Sets

Coordinate Geometry

Length of a Line

\((x^2​−x^1​)^2+(y^2​−y^1​)^2​\)

Mid-point of a Line

\( (\cfrac{x_1 + x_2}{2}, \cfrac{y_1 + y_2}{2}) ​\)

Gradient of a Line

\( \cfrac{x_2 - x_1}{y_2 - y_1} ​\)

Gradient of Parallel Lines

They have the SAME Gradients

Equations of a Straight Line

Eqn. 1

\( y=mx+c \)

where:

m = Gradient

c - y-intercept

Eqn. 2

\( y−y_1​=m(x−x_1​) \)

where:

m - Gradient

Gradient of Perpendicular Lines

\( M_1​ \times M_2​=−1 \)

where \(M_1\) and \(M_2\) are the gradients of the 2 perpendicular lines.

Consumer Arithmetic

Discount

Selling Price=Marked Price−Discount on Marked Price

Sketching Quadratic Curve

Max or Min?

a>0; Minimum Curve

a<0; Maximum Curve

y-Intercept

substitute x as 0 in equation.

c = y-intercept in quadratic equation

Turning Point (Max/Min Point)

Complete Square

\(a(x+h)^2+k \)

Turning Point = \((-h,k)\)

Roots

Substitute y as 0 & solve quadratic equation

\( x = \cfrac{-b \pm \sqrt{(b^2 - 4ac)}}{2a} \)

Axis of Symmetry

Completing the Square

Formula Method

Form: \(a(x+h)^2+k\)

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Actual Completing Square Method

See Video Below → 8:33

www.youtube.com

Statistics

Mean

\( \bar{x} = \cfrac{\sum fx}{\sum f} \)

\( \sum \) → sum

\( f \) → frequency

\( x \) → observations

Probability

Total number of possible outcomesnumber of favourable outcomes​

Histograms

Frequency Polygons