The resource covers: Integration hyperbolic functions and inverses Derive and use reduction formulae for the evaluation of definite integrals Approximating area under a curve using area of rectangles and use rectangles to estimate or set bounds for the area under a curve or to derive inequalities or limits concerning sums Use integration to find arc lengths for curves with equations in Cartesian coordinates, including the use of a parameter, or in polar coordinates Use integration to find surface areas of revolution about one of the axes for curves with equations in Cartesian coordinates, including the use of a parameter.

The resource covers: Integration hyperbolic functions and inverses Derive and use reduction formulae for the evaluation of definite integrals Approximating area under a curve using area of rectangles and use rectangles to estimate or set bounds for the area under a curve or to derive inequalities or limits concerning sums Use integration to find arc lengths for curves with equations in Cartesian coordinates, including the use of a parameter, or in polar coordinates Use integration to find surface areas of revolution about one of the axes for curves with equations in Cartesian coordinates, including the use of a parameter.

The resource covers Maclaurin’s series

The resource covers differentiation of inverse trigonometric functions

The resource covers the differentiation of parametric equations

The resource covers the differentiation of implicit functions

The resource covers the differentiating hyperbolic functions and inverses

The resource covers : Differentiating hyperbolic functions and inverses Differentiation implicit functions Differentiating parametric equations Differentiating inverse of trigonometric functions Maclaurin series

The resource covers : Differentiating hyperbolic functions and inverses Differentiation implicit functions Differentiating parametric equations Differentiating inverse of trigonometric functions Maclaurin series

The resource covers : Differentiating hyperbolic functions and inverses Differentiation implicit functions Differentiating parametric equations Differentiating inverse of trigonometric functions Maclaurin series

Carry out operations of matrix addition, subtraction and multiplication, and recognise the terms zero matrix and identity (or unit) matrix Recall the meaning of the terms ‘singular’ and ‘non-singular’ as applied to square matrices and, for 2 x 2 and 3 x 3 matrices, evaluate determinants and find inverses of non-singular matrices understand and use the result, for non-singular matrices, (AB)^ –1 = B^ –1 A^-1 The notations det M for the determinant of a matrix M, and I for the identity matrix Understand the use of 2 x 2 matrices to represent certain geometric transformations in the x-y plane, in particular – understand the relationship between the transformations represented by A and A^–1 – recognise that the matrix product AB represents the transformation that results from the transformation represented by B followed by the transformation represented by A – recall how the area scale factor of a transformation is related to the determinant of the corresponding matrix – find the matrix that represents a given transformation or sequence of transformations Understand the meaning of ‘invariant’ as applied to points and lines in the context of transformations represented by matrices, and solve simple problems involving invariant points and invariant lines

Carry out operations of matrix addition, subtraction and multiplication, and recognise the terms zero matrix and identity (or unit) matrix Recall the meaning of the terms ‘singular’ and ‘non-singular’ as applied to square matrices and, for 2 x 2 and 3 x 3 matrices, evaluate determinants and find inverses of non-singular matrices understand and use the result, for non-singular matrices, (AB)^ –1 = B^ –1 A^-1 The notations det M for the determinant of a matrix M, and I for the identity matrix Understand the use of 2 x 2 matrices to represent certain geometric transformations in the x-y plane, in particular – understand the relationship between the transformations represented by A and A^–1 – recognise that the matrix product AB represents the transformation that results from the transformation represented by B followed by the transformation represented by A – recall how the area scale factor of a transformation is related to the determinant of the corresponding matrix – find the matrix that represents a given transformation or sequence of transformations Understand the meaning of ‘invariant’ as applied to points and lines in the context of transformations represented by matrices, and solve simple problems involving invariant points and invariant lines

Carry out operations of matrix addition, subtraction and multiplication, and recognise the terms zero matrix and identity (or unit) matrix Recall the meaning of the terms ‘singular’ and ‘non-singular’ as applied to square matrices and, for 2 x 2 and 3 x 3 matrices, evaluate determinants and find inverses of non-singular matrices understand and use the result, for non-singular matrices, (AB)^ –1 = B^ –1 A^-1 The notations det M for the determinant of a matrix M, and I for the identity matrix Understand the use of 2 x 2 matrices to represent certain geometric transformations in the x-y plane, in particular – understand the relationship between the transformations represented by A and A^–1 – recognise that the matrix product AB represents the transformation that results from the transformation represented by B followed by the transformation represented by A – recall how the area scale factor of a transformation is related to the determinant of the corresponding matrix – find the matrix that represents a given transformation or sequence of transformations Understand the meaning of ‘invariant’ as applied to points and lines in the context of transformations represented by matrices, and solve simple problems involving invariant points and invariant lines

Use the equation of a plane in any of the forms ax + by + cz = d or r.n = p or r = a + λb + μc and convert equations of planes from one form to another as necessary in solving problems Recall that the vector product a × b of two vectors can be expressed either as absinθn ̂ ,where n ̂ is a unit vector, or in component form ai+bj+ck Use equations of lines and planes, together with scalar and vector products where appropriate, to solve problems concerning distances, angles and intersections, including – determining whether a line lies in a plane, is parallel to a plane or intersects a plane, and finding the point of intersection of a line and a plane when it exists – finding the foot of the perpendicular from a point to a plane – finding the angle between a line and a plane, and the angle between two planes – finding an equation for the line of intersection of two planes – calculating the shortest distance between two skew lines – finding an equation for the common perpendicular to two skew lines.

Use the equation of a plane in any of the forms ax + by + cz = d or r.n = p or r = a + λb + μc and convert equations of planes from one form to another as necessary in solving problems Recall that the vector product a × b of two vectors can be expressed either as absinθn ̂ , where n ̂ is a unit vector, or in component form ai+bj+ck Use equations of lines and planes, together with scalar and vector products where appropriate, to solve problems concerning distances, angles and intersections, including – determining whether a line lies in a plane, is parallel to a plane or intersects a plane, and finding the point of intersection of a line and a plane when it exists – finding the foot of the perpendicular from a point to a plane – finding the angle between a line and a plane, and the angle between two planes – finding an equation for the line of intersection of two planes – calculating the shortest distance between two skew lines – finding an equation for the common perpendicular to two skew lines.

Use the equation of a plane in any of the forms ax + by + cz = d or r.n = p or r = a + λb + μc and convert equations of planes from one form to another as necessary in solving problems Recall that the vector product a × b of two vectors can be expressed either as absinθn, where n is a unit vector, or in component form ai+bj+ck Use equations of lines and planes, together with scalar and vector products where appropriate, to solve problems concerning distances, angles and intersections, including – determining whether a line lies in a plane, is parallel to a plane or intersects a plane, and finding the point of intersection of a line and a plane when it exists – finding the foot of the perpendicular from a point to a plane – finding the angle between a line and a plane, and the angle between two planes – finding an equation for the line of intersection of two planes – calculating the shortest distance between two skew lines – finding an equation for the common perpendicular to two skew lines.

Understand the relations between Cartesian and polar coordinates, and convert equations of curves from Cartesian to polar form and vice versa Sketch simple polar curves, for 0≤θ<2π or -π≤θ<π or a subset of either of these interval Recall the formula 1/2 ∫r^2 dθ for the area of a sector and use this formula in simple cases.

Understand the relations between Cartesian and polar coordinates, and convert equations of curves from Cartesian to polar form and vice versa Sketch simple polar curves, for 0≤θ<2π or -π≤θ<π or a subset of either of these interval Recall the formula 1/2 ∫r^2 dθ for the area of a sector and use this formula in simple cases.

Understand the relations between Cartesian and polar coordinates, and convert equations of curves from Cartesian to polar form and vice versa Sketch simple polar curves, for 0≤θ<2π or -π≤θ<π or a subset of either of these interval Recall the formula 1/2 ∫r^2 dθ for the area of a sector and use this formula in simple cases.

Sketch graphs of simple rational functions, including the determination of oblique asymptotes, in cases where the degree of the numerator and the denominator are at most 2 Show significant features of rational graphs, such as turning points, asymptotes and intersections with the axes. Determination of the set of values taken by the function, e.g. by the use of a discriminant. Understand and use relationships between the graphs of y = f(x), y^2 = f(x), y = 1/f(x) , y = If(x)I and y = f(IxI)