Update 'docs/sph3u7.md'

docs/sph3u7.md

@@ -18,6 +18,27 @@ Every other SI unit is derived from the fundamental SI units. Memorise these!
 | Amount of substance | Mole | mol |
 | Luminous intensity | Candela | cd |
 
+### Derived units
+
+These are units that are derived from SI units, meaning that they can be broken down into an expression of SI units. These are also known as **preferred units**.
+
+TODO: add more derived units
+
+|Name|Symbol|Concept|Broken down into SI units|
+|---|---|---|---|
+|Newton|$N$|Force or weight|$$\frac{Kg \times m}{s^2}$$|
+|Joule|$J$|Energy or work|$$\frac{kg \times m^2}{s^2}$$|
+|Watt|$W$|Power|$$\frac{kg \times m^2}{s^3}$$|
+|Pascal|$Pa$|Pressure|$$\frac{kg}{m \times s^2}$$|
+
+!!! info "Reminder"
+    Note that on an assesment, you are expected to derive the SI unit expression given the equation of unit.
+    For example Force = mass x acceleration = mass x distance / time / time = $kg \times m \times s^{-2}$. 
+
+!!! note "Definition"
+    Physical Quantity: must always be expressed as the product of **magnitude**(number) and a **unit**.
+    Example: $$10m$$ (10 meters).
+
 ### Metric prefixes
 
 Every SI unit can be expanded with metric prefixes.
@@ -145,9 +166,9 @@ Error bars represent the uncertainty of the data, typically representing that da
 <img src="/resources/images/error-slopes.png" width=700>(Source: Kognity)</img>
 
 The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes.
-$$m_{\text{best fit}} ± \dfrac{m_{\max}-m_{\min}}{2}$$
+$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$
 The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
-$$\text{intercept}_{\text{best fit}} ± \dfrac{\text{intercept}_{\max} - intercept_{\min}}{2}$$
+$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - intercept_{\min}}{2}$$
 
 
 ## 1.3 - Vectors and scalars