Edexcel Core 1 Maths - Key Facts

Question	Answer
Formula for the gradient of a line joining two points	$m=\frac{y_2-y_1}{x_2-x_1}$
The midpoint of $(x_1, y_1)$ and $(x_2, y_2)$ is...	$\left ( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right )$ Think of this as the mean of the coordinates $(x_1, y_1)$ and $(x_2, y_2)$
The quadratic equation formula for solving $ax^2+bx+c=0$	$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
A line has gradient $m$ . A line perpendicular to this will have a gradient of...	$\frac{-1}{m}$
If we know the gradient of a line and a point on the line, a formula to work out the equation of the line is...	$y-y_1=m(x-x_1)$
Formula for the distance between two points...	$\sqrt{\left ( x_2-x_1 \right )^2 + \left ( y_2-y_1 \right )^2}$
To find where two graphs intersect each other...	... solve their equations simultaneously.
To simplify $\frac{a}{\sqrt{b}}$ ... (a.k.a. 'rationalising the denominator')	Multiply by $\frac{\sqrt{b}}{\sqrt{b}}$
To simplify $\frac{a}{b+\sqrt{c}}$ ... (a.k.a. 'rationalising the denominator')	Multiply by $\frac{b-\sqrt{c}}{b-\sqrt{c}}$
$\left(\sqrt{m} \right)^{3}=...$	$\left(\sqrt{m} \right)^{3}=\sqrt{m}\sqrt{m}\sqrt{m}=m\sqrt{m}$
$\sqrt{a}\times \sqrt{b}=...$	$\sqrt{a}\times \sqrt{b}=\sqrt{ab}$
$\frac{\sqrt{a}}{\sqrt{b}}=...$	$\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$
To find the gradient of a curve at any point, use...	Differentiation
Parallel lines have the same...	Gradient
To find the gradient of the line $ax+by+c=0$ ...	Rearrange into the form $y=mx+c$ . The value of $m$ is the gradient.
Where is the vertex of the graph $y=\left ( x+a \right )^2+b$ ?	$\left ( -a,b \right )$
The discriminant of $ax^2+bx+c$ is...	$b^2-4ac$
The discriminant of a quadratic equation tells us...	How many roots (or solutions) it has. This will be how many times it crosses the $x$ -axis
If a quadratic equation has two distinct real roots, what do we know about the discriminant?	$b^2-4ac>0$
If a quadratic equation has two equal roots, what do we know about the discriminant?	$b^2-4ac=0$
If a quadratic equation has no real roots, what do we know about the discriminant?	$b^2-4ac<0$
Here is the graph of $y=x^2-8x+7$ . Use it to solve the quadratic inequality $x^2-8x+7>0$ Image: 130ce81d-812c-4c26-adf3-3249e2f6daae.gif (image/gif)	$x<1$ or $x>7$ These are the red sections of the curve. Note - do not write $x<1$ and $x>7$ - the word 'and' implies $x$ would need to be $<1$ and $>7$ at the same time... which is clearly not possible!
If $y=ax^n$ , then $\frac{dy}{dx} =...$	$\frac{dy}{dx} =anx^{n-1}$
If $y=ax^n$ , then $\int y\; dx = ...$	$\int ax^n \, dx = \frac{ax^{n+1}}{n+1}+c$
What effect will the transformation $y=f(x)+a$ have on the graph of $y=f(x)$ ?	Translation $a$ units in the $y$ direction. i.e. the graph will move UP by $a$ units
What effect will the transformation $y=f(x+a)$ have on the graph of $y=f(x)$ ?	Translation $-a$ units in the $x$ direction. i.e. the graph will move LEFT by $a$ units
What effect will the transformation $y=af(x)$ have on the graph of $y=f(x)$ ?	Stretch, scale factor $a$ in the $y$ direction. i.e. the $y$ values will be multiplied by $a$
What effect will the transformation $y=f(ax)$ have on the graph of $y=f(x)$ ?	Stretch, scale factor $\frac{1}{a}$ in the $x$ direction. i.e. the $x$ values will be divided by $a$ [This could also be described as a 'squash', scale factor $a$ in the $x$ direction]
If we differentiate $y$ twice with respect to $x$ , what do we get?	$\frac{d^2 y}{dx^2}$
What effect will the transformation $y=f(-x)$ have on the graph of $y=f(x)$ ?	Reflection in the $y$ axis
What effect will the transformation $y=-f(x)$ have on the graph of $y=f(x)$ ?	Reflection in the $x$ axis
$\left ( \sqrt[n]{x} \right )^m=... ?$	$\left ( \sqrt[n]{x} \right )^m=x^\frac{m}{n}$
$a^{-n}=...?$	$a^{-n}=\frac{1}{a^n}$
$a^0=...?$	$a^0=1$
$x^{\frac{1}{n}}=...?$	$x^{\frac{1}{n}}=\sqrt[n]{x}$
$\left ( ab \right )^n=...?$	$\left ( ab \right )^n=a^n b^n$
What does the graph of $y=\frac{1}{x}$ look like?	Image: 70d4cc6d-5ad1-490d-a0ef-78e4ae4ece26 (image/jpg)
What does the graph of $y=a^x$ , where $a>0$ look like?	The $x$ axis is an asymptote Image: 068f39af-78c6-4e8f-aa2b-a8319aaf9bd3.gif (image/gif)
What do the graphs $y=x^3$ and $y=-x^3$ look like?	Image: 2ca4c950-b848-4f85-a75b-bf2e0f361e6d (image/jpg)
What does $\sum_{r=1}^{4}a_r$ mean?	$\sum_{r=1}^{4}a_r=a_1+a_2+a_3+a_4$
Formula for the $n$ th term of an arithmetic sequence... [given in the formulae booklet]	$u_n=a+(n-1)d$
Formula for the sum of the first $n$ terms of an arithmetic sequence... [given in the formulae booklet]	$S_n=\frac{n}{2}\left ( 2a+(n-1)d \right )$ or $S_n=\frac{n}{2}\left ( a+l \right )$ where $l$ is the last term
If we are given $\frac{dy}{dx}$ or $f'(x)$ and told to find $y$ or $f(x)$ , we need to...	Integrate [remember to include $+c$ ]
Integration is the reverse of ... ?	Differentiation
Differentiation is the reverse of ... ?	Integration
The rate of change of $y$ with respect to $x$ is also called...?	$\frac{dy}{dx}$
The formula for finding the roots of $ax^2+bx+c=0$	$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$a^m \div a^n = ... ?$	$a^m \div a^n = a^{m-n}$
$\left (a^m \right )^n=...?$	$\left (a^m \right )^n=a^{mn}$
To simplify $\frac{a}{b-\sqrt{c}}$ ... (a.k.a. 'rationalising the denominator')	Multiply by $\frac{b+\sqrt{c}}{b+\sqrt{c}}$

Next up

Edexcel Core 1 Maths - Key Facts

Description

Resource summary

0 comments

Similar

	Created by Daniel Cox about 9 years ago

	Copied by Daniel Cox about 9 years ago

	Copied by Charlotte Cook over 7 years ago