This comprehensive exam preparation package for Cambridge IGCSE Mathematics (0580) details the structure of Core and Extended components, presents a high-impact study guide, categorizes critical pitfalls from examiner reports (2023–2025), and offers practical scientific calculator techniques to prevent precision errors.
閱讀時間 5 分鐘更新於: 2026年6月21日
試卷概覽
卷數
2
總分
200
考試時間
4小時
題型
4
試卷
時間
分數
題數
比重
題型
Paper 2 (Extended, Non-calculator)
2小時
100
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Paper 4 (Extended, Calculator)
2小時
100
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評級
A*ABCDEFGU
計算機規定
A silent scientific calculator may be used on papers where calculators are permitted (some papers are non-calculator). It must not be graphical or programmable and must hold no stored information.
AO1: Knowledge and understanding of mathematical techniques (50%)
AO2: Apply mathematical techniques to solve problems (50%)
根據歷屆試題與評分準則整理（2023–2025）。
計算機程式
Table mode for roots & turning points
Scientific calculator (e.g. Casio fx-991 series)
用途: Tabulate \(y\) across a range of \(x\) to locate sign changes (roots) and approximate maxima/minima.
使用時機: Solving or sketching a function when you want to find where its graph crosses or turns.
步驟
Enter the function in TABLE mode, set the start, end and step, then read where the sign of \(y\) changes or where it peaks.
考試提示: Allowed on papers where a calculator is permitted; use a silent scientific calculator with no stored content and show your method.
Statistics mode (mean, SD & regression)
Scientific calculator (e.g. Casio fx-991 series)
用途: Read the mean \(\bar{x}\) and standard deviation directly, and the gradient/intercept (and \(r\)) of a linear regression for bivariate data.
使用時機: Any data-handling, statistics, or required-practical analysis question.
步驟
Enter the data in STAT mode (1-VAR or A+BX), then recall \(\bar{x}\), \(\sigma\) or the regression coefficients.
考試提示: Allowed on papers where a calculator is permitted; use a silent scientific calculator with no stored content and show your method.
Carry exact values with Ans & memory
Scientific calculator (e.g. Casio fx-991 series)
用途: Keep full-precision intermediate values to avoid rounding errors.
使用時機: Multi-step calculations where premature rounding loses the final accuracy mark.
步驟
Use Ans, STO/RCL or the M+ memory to reuse the unrounded result of each step; round only the final answer.
考試提示: Allowed on papers where a calculator is permitted; use a silent scientific calculator with no stored content and show your method.
Equation solver — to CHECK your working
Scientific calculator (e.g. Casio fx-991 series)
用途: Use the built-in EQN/SOLVE mode to verify roots of quadratics or simultaneous equations you have already solved by algebra.
使用時機: As a check only, after solving by hand.
步驟
Enter the coefficients in EQN mode (or use SOLVE) and confirm they match your worked solution.
考試提示: Allowed on papers where a calculator is permitted; use a silent scientific calculator with no stored content and show your method.
常見錯誤
1high涉及分數: 2Trigonometry
Premature rounding of intermediate decimals to 2 or 3 significant figures during multi-step trigonometry or similarity calculations.
如何避免: Retain intermediate calculated numbers as exact fractions, surds, or stored memory values on your scientific calculator, and only round the final answer to 3 significant figures.
2high涉及分數: 3Similarity
Applying linear scale factors directly to problems dealing with mathematically similar volumes or areas.
如何避免: Always square the linear scale factor (k^2) to scale surface areas, and cube it (k^3) to scale volumes and capacities.
3high涉及分數: 2Algebraic manipulation
Failing to write down intermediate substitutions and equations in 'Show that' and 'Write down and solve' questions.
如何避免: Show the substitution of all known values into formulas explicitly, and never write down exact values or algebraic models without their progressive structural derivations.
4medium涉及分數: 2Probability of combined events
Forgetting to reduce denominators in sequential 'without replacement' combined probability calculations.
如何避免: For each subsequent selection, reduce both the numerator and the denominator of your fraction by 1 to reflect the decrease in the available items.
5high涉及分數: 2Surface area and volume
Substituting diameter values directly into cylindrical or spherical surface area and volume formulas instead of radius.
如何避免: Halve the diameter to find the radius (r = d/2) before substituting values into any mensuration formula.
6medium涉及分數: 3Equations of linear graphs
Omitting the calculation of the midpoint when finding the equation of a perpendicular bisector.
如何避免: Remember that a perpendicular bisector must pass through the midpoint of the segment. Calculate the midpoint coordinates first and substitute them into y = mx + c to solve for c.