Matrices and Transformations
Students will know how to find the matrix associated with a linear transformation and vice versa; know about the matrices that represent reflection in both the x and y axes; know about the matrices that represent rotations centre the origin; know about the matrices that represent enlargements centre the origin and stretches parallel to the x𝑥 and y𝑦 axes; know about the 3×3 matrices that represent reflections in x=0, y=0 or z=0; know about the 3×3 matrices that represent rotations through multiplies of 90° about the x𝑥, y𝑦 or z𝑧 axes and that the matrix representing a combined transformation can be found by matrix multiplication: the transformation represented by A followed by the transformation represented by B is represented by the matrix BA; be able to find invariant points for a linear transformation and be able to find invariant lines for a linear transformation. Assessment will be via continuous scrutiny of class and homework.
Proof by Induction
Students will know how to construct and present a proof using mathematical induction for sums of series, powers of matrices and divisibility results. Assessment will be via continuous scrutiny of class and homework.
Vectors and 3-D Space
Students will know how to calculate the scalar product of two vectors; be able to use the scalar product to find the angle between two vectors; find the vector equation of a line in three dimensions in vector form and the Cartesian equation of a line in three dimensions; calculate the angle between two lines using the scalar product; find the point of intersection of two straight lines given in vector form; know that two lines in three dimensions may either intersect, be parallel or be skew; be able to form and use vector equation of a plane and the Cartesian equation of a plane; convert between the different forms for the equation of a plane; know that a vector which is perpendicular to a plane is perpendicular to any vector in the plane; be able to find the angle between two planes by finding the angle between their normal; find the angle between a line and a plane; find the point of intersection of a line and a plane; find the perpendicular distance from a point to a plane; find the perpendicular distance from a point to a line and find the perpendicular distance between two lines. Assessment will be via continuous scrutiny of class and homework.
Work, Energy and Power
Students will be able to find the work done by a force; calculate the kinetic energy of a moving object; calculate the gravitational potential energy of an object relative to a defined zero level; know about the principle of conservation of energy and about the work-energy principle; that power is the rate of doing work and be able to solve problems involving power. Assessment will be via continuous scrutiny of class and homework.
Impulse and Momentum
Students will know what is meant by momentum and impulse; about the connection between impulse and momentum; be able to solve problems involving collisions using the law of conservation of momentum; know about Newton’s law of restitution and about the coefficient of restitution and be able to solve problems involving collisions by using conservation of linear momentum and Newton’s experimental law. Assessment will be via continuous scrutiny of class and homework.