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Different forms of complex numbers (Cartesian and modulus-argument) and how to convert

Loci of circles and half lines

Arithmetic with complex numbers

Timeframe

September - October

Key vocabulary

Word/phrase

Definition

Modulus

Length of the line segment drawn from the origin of the complex plane to the point representing the complex number in the Argand diagram

Argument

Angle that the line segment drawn from the origin of the complex plane to the point representing the complex number in the Argand diagram makes with the real axis

Imaginary number

A number that is expressed in terms of the square root of a negative number

Complex number

A number made up of real and imaginary parts

Radian

A measure of angle such that 2π radians is equal to a full turn (360 degrees)

Finding asymptotes, turning points, intercepts and limits

Solving rational inequalities graphically

Conversion between polar and Cartesian coordinates

Sketching equations given as polar functions

Graphs of conic sections - parabolas, elipses and hyperbolae

Equations and graphs of linear transformations of conic sections

Know the exponential form of hyperbolic functions

Sketching graphs of hyperbolic functions

Timeframe

September - October

Key vocabulary

Word/phrase

Definition

Intercept

The value at which a give function crosses the x axes

Asymptote

A line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

Conic section

These functions can be found by cuting into a cone. Conic sections incolude: circles, parabolas, ellipses and hyperboae

Pole

When working in polar coordinates the pole is the point (0,0)

Parabola

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this formshape.

Wider reading

Aeronautical engineering
Cartography
Analysis of performance in sport
Birch and Swinerton-Dyer conjecture

Differentiation of inverse trigonometric functions

Differentiation of hyperbolic functions

Integration by splitting expressions into partial fractions

Use of reduction formulae

Integration of polar functions to find areas and arc lengths

Timeframe

September - October

Key vocabulary

Word/phrase

Definition

Improper integral

A definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration

Reduction formulae

An integral which is of the same type as the given integral but of a lower degree. The repeated application of the reduction formula helps us to evaluate the given integral.

Archimedean spiral

The locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity

Integrate

A method of adding or summing up the parts to find the whole. It is a reverse process of differentiation

Differentiate

The process of finding the rate of change of a function

Differentiation of inverse trigonometric functions

Differentiation of hyperbolic functions

Integration by splitting expressions into partial fractions

Use of reduction formulae

Integration of polar functions to find areas and arc lengths

Timeframe

September - October

Key vocabulary

Word/phrase

Definition

Improper integral

A definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration

Reduction formulae

An integral which is of the same type as the given integral but of a lower degree. The repeated application of the reduction formula helps us to evaluate the given integral.

Archimedean spiral

The locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity

Integrate

A method of adding or summing up the parts to find the whole. It is a reverse process of differentiation

Differentiate

The process of finding the rate of change of a function

Calculating key statistics of mixed random variables

Rectangular and exponential probability models to calculate probabilities

Understand and use the relationship between the probability distribution function and the cummulative distribution function

Derive the formulae for mean and variance of rectangular and exponential random variables

Timeframe

September - October

Key vocabulary

Word/phrase

Definition

Cummulative

Increasing or increased in quantity, degree, or force by successive additions

Dummy variable

A variable used as a place holder when the primary variable is utilised in several ways throughout the calculation. The dummy variable enables the calculation to occur without misunderstanding of the multiple use.

Probability density

The density of probability rather than the probability mass

Application of energy equations to vertical circular motion

Timeframe

September - October

Key vocabulary

Word/phrase

Definition

Conical pendulum

A weight (or bob) fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum; however, instead of swinging back and forth, the bob of a conical pendulum moves at a constant speed in a circle with the string (or rod)

Radial components

The aspects of motion moving radially in an outward direction from point O

Transverse components

The aspects of motion moving tangentially to the direction of movement

Energy equation

The mathematical formulation of the law of conservation of energy.