diff --git a/docs/sph3u7.md b/docs/sph3u7.md
index 0ac9314..e9f452a 100644
--- a/docs/sph3u7.md
+++ b/docs/sph3u7.md
@@ -18,6 +18,10 @@ Every other SI unit is derived from the fundamental SI units. Memorise these!
| Amount of substance | Mole | mol |
| Luminous intensity | Candela | cd |
+!!! 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 = $kg \times m \times s^{-2}$.
+
### Metric prefixes
Every SI unit can be expanded with metric prefixes.
@@ -36,6 +40,9 @@ Every SI unit can be expanded with metric prefixes.
| peta- | P | $10^{15}$ | f | femto- |
| exa- | E | $10^{18}$ | a | atto- |
+!!! note
+ For easier memorization, notice that most of these prefixes are in multiples of $3$.
+
### Significant figures
- The leftmost non-zero digit is the **most significant digit**.
@@ -112,7 +119,7 @@ Uncertainties are stated in the form of [value] ± [uncertainty]. A value is onl
To determine a measurement's absolute uncertainty, if:
- the instrument states its uncertainty, use that.
- - an analog instrument is used, the last digit is estimated and appended to the end of the reported value. The estimated digit is uncertain by 5 at its order of magnitude.
+ - an analog instrument is used, the uncertainty is half of the smallest scale.
- a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude.
!!! example
@@ -142,9 +149,9 @@ Error bars represent the uncertainty of the data, typically representing that da
(Source: Kognity)
The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes.
-$$m_{best fit} ± m_{max}-m_{min}$$
+$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$
The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
-$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
+$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - \text{intercept} _{\min}}{2}$$
## 1.3 - Vectors and scalars
@@ -152,6 +159,7 @@ $$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
!!! note "Definition"
- **Scalar:** A physical quantity with a numerical value (magnitude) and a unit.
- **Vector:** A physical quantity with a numerical value (magnitude), a unit, and a **direction.**
+ - The **minimum magnitude** for any vector must be $`\ge 0`$
??? example
- Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more.
@@ -166,6 +174,7 @@ $$\vec{a} = (1, 1)$$
- The **magnitude** of a vector can be expressed as the absolute value of a vector.
$$|\vec{a}| = 1 \text{ m}$$
+
### Adding/subtracting vectors diagrammatically
1. Draw the first vector.
@@ -179,6 +188,9 @@ When subtracting a vector, **negate** the vector being subtracted by giving it a
(Source: Kognity)
+!!! note
+ Notice that when we are subtracting vectors ($\vec{a} - \vec{b}$), we have **tail** to **tail** and the difference vector has a direction from ($\vec{b} to \vec{a}$)
+
### Adding/subtracting vectors algebraically
Vectors can be broken up into two vectors (**"components"**) laying on the x- and y-axes via trigonometry such that the resultant of the two components is the original vector. This is especially helpful when adding larger (3+) numbers of vectors.