Mathematics - J560 考試技巧

計算機程式

常見錯誤

1. 1high涉及分數: 3Similarity

   Failing to square the linear scale factor when working with surface areas, or to cube it for volume scaling on mathematically similar models.

   如何避免: Always identify the linear scale factor first, then explicitly calculate and write down the area scale factor \( k^2 \) and volume scale factor \( k^3 \) before doing any multiplication.
2. 2high涉及分數: 2Triangle mensuration

   Losing final accuracy marks due to premature rounding of intermediate values during multi-step trigonometry calculations.

   如何避免: Keep the full decimal expansions on your calculator screen or store intermediate steps to at least 5 significant figures on paper.
3. 3high涉及分數: 2Circles

   Omitting explicit geometric reasons in circle theorems and parallel line angle proofs.

   如何避免: Write down the exact mathematical name of the rule (e.g., 'alternate segment theorem' or 'angles subtended by the same arc are equal') alongside your angle calculations.
4. 4medium涉及分數: 3Discrete growth and decay

   Applying a simple interest calculation to a multi-year investment or savings account instead of compound interest.

   如何避免: Always verify if the question states 'simple' or 'compound'. For compound interest, use the exponential multiplier formula: \( \text{Initial} \times (\text{multiplier})^n \).
5. 5medium涉及分數: 2Combined events and probability diagrams

   Failing to subtract the intersection 'x' from the individual totals of a Venn diagram when calculating conditional probabilities or ratios.

   如何避免: Always construct the Venn Diagram from the middle outwards, subtracting overlapping regions from individual category totals before completing the outer elements.
6. 6medium涉及分數: 1Interpreting and representing data

   Plotting points at the group midpoints instead of the upper boundaries on a cumulative frequency curve.

   如何避免: Always plot the cumulative frequency against the upper class boundary of each interval.
7. 7medium涉及分數: 2Ruler and compass constructions

   Failing to draw supportive construction arcs when performing perpendicular bisectors or angle bisectors.

   如何避免: Never draw boundary lines freehand or erase your compass construction marks; examiners require visible intersecting arcs to award full marks.
8. 8high涉及分數: 2Algebraic equations

   Expanding sequential squared algebraic brackets, e.g., \( (n+1)^2 \), as \( n^2 + 1 \) instead of \( n^2 + 2n + 1 \).

   如何避免: Write the expression as double brackets \( (n+1)(n+1) \) and expand methodically using FOIL (First, Outer, Inner, Last).