Straight line graphs. The graph of each of equations is a straight line: If an equation can be rearranged into the form y = mx +c, then its graph will be a straight line. ax +by= c can be rearranged as (which can be re-written as y = mx+c). Therefore vertical lines have equations have slope undefined form x =k . Hence graph depend on […]
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Category: Additional Maths
Kinematics
Kinematic is the branch of classical mechanics. describes the motion of points, objects and systems of groups of objects, without reference to the causes of motion. The symbol a stands for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object. The derivative of displacement with time is velocity […]
Binomial Theorem
Binomial theorems is another ways of expansion of two terms. Another way it is generalised form of expansion. Due to expansion of two term it is binomial. “What are the binomial coefficients?” . It shows how to calculate the coefficients in the expansion of (a + b) n. The symbol for a binomial coefficient nCr. As well as pascal […]
Volume of revolution
To get a solid of revolution we start out with a function, y=f (x), on an interval [a,b]. We then rotate this curve about a given axis to get the surface of the solid of revolution Volume of Revolution
Double angle trigonometric equation
Double angle equations are allowing the expression of trigonometric functions of angles equal to 2u in terms of u. The double angle formulas can simplify the functions and gives ease to perform more complex calculations. The double angle formulas are useful for finding the values of unknown trigonometric functions. Therefore in double angle equation we need to consider two rotation. […]
A Double angles identity
A Double angles identity is written2θ, for example, as sin 2θ, cos 2α, or tan 2x, where 2θ, 2α, and 2x. The angle measures and the assumption is that you mean sin(2θ), cos(2α), or tan(2x). Because tangent is equal to the ratio of sine and cosine . Therefor its identity comes from their double-angle identities. double angle identity
Double Angle trigonometric Identity
A Double angles identity is written2θ, for example, as sin 2θ, cos 2α, or tan 2x, where 2θ, 2α, and 2x. The angle measures and the assumption is that you mean sin(2θ), cos(2α), or tan(2x). Because tangent is equal to the ratio of sine and cosine . Therefor its identity comes from their double-angle identities. Double angle
Maxima and Minima
Maximum and minimum of Points of Inflection. The value f ‘(x) is the gradient at any point but often we want to find the Turning or Stationary Point (Maximum and Minimum points) or Point of Inflection These happen where the gradient is zero, f ‘(x) = 0. Critical Points include Turning points and Points where f ‘ (x) does […]
Equation of Tangent and Normal
Tangents to a curve are a line that touches the curve at one point and has the same slope as the curve at that point. A normal to a curve is a line perpendicular to a tangent to the curve. Tangent and Normal
Trigonometric equations
Trigonometric equations use both the reference angles and trigonometric identities The general method of solving an equation is to convert it into the form of one ratio only. Hence, we can obtain solutions. Trigonometric Equation
