---
title: "What a 18-year-old learns"
description: "8 topics are written for age 18, across 1 subjects."
canonical: https://lightmysky.com/learn/age/18
source: https://lightmysky.com/learn/age/18.md
retrieved: 2026-09-02
---

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# What a 18-year-old learns

8 topics are written for age 18, across 1 subjects.
Topics are placed by what they need, not by school year, so this is a starting point
rather than a syllabus.

Page: https://lightmysky.com/learn/age/18

## Mathematics

- [The Power Rule for Differentiating Polynomials](https://lightmysky.com/learn/mathematics/the-power-rule-for-differentiating-polynomials-mt_l7f4j44bR3): Differentiate any sum of powers of x with the rule that xⁿ becomes nxⁿ⁻¹, including negative and fractional powers once the term is rewritten as a power.
- [The Derivative as a Rate of Change](https://lightmysky.com/learn/mathematics/the-derivative-as-a-rate-of-change-mt_RqyLE3jrAW): Read dy/dx as how fast one quantity changes per unit of another, with the units to match, so a derivative answers questions about cost per item, litres per second or metres per second.
- [Tangents and Normals to a Curve](https://lightmysky.com/learn/mathematics/tangents-and-normals-to-a-curve-mt_BzMw7IT6kp): Find the equation of the tangent at a point on a curve from the derivative there, and the normal from the perpendicular gradient.
- [Increasing and Decreasing Functions](https://lightmysky.com/learn/mathematics/increasing-and-decreasing-functions-mt_KOrXxQvBrZ): Use the sign of the derivative to say where a curve rises and where it falls, which turns a question about shape into an inequality in x.
- [Stationary Points and the Second Derivative](https://lightmysky.com/learn/mathematics/stationary-points-and-the-second-derivative-mt_VbGJEFFgfs): Solve f'(x) = 0 to locate maximum, minimum and inflection points, then use the sign of f''(x) to decide which is which.
- [Optimisation with Calculus](https://lightmysky.com/learn/mathematics/optimisation-with-calculus-mt_9I0ql39Lzw): Turn a worded problem into one function of one variable, use a constraint to remove the second variable, then differentiate to find the best value and justify that it is a maximum or minimum.
- [Integration as the Reverse of Differentiation](https://lightmysky.com/learn/mathematics/integration-as-the-reverse-of-differentiation-mt_edtk3ArxRk): Recover a function from its derivative by raising the power and dividing, and carry the constant of integration that differentiation destroyed. Use a known point to pin that constant down.
- [Kinematics with Calculus](https://lightmysky.com/learn/mathematics/kinematics-with-calculus-mt_2kNspOOoDw): When the acceleration is not constant, differentiate displacement to get velocity and velocity to get acceleration, and integrate back the other way, using an initial condition to fix each constant.