# Edexcel Core 2 Maths - Key Facts

Flashcards by , created almost 3 years ago

## Key facts and formulae which must be known for the Edexcel Core 2 examination.

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 Created by Daniel Cox about 3 years ago Copied by Daniel Cox almost 3 years ago
S2 - Chapter 1 to 5
Trig Values
Core Mathematics-Two
Chemical Symbols
Resumo para o exame nacional - Fernando Pessoa Ortónimo, Alberto Caeiro , Ricardo Reis e Álvaro Campos
Edexcel Core 1 Maths - Key Facts
All AS Maths Equations/Calculations and Questions
HISTOGRAMS
Integration and differentiation BASICS ONLY
Core 4 flashcards
 Question Answer $\log_a x+\log_a y = ?$ $\log_a x+\log_a y = \log_a(xy)$ $\log_a x-\log_a y = ?$ $\log_a x-\log_a y = \log_a\left (\frac{x}{y} \right )$ NOT $$\frac{\log_a x}{\log_a y}$$ $k \log_a x = ?$ $k \log_a x = \log_a\left (x^k \right )$ State the sine rule $$\frac{a}{\sin A}=\frac{b}{\sin B}$$ or $$\frac{\sin A}{a}=\frac{\sin B}{b}$$ True or false? $\log_a\left (xy^k \right )=k \log_a\left ( xy \right )$ FALSE \begin{align*} \log_a\left (xy^k \right )&=\log_a x +\log_a \left (y^k \right )\\ &=\log_a x + k \log_a y \end{align*} What is the trigonometric formula for the area of a triangle? $Area=\frac{1}{2} ab \sin C$ Here, the sides $$a$$ and $$b$$ surround the angle $$C$$ What is the Pythagorean trigonometric identity? (Hint: it involves $$\sin^2 x$$ and $$\cos^2 x$$ $\sin^2 x + \cos^2 x = 1$ If $$y=a^x$$, then $$x=?$$ If $$y=a^x$$, then $$x=\log_a y$$ State the cosine rule [given in the formulae booklet] $a^2=b^2+c^2-2bc \cos A$ $\log_a a =?$ $\log_a a =1$ $\log_a 1 =?$ $\log_a 1 =0$ State an identity relating $$\sin x$$, $$\cos x$$ and $$\tan x$$ $\frac{\sin x}{\cos x}=\tan x$ How many degrees is $$\pi$$ radians? $$\pi$$ radians is $$180^{\circ}$$ Formula for the area of a sector? 246e5789-f0a7-4bdd-adf3-6c292cebdf77.png (image/png) $Area=\frac{1}{2}r^2 \theta$ d9908c47-eea7-4a82-8040-ff473cf307cf.png (image/png) Formula for the length of an arc? 7b0c27d1-8771-4950-8671-09fd560d29b0.gif (image/gif) $s=r \theta$ 33c8b397-c996-4ddc-be92-21aa0cb46497.gif (image/gif) How would you find the area of a segment of a circle? 3f2f7ddf-b1c4-480f-86b7-8009148d4c6a.gif (image/gif) \begin{align*} \mathrm{Segment}&= \mathrm{Sector}-\mathrm{Triangle}\\ &=\frac{1}{2}r^2\theta-\frac{1}{2}r^2 \sin\theta\\ &=\frac{1}{2}r^2\left ( \theta - \sin\theta \right ) \end{align*} Formula for the $$n$$th term of a geometric sequence... [given in the formulae booklet] $u_n=ar^{n-1}$ Formula for the sum of the first $$n$$ terms of a geometric sequence... [given in the formulae booklet] $S_n=\frac{a\left ( 1-r^n \right )}{1-r}$ Formula for the sum to infinity of a convergent geometric series (one where $$\left | r \right |<1$$) [given in the formulae booklet] $S_\infty=\frac{a}{1-r}$ $\int ax^n \, dx=\, ?$ $\int ax^n \, dx= \frac{ax^{n+1}}{n+1}+c$ How would you find this shaded area? 0a3690b2-1482-449a-aae6-dff7cd33d632.png (image/png) Work out $$\int_{a}^{b} f(x) \, dx$$ General equation of a circle, centre $$\left ( a,b \right )$$ and radius $$r$$ $\left ( x-a \right )^2+\left ( y-b \right )^2=r^2$ What is the angle between the tangent and radius at $$P$$? 836b171c-39e7-4991-8c29-be862870372c.jpg (image/jpg) $90^{\circ}$ This is always true at the point where a radius meets a tangent 7b9e0001-91f1-483e-9305-f4ace70cf194.png (image/png) What does the graph of $$y=a^x$$ look like? Where does it cross the axes? It goes through the $$y$$-axis at $$\left ( 0,1 \right )$$. It does not cross the $$x$$-axis. The $$x$$-axis is an asymptote. 16493cc7-79d3-45f7-b601-63787610188f.jpg (image/jpg) This is a triangle inside a semicircle, where one side of the triangle is the diameter of the circle. What is the size of angle $$C$$? 7528b419-763e-4ed3-95f2-3fd66f8da729.gif (image/gif) $90^{\circ}$ Draw the graph of $$y=\sin x$$ for $$0\leq x \leq 2\pi$$ c5195b8d-e25a-460f-a4a3-3189515f3468.gif (image/gif) Draw the graph of $$y=\cos x$$ for $$0\leq x \leq 2\pi$$ eda70f8f-b1c3-4e65-9f56-d06139c3c3ad.gif (image/gif) Draw the graph of $$y=\tan x$$ for $$0\leq x \leq 2\pi$$ The lines $$x=\frac{\pi}{2}$$ and $$x=\frac{3\pi}{2}$$ are asymptotes 9e44c61a-ff49-4279-92e9-50bbaf346ee4.png (image/png) If $$\left (x+a \right )$$ is a factor of $$f(x)$$, then... $f(-a)=0$ This is known as the Factor Theorem If the remainder, when $$f(x)$$ is divided by $$(x+a)$$ is R, then... $f(-a)=R$ This is known as the Remainder Theorem If we draw the perpendicular bisector of any chord on a circle, which point will it definitely go through? The perpendicular bisector of a chord always passes through the centre of the circle 4652850b-01de-4209-ac80-e44d81393c43.png (image/png) What does $$n!$$ mean? $n!=n(n-1)(n-2)\times \ldots \times 3 \times 2 \times 1$ For example, $$4!=4\times 3\times 2\times 1=24$$ How would you use the second derivative, $$\frac{d^2 y}{dx^2}$$ to determine the nature of the stationary points on a graph? Substitute the $$x$$ co-ordinates of the stationary points into $$\frac{d^2 y}{dx^2}$$. If you get a positive answer, it's a MIN. If you get a negative answer, it's a MAX. A function is said to be 'increasing' when its gradient is... Positive A function is said to be 'decreasing' when its gradient is... Negative