solve inequalities involving cubic and quartic functions. (41 Slides)