Sets

Coordinate Geometry

Length of a Line

$(x^2-x^1{)}^2+(y^2-y^1{)}^2$

Mid-point of a Line

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Gradient of a Line

$\frac{x_2-x_1}{y_2-y_1}$

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

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

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

$\overline{x}=\frac{\sum fx}{\sum f}$

$\sum$ → sum

$f$ → frequency

$x$ → observations

Probability

$\frac{\text{Number of Favourable Outcomes}}{\text{Number of Possible Outcomes}}$

Histograms

Frequency Polygons