Writing the conclusion

What a conclusion has to contain

The conclusion is where the Achieved and Merit criteria are actually awarded, and it is usually the shortest part of a report. Two sentences, written properly, are worth more than a page of description.

• Achieved needs the type of relationship: "$T$ is proportional to the square root of $L$."
• Merit needs the mathematical relationship obtained from your data: the equation, with the gradient you measured and its unit.
• Both must be written in terms of your own variables, not $x$ and $y$.

The four parts of a complete conclusion

1. State what was found, naming both variables.
   • "The period $T$ of the pendulum is proportional to the square root of its length $L$."
2. Give the equation from your graph, with the measured gradient.
   • "The graph of $T^2$ against $L$ was a straight line through the origin with gradient $4.0$ s² m⁻¹, so $T^2 = 4.0L$ and therefore $T = 2.0\sqrt{L}$."
3. Say what evidence supports it.
   • "The linearised graph was a straight line passing close to all six points and through the origin, which supports this relationship over the range tested."
4. State the range it applies over.
   • "This relationship was tested for lengths from $0.20$ m to $1.00$ m."

Turning a gradient into a relationship

• If you plotted $y$ against $x^2$ and got gradient $m$, then $y = mx^2$.
• If you plotted $y$ against $\sqrt{x}$ and got gradient $m$, then $y = m\sqrt{x}$.
• If you plotted $y$ against $\dfrac{1}{x}$ and got gradient $m$, then $y = \dfrac{m}{x}$.
• If you plotted $y^2$ against $x$ and got gradient $m$, then $y^2 = mx$, so $y = \sqrt{mx}$.

In each case, substitute your own variable names in place of $x$ and $y$ before you write the final sentence.

Common weak conclusions and how to fix them

Weak conclusion	Why it loses marks	Fixed version
"The relationship is non-linear."	Says only what it is not	"$T$ is proportional to $\sqrt{L}$"
"$y \propto x^2$"	Generic letters, no data	"$P$ is proportional to $V^2$, with $P = 0.25V^2$"
"The gradient was 4.0."	No unit, no relationship stated	"The gradient was $4.0$ s2 m−1, so $T^2 = 4.0L$"
"My results proved the theory."	This standard asks what your data shows, not what theory says	"My data supports $T \propto \sqrt{L}$ over the range $0.20$–$1.00$ m"