Mathematics M1 (Calculus and Statistics) 試験対策

電卓プログラム

?→N:?→R:?→P:(N nCr R)×P^R×(1-P)^(N-R)

?→L:?→R:e^(-L)×L^R÷R!

?→X:?→M:?→S:(X-M)÷S

よくあるミス

1. 1high影響する配点: 1Standardisation of a normal variable and use of the standard normal table

   Truncating intermediate probability values, resulting in final answers that deviate from the required 4 d.p. standard.

   回避方法: Store intermediate calculation results in the calculator's memory registers (A, B, C, etc.) or write them down to at least 6 decimal places.
2. 2high影響する配点: 2Sampling distribution and point estimates

   Neglecting to divide the variance or standard deviation by \( \sqrt{n} \) when standardising the sample mean under the Central Limit Theorem.

   回避方法: Always check whether the variable is an individual observation \( X \) or a sample mean \( \bar{X} \). For the latter, use \( \text{Var}(\bar{X}) = \sigma^2/n \).
3. 3medium影響する配点: 2Definite integration and its applications

   Failing to write down the differential symbol dx or dt, or failing to change the limits of integration when performing integration by substitution.

   回避方法: Always write the differential step explicitly (e.g., \( du = g'(x)dx \)) and construct a small table to convert \( x \)-limits to \( u \)-limits before integrating.
4. 4medium影響する配点: 2Confidence interval for a population mean

   Using the sample standard deviation \( s \) directly as the margin of error without dividing by \( \sqrt{n} \) when calculating Confidence Intervals.

   回避方法: Recall the confidence interval formula: \( \bar{x} \pm z_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) \). The term \( s/\sqrt{n} \) is mandatory.
5. 5high影響する配点: 3Conditional probability and Bayes’ theorem

   Incorrectly defining the conditional probability space in Bayes' Theorem, especially missing complementary events in the denominator.

   回避方法: Draw a probability tree diagram immediately. Ensure that all branches leading to the target event are summed in the denominator.