CCEA GCSE Further Mathematics: how the 250 marks split across Pure, Mechanics, Statistics and Discrete units, the exact spots (sign conventions, tied ranks, backward passes) where marks go missing, and a timed plan for all four papers.
閱讀時間 5 分鐘更新於: 2026年9月3日
試卷概覽
卷數
4
總分
250
考試時間
5小時
題型
12
試卷
時間
分數
題數
比重
題型
Unit 1: Pure Mathematics
2小時
100
14
40%
Short Structured Procedural, Calculus & Coordinate Geometry, Extended Algebraic Modeling & Systems
Summary Statistics & Rank Correlation, Probability & Distributions (Binomial/Normal)
Unit 4: Discrete and Decision Mathematics
1小時
50
5
20%
Combinatorics & Permutations, Linear Programming & Graph Optimization, Moving Averages & Time Series, Formal Propositional Logic, Critical Path Analysis
評級
A*ABC*CDEFG
計算機規定
Candidates must use electronic calculators with trigonometric, logarithmic and relevant statistical functions in all four units, there is no non-calculator paper in GCSE Further Mathematics. Calculators must not have any retrievable information stored in them, and must not offer symbolic algebra manipulation, symbolic differentiation or integration, language translation, or communication with other machines or the internet.
AO1: AO1: use and apply standard techniques, accurately recalling facts, terminology and definitions, using and interpreting notation correctly, and accurately carrying out routine procedures or set tasks requiring multi-step solutions. (40%)
AO2: AO2: reason, interpret and communicate mathematically, making deductions, inferences and conclusions from mathematical information, constructing chains of reasoning, presenting arguments and proofs, and assessing the validity of an argument. (30%)
AO3: AO3: solve problems in mathematics and other contexts, translating problems into mathematical processes, connecting different parts of mathematics, interpreting results in context, and evaluating methods, results and the assumptions behind them. (30%)
用途: Get the mean, standard deviation, and product-moment or rank correlation coefficient directly from a data table.
使用時機: Unit 3 Statistics questions on summary statistics or correlation, used to check working you have already shown rather than as a substitute for it.
步驟
Open the statistics menu, choose 1-variable or 2-variable as needed, key in each value or pair from the question, then read the required statistic from the variable menu.
考試提示: This is a live keystroke sequence performed on data printed in the exam, not a stored program. CCEA and JCQ ban any retrievable stored information.
Table mode for sign checks
Casio fx-991EX ClassWiz (or equivalent with a table function)
用途: Check the sign of a function around a suspected root or turning point before committing to a full algebraic argument.
使用時機: Unit 1 Pure Mathematics questions involving roots, turning points, or curve sketching.
步驟
Enter the function into table mode, set a start and end value either side of the suspected root with a small step size, generate the table, and read off where the sign changes.
考試提示: Table mode only uses the function typed in during the exam, it stores nothing between questions.
Memory recall for repeated intermediate values
Casio fx-991EX ClassWiz (or equivalent)
用途: Hold an intermediate value, such as a mean needed again a few lines later in a standard deviation calculation, without retyping it.
使用時機: Any multi-step calculation across Units 2, 3 or 4 where an earlier result feeds into a later step.
步驟
Calculate the value, press the memory store key and a letter to save it, continue with the rest of the working, then recall it with the same letter when needed again.
考試提示: Clear the memory at the start of the exam and only store values calculated live during the paper, this is not a saved program.
常見錯誤
1high涉及分數: 2Pure Mathematics, calculus
Omitting the negative sign or misapplying power laws when differentiating or integrating negative powers of x.
如何避免: Rewrite the term with the power rule in full before differentiating, bringing the power down and reducing it by one, sign included, then simplify.
2medium涉及分數: 2Pure Mathematics, integration
Forgetting to find the constant of integration from the given coordinates after indefinite integration.
如何避免: Substitute the given point into the integrated expression as a separate final step and solve for the constant explicitly, do not leave a general answer with c undetermined.
3medium涉及分數: 2Pure Mathematics, calculus
Believing the condition for a minimum turning point is a negative second derivative, when it is positive.
如何避免: State the rule as second derivative positive means minimum, negative means maximum, and quote the calculated value explicitly in the conclusion.
4high涉及分數: 3Mechanics
Sign errors when applying Newton's second law to connected particles, using an inconsistent acceleration direction for a hanging mass against a mass sliding on a surface.
如何避免: Choose one direction of positive acceleration for the whole system before writing any equation, and keep it for both particles' equations of motion.
5medium涉及分數: 2Statistics, correlation
Assigning consecutive whole-number ranks to tied values in Spearman's rank correlation instead of the mean of the tied positions.
如何避免: When two or more values tie, give every tied value the average of the ranks they would have occupied, then continue ranking from the next available position.
6medium涉及分數: 2Statistics, measures of spread
Assuming that adding a constant to every value in a data set changes the standard deviation.
如何避免: Remember that adding or subtracting a constant shifts the mean only, standard deviation is unchanged, while multiplying by a constant m scales the standard deviation by |m|.
7medium涉及分數: 3Discrete and Decision Mathematics, linear programming
Shading the feasible region instead of the rejected region in linear programming, or picking a non-integer vertex when the context needs whole numbers.
如何避免: Shade out the rejected side of each inequality so the feasible region is left clear, then for integer contexts check the lattice points nearest the optimal vertex against every constraint.
8medium涉及分數: 2Discrete and Decision Mathematics, critical path analysis
Making backward-pass errors in critical path networks when several activities converge at one event, especially before the forward pass across the whole network is finished.
如何避免: Complete the forward pass at every node first, then run the backward pass from the final node back to the start, taking the minimum of the converging paths at each node.