Note format reference

Notes are Markdown with three additions: maths in dollar signs, teaching blocks written as ::: directives, and ```graph fences for figures. Everything is compiled at build time, so what you see in pnpm dev is exactly what students get. Every example on this page is rendered by the same pipeline, so you can see the result under each snippet.

Teaching blocks#

A block opens with three colons and its name, and closes with three colons on their own line. Any block takes an optional title:

:::definition{title="Specific heat capacity"}
**Specific heat capacity** is the energy required per unit mass to raise the temperature by one kelvin.
:::

Without a title, each block shows its default label.

Definition#

:::definition
**Specific heat capacity** is the energy required per unit mass to raise the temperature by one kelvin.
:::

Key result and formula#

:::key
$$
E = mc\Delta\theta
$$
where $m$ is the mass, $c$ the specific heat capacity and $\Delta\theta$ the change in temperature.
:::

formula looks the same and is for results that are given in the formula list or simply used along the way.

Method#

:::method{title="Finding a stationary point"}
1. Differentiate to find $\dfrac{dy}{dx}$.
2. Solve $\dfrac{dy}{dx} = 0$ for $x$.
3. Substitute each $x$ into the original equation to find $y$.
4. Use $\dfrac{d^2y}{dx^2}$ to decide whether each point is a maximum or a minimum.
:::

Example and solution#

An example contains a solution, so the outer block needs four colons and the inner one three:

::::example{title="Heating water"}
How much energy is needed to heat $0.50\ \text{kg}$ of water from $20\ ^\circ\text{C}$ to $80\ ^\circ\text{C}$?

:::solution
$$
E = mc\Delta\theta = 0.50 \times 4200 \times 60 = 1.26 \times 10^{5}\ \text{J}
$$
:::
::::

Give every example a title that says what it is about. Solutions are collapsed until the reader opens them.

Practice questions#

End every note with one question block holding all the practice questions, followed by a solution titled Answers:

:::question{title="Practice questions"}
1. Find the energy needed to heat $2.0\ \text{kg}$ of water by $15\ \text{K}$.
2. A $0.80\ \text{kg}$ block absorbs $7200\ \text{J}$ and warms by $20\ \text{K}$. Find its specific heat capacity.
:::

:::solution{title="Answers"}
1. $E = 2.0 \times 4200 \times 15 = 1.26 \times 10^{5}\ \text{J}$
2. $c = \dfrac{7200}{0.80 \times 20} = 450\ \text{J kg}^{-1}\ \text{K}^{-1}$
:::

Proof#

:::proof{title="Sum of an arithmetic progression"}
Write the sum forwards and backwards and add:
$$
2S_n = n\bigl(2a + (n-1)d\bigr) \quad\Rightarrow\quad S_n = \tfrac{n}{2}\bigl(2a + (n-1)d\bigr)
$$
:::

Tip, warning and exam tip#

:::tip
Check a factorisation by expanding it again.
:::

:::warning
$\sqrt{a + b}$ is not $\sqrt{a} + \sqrt{b}$.
:::

:::exam
"Hence" means you must use the previous result. Another method earns no marks.
:::

Practical skills and summary#

:::practical{title="Measuring specific heat capacity"}
- **Apparatus:** metal block, immersion heater, joulemeter, thermometer, insulation.
- **Uncertainty:** heat lost to the surroundings makes $c$ too large; insulate the block.
:::

:::summary
- $E = mc\Delta\theta$, with $\Delta\theta$ in kelvin or degrees Celsius.
- Water's high specific heat capacity makes it a good coolant.
:::

Maths#

• Inline maths in single dollars: $x^2 + 1$ gives $x^2 + 1$.
• Displayed maths in double dollars, on their own lines.
• Never use \(, \[ or a bare $ for currency inside maths. Write a literal dollar sign as \$, outside maths only.

The roots are given by
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

The roots are given by

Maths is rendered by KaTeX at build time, so any KaTeX-supported command works. pnpm notes:check reports KaTeX errors. Because each formula keeps its LaTeX source, students can select it to graph it, copy it or add it to their cheat sheet, so write formulas as maths rather than as text.

Units#

Units are upright, separated from the number by a space, in the syllabus's SI style:

$9.81\ \text{m s}^{-2}$, $1.26 \times 10^{5}\ \text{J}$, $4200\ \text{J kg}^{-1}\ \text{K}^{-1}$

$9.81\ \text{m s}^{-2}$, $1.26 \times 10^{5}\ \text{J}$, $4200\ \text{J kg}^{-1}\ \text{K}^{-1}$

Write m s^{-1}, never m/s.

Chemistry#

Chemical formulas and equations use mhchem's \ce{} inside maths:

$\ce{CH3CH2OH + 3O2 -> 2CO2 + 3H2O}$

$\ce{N2(g) + 3H2(g) <=> 2NH3(g)}$

$\ce{Fe^{3+}}$, $\ce{SO4^{2-}}$, $\ce{NaCl(aq)}$

$\ce{CH3CH2OH + 3O2 -> 2CO2 + 3H2O}$

$\ce{N2(g) + 3H2(g) <=> 2NH3(g)}$

$\ce{Fe^{3+}}$, $\ce{SO4^{2-}}$, $\ce{NaCl(aq)}$

Describe mechanisms in numbered steps, with each curly-arrow movement written out: where the electron pair starts and where it goes.

Code#

Use fenced code blocks with a language. They are highlighted at build time in the monochrome theme.

Pseudocode follows the 9618 pseudocode guide exactly: DECLARE, ←, ENDIF, ENDWHILE, PROCEDURE … ENDPROCEDURE, FUNCTION … RETURNS.

```pseudocode
DECLARE Total : INTEGER
Total ← 0
FOR Count ← 1 TO 10
    Total ← Total + Count
NEXT Count
OUTPUT Total
```

DECLARE Total : INTEGER
Total ← 0
FOR Count ← 1 TO 10
    Total ← Total + Count
NEXT Count
OUTPUT Total

Tables#

Use GitHub Markdown tables, especially for comparisons such as mitosis and meiosis, $\mathrm{S_N1}$ and $\mathrm{S_N2}$, or TCP and UDP. Wide tables scroll sideways on phones.

| | Mitosis | Meiosis |
| --- | --- | --- |
| Divisions | One | Two |
| Daughter cells | Two, diploid | Four, haploid |
| Genetically identical | Yes | No |

Graphs#

Anything that is a curve is a ```graph fence, one instruction per line: motion graphs, decay curves, enzyme activity against temperature as a sketched function, the Maxwell–Boltzmann shape, titration curves, normal distributions.

```graph
view 0 10 0 50
y = 4.9 x^2
(2, 0) -- (2, 19.6)
fill 0 2 y = 4.9 x^2
```

Graphs are drawn live in the reader's theme, and Open loads them into the grapher. See Grapher syntax for every instruction.

Diagrams#

For genuine diagrams, such as circuits, ray diagrams, cell structures, apparatus, logic gates and data structures, inline a simple SVG inside <figure class="diagram"> with a <figcaption>:

<figure class="diagram">
  <svg viewBox="0 0 240 90" fill="none" stroke="currentColor" stroke-width="1.5" font-family="inherit" font-size="13">
    <rect x="20" y="25" width="60" height="40" rx="4" />
    <rect x="160" y="25" width="60" height="40" rx="4" />
    <path d="M80 45 H160" />
    <path d="M150 40 L160 45 L150 50" />
    <text x="50" y="50" text-anchor="middle" fill="currentColor" stroke="none">Input</text>
    <text x="190" y="50" text-anchor="middle" fill="currentColor" stroke="none">Output</text>
  </svg>
  <figcaption>A process with one input and one output.</figcaption>
</figure>

Rules for diagrams:

• a viewBox and no fixed width, so the diagram scales
• stroke="currentColor" and fill="none", or fill="currentColor" for small marks and text, so it follows light and dark mode
• font-size of 12 to 14 and font-family="inherit"
• no colours, gradients, filters or scripts
• every part labelled

Only draw a diagram when it is accurate and clearly helps. A precise table or description beats a wrong picture. Do not embed images: the build warns when a note contains one.

Links and emphasis#

• Link to another note with its URL: [the chain rule](/notes/pure-3/calculus/chain-rule). Links between notes open as tabs in the workspace.
• Use **bold** for the term being defined, not for emphasis in general.
• <mark> and <u> pass through for highlighting and underlining, sparingly.

Headings#

Use ## for the main sections of a note and ### for subsections. Both appear in the note's table of contents. Headings are in sentence case, with no numbers and no trailing punctuation.