Mathematics - Applications and Interpretation 考試技巧

計算機程式

常見錯誤

1. 1high涉及分數: 2Statistics and probability

   Stating statistical hypotheses using sample statistics (such as the sample mean x-bar or the sample correlation coefficient r) instead of population parameters (such as mu or rho).

   如何避免: Always write hypotheses using population symbols (e.g., \( H_0: \mu_A = \mu_B \) and \( H_1: \mu_A \neq \mu_B \)) or describe them strictly in words referencing the overall population parameter, never the sample statistics.
2. 2high涉及分數: 4Number and algebra

   Entering incorrect signs for cash flows (PV, PMT, FV) in the GDC Time Value of Money (TVM) financial solver, leading to math errors or impossible outcomes.

   如何避免: Apply strict cash-flow perspective: Cash inflows (loans received, withdrawals) are positive (+); cash outflows (deposits made, periodic payments) are negative (-).
3. 3high涉及分數: 1Number and algebra

   Rounding intermediate decimals too early in multi-step calculations, which leads to final answers falling outside the accepted range of the markscheme.

   如何避免: Store exact values in your GDC variables (e.g., A, B, C) or write down intermediate steps using at least 5-6 significant figures, rounding to 3 s.f. only on the final line.
4. 4medium涉及分數: 3Geometry and trigonometry

   Leaving the GDC in the wrong angle mode (Radian instead of Degree, or vice-versa) when performing trigonometric geometry or calculus modeling.

   如何避免: Always check your GDC setting at the start of each problem. Use Degree mode for triangles, bearings, and basic spatial geometry. Use Radian mode for trigonometric calculus and tide models involving continuous cyclic functions.
5. 5medium涉及分數: 1Number and algebra

   Writing final currency answers rounded to 3 significant figures rather than to exactly 2 decimal places as standard for monetary values.

   如何避免: When working with currency, round your final answer to exactly 2 decimal places (e.g., $5.58 or $86533.20) unless the question explicitly asks for a whole number.
6. 6high涉及分數: 1Geometry and trigonometry

   Writing coordinates (such as midpoints, vertices, or intersections on Voronoi diagrams) without surrounding parentheses, leading to an automatic accuracy penalty.

   如何避免: Ensure all spatial coordinates are written in proper coordinate format with enclosing brackets, for example: \( (8, 4) \) or \( (7, 3) \), instead of leaving them as plain numbers like '8, 4'.
7. 7high涉及分數: 2Statistics and probability

   Failing to declare or compare p-values directly to the significance level during hypothesis testing conclusions.

   如何避免: Always write out the explicit mathematical inequality (e.g., \( 0.102 > 0.05 \) or \( p > 0.05 \)) before stating whether you fail to reject or reject the null hypothesis.
8. 8medium涉及分數: 3Calculus

   Omitting the constant of integration (+c) when finding indefinite integrals (e.g., finding cost functions or plant growth functions from rates of change).

   如何避免: Always append \( +c \) to your integrated function immediately, then use the provided boundary/initial condition (such as \( h(2)=6.5 \) or \( C(500)=1750 \)) to solve for the value of \( c \).
9. 9medium涉及分數: 2Functions

   Attempting to reverse-engineer 'show that' questions by substituting target values back into the calculation instead of deriving them step-by-step.

   如何避免: Treat the target value in a 'show that' question as the finish line. Do not touch or use that number in your calculations; instead, write down each logical algebraic step starting from the raw formulas.