Formula for the gradient of a line joining two points

The midpoint of \( (x_1, y_1) \) and \( (x_2, y_2) \) is...

The quadratic equation formula for solving \[ax^2+bx+c=0\]

A line has gradient \(m\).
A line perpendicular to this will have a gradient of...

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...

Formula for the distance between two points...

To find where two graphs intersect each other...

To simplify \( \frac{a}{\sqrt{b}} \)...
(a.k.a. 'rationalising the denominator')

To simplify \( \frac{a}{b+\sqrt{c}} \)...
(a.k.a. 'rationalising the denominator')

\[\left(\sqrt{m} \right)^{3}=... \]

\[\sqrt{a}\times \sqrt{b}=...\]

\[\frac{\sqrt{a}}{\sqrt{b}}=...\]

To find the gradient of a curve at any point, use...

Parallel lines have the same...

To find the gradient of the line \(ax+by+c=0\)...

Where is the vertex of the graph \[y=\left ( x+a \right )^2+b\]?

The discriminant of \(ax^2+bx+c\) is...

The discriminant of a quadratic equation tells us...

If a quadratic equation has two distinct real roots, what do we know about the discriminant?

If a quadratic equation has two equal roots, what do we know about the discriminant?

If a quadratic equation has no real roots, what do we know about the discriminant?

If \(y=ax^n\),

then \(\frac{dy}{dx} =...\)

If \(y=ax^n\),
then \(\int y\; dx = ...\)

What effect will the transformation \(y=f(x)+a\) have on the graph of \(y=f(x)\)?

What effect will the transformation \(y=f(x+a)\) have on the graph of \(y=f(x)\)?

What effect will the transformation \(y=af(x)\) have on the graph of \(y=f(x)\)?

What effect will the transformation \(y=f(ax)\) have on the graph of \(y=f(x)\)?

If we differentiate \(y\) twice with respect to \(x\), what do we get?

What effect will the transformation \(y=f(-x)\) have on the graph of \(y=f(x)\)?

What effect will the transformation \(y=-f(x)\) have on the graph of \(y=f(x)\)?

\[\left ( \sqrt[n]{x} \right )^m=... ?\]

\[a^{-n}=...?\]

\[a^0=...?\]

\[x^{\frac{1}{n}}=...?\]

\[\left ( ab \right )^n=...?\]

What does the graph of \(y=\frac{1}{x}\) look like?

What does the graph of \(y=a^x\), where \(a>0\) look like?

What do the graphs \(y=x^3\) and \(y=-x^3\) look like?

What does \(\sum_{r=1}^{4}a_r\) mean?

Formula for the \(n\)th term of an arithmetic sequence...

[given in the formulae booklet]

Formula for the sum of the first \(n\) terms of an arithmetic sequence...

[given in the formulae booklet]

If we are given \(\frac{dy}{dx}\) or \(f'(x)\) and told to find \(y\) or \(f(x)\), we need to...

Integration is the reverse of ... ?

Differentiation is the reverse of ... ?

The rate of change of \(y\) with respect
to \(x\) is also called...?

The formula for finding the roots of \[ax^2+bx+c=0\]

\[a^m \div a^n = ... ?\]

\[\left (a^m \right )^n=...?\]

To simplify \( \frac{a}{b-\sqrt{c}} \)...
(a.k.a. 'rationalising the denominator')