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Autumn Term first half term Topics
Algebra and Functions
Indices
Surds
Quadratic Equations
Graphs of Quadratic Functions
Simultaneous Equations & Inequalities
Coordinate Geometry
Indices
Basic Index Notation
The Eight Laws of Indices
Simplifying Equations & Expressions involving Indices
Quadratic Equations
Standard form a times the square of x add b times x add c equals zero
The Roots of a Quadratic Equation are the solutions of the equation
The roots are found by;
Factorising
Completing the square
Using the Quadratic Formula
The Discriminant the square of b subtract the product of 4, a and c
Graphs of Quadratic Functions
Graph is non linearand has a turning point
Shape of curve entirely determined by the value of a
Position of turning point determined by the valuess of a, b, c
x coordinate of turning point is at the mean of the roots
Sketching Quadratic graphs
Complete the square of the standard form equation
Write it in the form y add k equals the product of a and the square of the sum x add h
The coordinates of the turning point are (-k, -h)
Set y equal to zero and solve for x to get the roots
Check that the mean of the roots is the x coordinate of the turning point
The y intercept is the value of c
Draw a pair of axese and mark the roots, the turning point and y intercept then sketch a smooth curve through those points
Coordinate Geometry of the straight line
Find the equation to a line given its gradient and a point through which it passes
Find the equation to a line given two points on it
Product of the gradients of two lines intersecting at right angles
Find the length of a line segment given the coordinates of its end points
Find the mid point of a line segment given the coordinates of its end points
Coordinate geometry of the circle
The equation of a circle centred at (a, b)
The equation of a circle centred at the origin
Find the equation of a circle given the end points of a diameter
Determine whether a line is a tangent, a chord or does not touch a circle of given equation