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Edu Level: CSEC
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
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
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