考前速通

Propagation Formulas (Must Know)

Original $Y$	$\Delta Y$
$\ln x$	$\Delta x / x$
$\lg x$	$0.434 \times \Delta x / x$
$1/x$	$\Delta x / x^2$
$1/\sqrt{x}$	$\Delta x / (2x^{3/2})$
$x^n$	$n x^{n-1} \Delta x$
$\sqrt{x}$	$\Delta x / (2\sqrt{x})$

Gradient Uncertainty Workflow

best fit line → gradient_best
worst line through all error bars → gradient_worst
Δgradient = |gradient_best - gradient_worst|
Answer: gradient ± Δgradient

Combined Uncertainty Workflow

Identify formula for constant C
Find all contributing uncertainties (ΔR, Δk, Δintercept, etc.)
Sum fractional/percentage uncertainties
ΔC = C × (sum of fractional uncertainties)
Answer: C ± ΔC (with units)

Red Flags

信号	可能的问题
看到 $\ln$	$\Delta(\ln x) = \Delta x / x$，无 0.434
看到 $\lg$	必须用 0.434 因子
看到 $1/x$	$\Delta(1/x) = \Delta x / x^2$
Table 中 $Y$	每个值旁必须有 uncertainty 列
题目要求 gradient	必须画 worst line
error bars 在图上	worst line 必须通过所有 error bars
y-intercept	从 x = 0 处读取，延长线可能需要

Quick Checklist

Part (b): Table with derived quantities

• All derived values calculated correctly
• Uncertainty formula stated
• Each value has uncertainty beside it
• Significant figures consistent

Part (c)(iii): Gradient uncertainty

• Best fit line drawn
• Large triangle used for best gradient
• Worst acceptable line drawn through all error bars
• Large triangle used for worst gradient
• $\Delta$gradient = |best - worst| calculated
• Final answer in form gradient $\pm$ uncertainty

Part (c)(iv): y-intercept uncertainty

• Best fit y-intercept read
• Worst fit y-intercept read
• $\Delta$intercept = |best - worst| calculated

Part (d)(ii): Combined uncertainty

• Fractional uncertainty formula correct
• Each contributing term included
• Final answer: value $\pm$ uncertainty with units
• uncertainty to 1 s.f., value aligned

提示

表格中 uncertainty 保留 1 位有效数字，derived quantity 的小数位数与之对齐。