# Maths - Misc

> Source: https://ollybritton.com/notes/a-level/maths/topics/misc/ · Updated: 2024-08-24 · Tags: maths

## Flashcards
##### $$\sqrt{3 - 2\sqrt{2}}$$ How can you simplify this??
Rewrite as

$$
\sqrt{2}^2 - 2\cdot\sqrt{2}\cdot + 1^2
$$

and complete the square.

### 2022-01-19
##### ![WACKY CIRCLE](paste-b0293ccaf34f94886d8c955237bb069718e6259d.jpg) How could you find the area of the shaded region??
Split it up into a sector and a right-angled triangle.

![WACKY CIRCLE ANSWER](paste-597c2ad362fd4c96775025b5211e9a54872b0788.jpg)

### 2022-02-02
##### Given a parametric curve $$(x(t), y(t))$$ how can you work out the parametric curve for rotating it by an angle $\theta$??
$$
\left(\begin{matrix} \cos \theta & -\sin \theta \\\\ \sin \theta & \cos \theta \end{matrix}\right)
$$

### 2022-02-03
##### What is the formula for the area of a triangle with coordinates $(0, 0)$, $(x_1, y_1)$ and $(x_2, y_2)$??
$$
\frac{1}{2} \left|\begin{matrix} x_1 \& y_1 \\\\ x_2 \& y_2 \end{matrix}\right|
$$

##### What is the formula for the area of a triangle with coordinates $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$??
$$
\frac{1}{2} \left|\begin{matrix} x_1 \& y_1 \& 1 \\\\ x_2 \& y_2 \& 1 \\\\ x_3 \& y_3 \& 1 \end{matrix}\right|
$$

### 2022-04-12
##### Careful: What is an alternative way of writing $2\sin (2x)$??
$$
4\sin x \cos x
$$

##### Careful: What is $e^{-\ln x}$??
$$
\frac{1}{x}
$$

### 2022-04-18
##### When giving a set as an answer, like $x$ is a real number above $4$, where does the $x \in \mathbb{R}$ go??
At the start

$$
\{ x \in \mathbb{R}\ |\ x > 4 \}
$$

### 2022-06-03
##### $$\frac{1}{5}\ln\left| \frac{t + 2}{1 - 2t} \right| + c$$ doesn't look the same as $$\frac{1}{5}\ln\left| \frac{2t + 4}{2t - 1} \right|$$ but they are. How??
You can flip the order of the minuses thanks to the modulus sign and the factor of 2 and top can become part of the constant when you take it out of the $\log$.

### 2022-06-07
##### $$p^3 - q^3$$ How could you rewrite this??
$$
(p-q)(p^2 + pq + q^2)
$$

### 2022-06-18
##### If data is skew, is it better to use the median and IQR or the mean and s.d.??
The median and IQR.

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