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A-Level Further Pure Maths 2- Matrices PPT
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A-Level Further Pure Maths 2- Matrices PPT

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The resource covers: Formulate a problem involving the solution of 3 linear simultaneous equations in 3 unknowns as a problem involving the solution of a matrix equation, or vice versa* Prove de Moivre’s theorem for a positive integer exponent Understand the cases that may arise concerning the consistency or inconsistency of 3 linear simultaneous equations, relate them to the singularity or otherwise of the corresponding matrix Solve consistent systems, and interpret geometrically in terms of lines and planes – to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle Understand the terms ‘characteristic equation’, ‘eigenvalue’ and ‘eigenvector’, as applied to square matrices Find eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices express a square matrix in the form QDQ^–1, where D is a diagonal matrix of eigenvalues and Q is a matrix whose columns are eigenvectors, and use this expression Use the fact that a square matrix satisfies its own characteristic equation.
A-Level Further Pure Maths 2-Integration Lesson Booklet + Answers
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A-Level Further Pure Maths 2-Integration Lesson Booklet + Answers

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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.
A-Level Further Pure Maths 2-Integration PPT
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A-Level Further Pure Maths 2-Integration PPT

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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.
A-Level Further Mechanics - Circular Motion PPT
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A-Level Further Mechanics - Circular Motion PPT

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Understand the concept of angular speed for a particle moving in a circle, and use the relation v = rw Understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae r w^2 and v^2/r Solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed Solve problems which can be modelled by the motion of a particle in a vertical circle without loss of energy. Find a normal contact force or the tension in a string, locating points at which these are zero, and conditions for complete circular motion.
A-Level Further Maths-Rational Functions and Graphs Booklet + Answers
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A-Level Further Maths-Rational Functions and Graphs Booklet + Answers

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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)
A-Level Further Mechanics - Hooke’s Law PPT and Lesson Booklet
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A-Level Further Mechanics - Hooke’s Law PPT and Lesson Booklet

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Use Hooke’s law as a model relating the force in an elastic string or spring to the extension or compression, and understand the term modulus of elasticity Use the formula for the elastic potential energy stored in a string or spring Solve problems involving forces due to elastic strings or springs, including those where considerations of work and energy are needed
A-Level Further Maths-Vectors PPT
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A-Level Further Maths-Vectors PPT

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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.
A-Level Further Maths-Matrices PPT
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A-Level Further Maths-Matrices PPT

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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
A-Level Further Mechanics-Circular Motion PPT and Lesson Booklets
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A-Level Further Mechanics-Circular Motion PPT and Lesson Booklets

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Understand the concept of angular speed for a particle moving in a circle, and use the relation v = rw Understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae r w^2 and v^2/r Solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed Solve problems which can be modelled by the motion of a particle in a vertical circle without loss of energy. Find a normal contact force or the tension in a string, locating points at which these are zero, and conditions for complete circular motion.
A-Level Further Mechanics - Circular Motion Booklet + Answers
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A-Level Further Mechanics - Circular Motion Booklet + Answers

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Understand the concept of angular speed for a particle moving in a circle, and use the relation v = rw Understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae r w^2 and v^2/r Solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed Solve problems which can be modelled by the motion of a particle in a vertical circle without loss of energy. Find a normal contact force or the tension in a string, locating points at which these are zero, and conditions for complete circular motion.
A-Level Further Mechanics – Equilibrium of a Rigid Body PPT and Lesson Booklet
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A-Level Further Mechanics – Equilibrium of a Rigid Body PPT and Lesson Booklet

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Calculate the moment of a force about a point Use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry Use given information about the position of the centre of mass of a triangular lamina and other simple shapes Determine the position of the centre of mass of a composite body by considering an equivalent system of particles Use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this Solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.
A-Level Further Mechanics - Equilibrium of a Rigid Body Booklet + Answers
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A-Level Further Mechanics - Equilibrium of a Rigid Body Booklet + Answers

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Calculate the moment of a force about a point Use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry Use given information about the position of the centre of mass of a triangular lamina and other simple shapes Determine the position of the centre of mass of a composite body by considering an equivalent system of particles Use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this Solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.
A-Level Further Mechanics - Equilibrium of a Rigid Body PPT
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A-Level Further Mechanics - Equilibrium of a Rigid Body PPT

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Calculate the moment of a force about a point Use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry Use given information about the position of the centre of mass of a triangular lamina and other simple shapes Determine the position of the centre of mass of a composite body by considering an equivalent system of particles Use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this Solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.
A-Level Further Mechanics – Momentum PPT and Lesson Booklet
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A-Level Further Mechanics – Momentum PPT and Lesson Booklet

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Recall Newton’s experimental law and the definition of the coefficient of restitution, the property 0 ≤ e ≤ 1, and the meaning of the terms ‘perfectly elastic’ (e = 1) and ‘inelastic’ (e = 0) Use conservation of linear momentum and/or Newton’s experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.
A-Level Further Mechanics - Momentum PPT
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A-Level Further Mechanics - Momentum PPT

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Recall Newton’s experimental law and the definition of the coefficient of restitution, the property 0 ≤ e ≤ 1, and the meaning of the terms ‘perfectly elastic’ (e = 1) and ‘inelastic’ (e = 0) Use conservation of linear momentum and/or Newton’s experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.
A-Level Further Mechanics Momentum Booklet + Answers
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A-Level Further Mechanics Momentum Booklet + Answers

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Recall Newton’s experimental law and the definition of the coefficient of restitution, the property 0 ≤ e ≤ 1, and the meaning of the terms ‘perfectly elastic’ (e = 1) and ‘inelastic’ (e = 0) Use conservation of linear momentum and/or Newton’s experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.
A-Level Further Statistics - Continuous Random Variables Lesson Worksheet + Answers
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A-Level Further Statistics - Continuous Random Variables Lesson Worksheet + Answers

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Use a probability density function which may be defined piecewise Use the general result E(g(x)) =∫f(x)g(x) dx where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X Understand and use the relationship between the probability density function (PDF) and the cumulative distribution function (CDF), and use either to evaluate probabilities or percentiles Use cumulative distribution functions (CDFs) of related variables in simple cases e.g. given the CDF of a variable X, find the CDF of a related variable Y, and hence its PDF, e.g. where Y = X^ 3.
A-Level Further Mechanics -Circular Motion Lesson Worksheet + Answers
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A-Level Further Mechanics -Circular Motion Lesson Worksheet + Answers

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Understand the concept of angular speed for a particle moving in a circle, and use the relation v = rw Understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae r w^2 and v^2/r Solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed Solve problems which can be modelled by the motion of a particle in a vertical circle without loss of energy. Find a normal contact force or the tension in a string, locating points at which these are zero, and conditions for complete circular motion.
A-Level Further Mechanics-Motion of a Projectile PPT and Lesson Booklets + Answers
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A-Level Further Mechanics-Motion of a Projectile PPT and Lesson Booklets + Answers

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Model the motion of a projectile as a particle moving with constant acceleration and understand any limitations of the model Use horizontal and vertical equations of motion to solve problems on the motion of projectiles, including finding the magnitude and direction of the velocity at a given time or position, the range on a horizontal plane and the greatest height reached Derive and use the Cartesian equation of the trajectory of a projectile, including problems in which the initial speed and/or angle of projection may be unknown.