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THE KNOWLEDGE / MATHS

6th Form Single knowledge

Facts currently selected by your teacher · 16 facts · questions and answers

Algebra

01

Discriminant and how it determines the number of roots of a quadratic

Δ=b2−4ac\Delta=b^2-4ac

Δ > 0: two distinct real roots. Δ = 0: one repeated real root. Δ < 0: no real roots.

02

Quadratic formula

x=−b±b2−4ac2ax=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
03

The factor theorem

(x−a) is a factor of f(x)  ⟺  f(a)=0(x-a)\text{ is a factor of }f(x)\iff f(a)=0

Trigonometry

05

The sine rule

asin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}
06

The cosine rule

a2=b2+c2−2bccos⁡Aa^2=b^2+c^2-2bc\cos A
07

Area of a triangle using two sides and the included angle

A=12absin⁡CA=\dfrac12 ab\sin C

Coordinate geometry

09

Equation of a straight line with gradient m passing through (x₁, y₁)

y−y1=m(x−x1)y-y_1=m(x-x_1)

Graphs

24

Sketch the graph of y = x²

y = x²
-2-1012(0, 0)xy
25

Sketch the graph of y = x³

y = x³
-2-1012(0, 0)xy
26

Sketch the graph of y = 1/x

y = 1/x
-2-10123xy

Neither axis is an intercept; both axes are asymptotes.

30

Transformation y = f(x) + a

Translate by (0a)\text{Translate by }\begin{pmatrix}0\\a\end{pmatrix}
31

Transformation y = f(x + a)

Translate by (−a0)\text{Translate by }\begin{pmatrix}-a\\0\end{pmatrix}
32

Transformation y = af(x)

Stretch parallel to the y-axis by scale factor a.

33

Transformation y = f(ax)

Stretch parallel to the x-axis by scale factor 1/a (for a > 0).

34

Transformation y = −f(x)

Reflect in the x-axis.

35

Transformation y = f(−x)

Reflect in the y-axis.