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.
อ่าน 5 นาทีอัปเดตเมื่อ: 3 ก.ย. 2569
ภาพรวมข้อสอบ
จำนวนฉบับ
4
คะแนนเต็ม
250
เวลาสอบ
5ชม.
ประเภทคำถาม
12
ฉบับ
เวลา
คะแนน
จำนวนข้อ
น้ำหนักคะแนน
ประเภทคำถาม
Unit 1: Pure Mathematics
2ชม.
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
1ชม.
50
5
20%
Combinatorics & Permutations, Linear Programming & Graph Optimization, Moving Averages & Time Series, Formal Propositional Logic, Critical Path Analysis
เกณฑ์เกรด
A*ABC*CDEFG
ข้อกำหนดเครื่องคิดเลข
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%)
วัตถุประสงค์: Get the mean, standard deviation, and product-moment or rank correlation coefficient directly from a data table.
ใช้เมื่อใด: Unit 3 Statistics questions on summary statistics or correlation, used to check working you have already shown rather than as a substitute for it.
ขั้นตอน
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.
ข้อควรระวังในการสอบ: 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)
วัตถุประสงค์: Check the sign of a function around a suspected root or turning point before committing to a full algebraic argument.
ใช้เมื่อใด: Unit 1 Pure Mathematics questions involving roots, turning points, or curve sketching.
ขั้นตอน
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.
ข้อควรระวังในการสอบ: 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)
วัตถุประสงค์: Hold an intermediate value, such as a mean needed again a few lines later in a standard deviation calculation, without retyping it.
ใช้เมื่อใด: Any multi-step calculation across Units 2, 3 or 4 where an earlier result feeds into a later step.
ขั้นตอน
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.
ข้อควรระวังในการสอบ: Clear the memory at the start of the exam and only store values calculated live during the paper, this is not a saved program.
Omitting the negative sign or misapplying power laws when differentiating or integrating negative powers of x.
วิธีหลีกเลี่ยง: Rewrite the term with the power rule in full before differentiating, bringing the power down and reducing it by one, sign included, then simplify.
Forgetting to find the constant of integration from the given coordinates after indefinite integration.
วิธีหลีกเลี่ยง: 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.
Believing the condition for a minimum turning point is a negative second derivative, when it is positive.
วิธีหลีกเลี่ยง: State the rule as second derivative positive means minimum, negative means maximum, and quote the calculated value explicitly in the conclusion.
4highคะแนนที่เกี่ยวข้อง: 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.
วิธีหลีกเลี่ยง: Choose one direction of positive acceleration for the whole system before writing any equation, and keep it for both particles' equations of motion.
Assigning consecutive whole-number ranks to tied values in Spearman's rank correlation instead of the mean of the tied positions.
วิธีหลีกเลี่ยง: 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.
6mediumคะแนนที่เกี่ยวข้อง: 2Statistics, measures of spread
Assuming that adding a constant to every value in a data set changes the standard deviation.
วิธีหลีกเลี่ยง: 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|.
7mediumคะแนนที่เกี่ยวข้อง: 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.
วิธีหลีกเลี่ยง: 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.
8mediumคะแนนที่เกี่ยวข้อง: 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.
วิธีหลีกเลี่ยง: 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.