DeMoivre's Theorem and Applications 2 (A-Level Further Maths)

DeMoivre's Theorem and Applications 2 (A-Level Further Maths)

A 'Teach Further Maths' Resource 57 Slides To find the cube roots of unity. To illustrate these cube roots on an Argand Diagram. To solve problems relating to the cube roots of unity. To find the nth roots of unity. To illustrate these nth roots on an Argand Diagram. To find the nth roots of any number.
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Roots of Polynomials (A-Level Further Maths)

Roots of Polynomials (A-Level Further Maths)

A 'Teach Further Maths Resource 65 slides To know the relationship between the roots of a polynomial equation and its coefficients. To be able to find polynomial equations with related roots. To know and use the result for the sums of the squares of roots.
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Trig. Ratios of Any Angle

Trig. Ratios of Any Angle

An excellent resource that shows alternative approaches to solving simple trig. ratio problems. Each problem is solved using (i) the CAST diagram (ii) a graphical approach (iii) a quick method. The PowerPoint begins with an explanation of how the CAST diagram works. These slides are aimed at the more inquisitive student and are not compulsory.
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Further Vectors 1 (A-Level Further Maths)

Further Vectors 1 (A-Level Further Maths)

A 'Teach Further Maths' Resource 43 Slides To be able to find the distance between 2 points in 3 dimensions. To be able to derive and use a useful formula for a point dividing a line in a given ratio. To understand when 2 (or more) vectors are parallel. To be able to find vector equation of a line in vector form. To be able to find vector equation of a line in Cartesian form. To be able to convert vector equations from vector form to Cartesian form and vice versa. To understand what direction ratios are.
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Further Vectors 2 (A-Level Further Maths)

Further Vectors 2 (A-Level Further Maths)

A 'Teach Further Maths' Resource 66 Slides To understand ‘scalar product’ and be able to calculate it. To be able to find the angle between two vectors using the scalar product To use the scalar product to show whether two lines are perpendicular or not. To be able to prove whether or not two lines intersect and, if they do, find their point of intersection. To understand what is meant when we say that 2 lines are ‘skew’. To be able to prove whether or not 2 lines are skew. To be able to solve simple vector problems involving scalar product and other simple vector properties.
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Further Vectors 4 (A-Level Further Maths)

Further Vectors 4 (A-Level Further Maths)

A 'Teach Further Maths Resource: 55 Slides To be able to find angle between a line and a plane To be able to find angle between 2 planes. To be able to find the equation of the line of intersection of 2 planes.
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Further Vectors 3 (A-Level Further Maths)

Further Vectors 3 (A-Level Further Maths)

A 'Teach Further Maths' Resource: 51 Slides To be able to find the Equation of a Plane in Scalar Product form. To be able to find the Equation of a Plane in Cartesian form. To be able to find the Equation of a Plane in Parametric form. To be able to find the Perpendicular Distance from a Point to a Plane.
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Matrix Solution of Simultaneous Equations 2

Matrix Solution of Simultaneous Equations 2

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’.
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Matrices and Linear Transformations (A-Level Further Maths)

Matrices and Linear Transformations (A-Level Further Maths)

A Teach Further Maths' Resource 73 Slides To understand what is meant by a ‘transformation’. To understand what is meant by a ‘linear transformation’. To be able to show that a given transformation is linear. To understand what is meant by an ‘inverse transformation’. To be able to find the inverse of a given linear transformation. To be able to find matrices that represent given linear transformations. To be able to find matrices that represent composite linear transformations. To understand what is meant by ‘invariant points’ and ‘invariant lines’. To be able to find invariant points/lines for a given transformation matrix. To be able to find matrices representing inverse linear transformations. To be able to find matrices representing inverse of composite linear transformations. To understand how to find the transpose of a matrix.
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Parabolas, Ellipses and Hyperbolas (A-Level Further Maths)

Parabolas, Ellipses and Hyperbolas (A-Level Further Maths)

A 'Teach Further Maths' Resource 70 Slides To be able to recognise the equations for simple parabolas, ellipses and hyperbolas. To be able to sketch their graphs. To be able to perform simple transformations on these curves. To be able to find the equations of the asymptotes for simple hyperbolas.
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Calculus (A-Level Maths)

Calculus (A-Level Maths)

A 'Teach Further Maths' Resource 31 Slides To be able to find the gradient of a curve at any point from first principles.
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Inverse Matrices and Determinants (A-Level Further Maths)

Inverse Matrices and Determinants (A-Level Further Maths)

A 'Teach Further Maths' Resource 54 Slides To understand what is meant by the ‘inverse’ of a matrix. To understand what is meant by the ‘determinant’ of a matrix. To be able to find the determinant of a 2x2 or 3x3 matrix. To be able to find the inverse of a 2x2 or 3x3 matrix. To be able to consider determinants of 2x2 matrices and 3x3 matrices geometrically.
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Roots of Polynomials (A-Level Further Maths)

Roots of Polynomials (A-Level Further Maths)

A 'Teach Further Maths Resource 65 slides To know the relationship between the roots of a polynomial equation and its coefficients. To be able to find polynomial equations with related roots. To know and use the result for the sums of the squares of roots.
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Numerical Methods (A-Level Maths/Further Maths)

Numerical Methods (A-Level Maths/Further Maths)

A 'Teach Further Maths' Resource 59 Slides To be able to solve equations of the form f(x) =0 using the method of interval bisection. To be able to solve equations of the form f(x) =0 using the method of linear interpolation. To be able to solve equations of the form f(x) =0 using the Newton-Raphson method. To be able to solve equations of the form dy/dx = f(x) using Euler's 'Step by Step' Method.
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DeMoivre's Theorem and Applications 2 (A-Level Further Maths)

DeMoivre's Theorem and Applications 2 (A-Level Further Maths)

A 'Teach Further Maths' Resource 57 Slides To find the cube roots of unity. To illustrate these cube roots on an Argand Diagram. To solve problems relating to the cube roots of unity. To find the nth roots of unity. To illustrate these nth roots on an Argand Diagram. To find the nth roots of any number.
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DeMoivre's Theorem and Applications 1 (A-Level Further Maths)

DeMoivre's Theorem and Applications 1 (A-Level Further Maths)

A 'Teach Further Maths' Resource 43 Slides To recall how to multiply and divide complex numbers in Modulus-Argument form. To understand DeMoivre’s Theorem. To use DeMoivre’s Theorem to find powers of complex numbers. To use DeMoivre’s Theorem to establish trigonometric identities.
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Composite Geometric Transformations Using Matrices (A-Level Further Maths)

Composite Geometric Transformations Using Matrices (A-Level Further Maths)

A 'Teach Further Maths' Resource 28 Slides To recall the rules of simple transformations. To be able to find matrices representing simple composite transformations. To know that composite transformation matrices are pre-multiplied. To be able to describe simple composite transformations represented by some matrices.
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