CCEA AS Further Mathematics: where the 200 marks across Pure and Applied papers go, the sign-error traps in matrices, vectors and complex numbers that cost the most marks, and a timed plan for both 90-minute papers.
อ่าน 5 นาทีอัปเดตเมื่อ: 3 ก.ย. 2569
ภาพรวมข้อสอบ
จำนวนฉบับ
2
คะแนนเต็ม
200
เวลาสอบ
3ชม.
ประเภทคำถาม
12
ฉบับ
เวลา
คะแนน
จำนวนข้อ
น้ำหนักคะแนน
ประเภทคำถาม
AS 1: Pure Mathematics
1ชม. 30นาที
100
8
50%
Roots of Polynomials & Algebraic Transformation, Matrices, Linear Systems & Transformations, Complex Numbers, Mod-Arg & Loci, 3D Vectors, Lines, Planes & Products
AS 2: Applied Mathematics
1ชม. 30นาที
100
10
50%
Applied option questions, answer two of four sections
เกณฑ์เกรด
ABCDE
ข้อกำหนดเครื่องคิดเลข
Calculators are required and permitted throughout both AS 1 and AS 2, there is no non-calculator paper. Computer algebra systems that manipulate algebra symbolically are explicitly banned for this specification, and calculators must not have any retrievable information stored in them, including formulae, notes or programs. A calculator capable of matrix operations to at least order 3 by 3, an iterative or numeric solve function, and summary statistics and standard-distribution probabilities is required for the applied options.
AO1: AO1: use and apply standard techniques, by selecting and correctly carrying out routine procedures and accurately recalling facts, terminology and definitions. (38%)
AO2: AO2: reason, interpret and communicate mathematically, by constructing rigorous mathematical arguments including proofs, making deductions and inferences, assessing the validity of mathematical arguments, explaining reasoning, and using mathematical language and notation correctly. (36%)
AO3: AO3: solve problems within mathematics and in other contexts, by translating problems into mathematical processes, interpreting solutions in their original context, translating situations into mathematical models, using those models, and evaluating outcomes and limitations. (26%)
วัตถุประสงค์: Get the mean, standard deviation and regression line from a set of data in one pass instead of computing sums by hand.
ใช้เมื่อใด: Any AS 2 Statistics option question giving a table of paired or single-variable data, and as a check on a Poisson or geometric probability once you have written the formula out yourself.
ขั้นตอน
Open the statistics menu, choose 1-variable or 2-variable as the question needs, clear any old data, key in each value or pair from the question paper pressing equals after each entry, then read the mean, standard deviation or regression coefficients from the variable menu.
ข้อควรระวังในการสอบ: This is a live keystroke sequence performed during the exam on data printed on the paper in front of you, not a stored program. CCEA and JCQ ban any retrievable stored information, formulae or notes.
Memory recall for repeated determinants
Casio fx-991EX ClassWiz (or equivalent)
วัตถุประสงค์: Hold a determinant or an intermediate value you will reuse two or three lines later without retyping it.
ใช้เมื่อใด: Matrix inverse or volume questions where the same determinant feeds into more than one 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 press recall and the same letter when you need the value again.
ข้อควรระวังในการสอบ: Clear the memory at the start of the exam and only store values you calculate live during the paper, this is not a saved program and holds nothing from before the exam.
Numeric equation solver as a check
Casio fx-991EX ClassWiz (or equivalent with a numeric solve function)
วัตถุประสงค์: Confirm a root you have already found algebraically, not replace the algebra.
ใช้เมื่อใด: After solving a cubic or quartic factorisation by hand, to catch an arithmetic slip before moving on.
ขั้นตอน
Enter the equation into the solve function, give a starting estimate close to your algebraic root, and compare the number the calculator returns against your own working.
ข้อควรระวังในการสอบ: CCEA mark schemes reward shown algebraic method, not a bare calculator answer, and computer algebra systems that solve equations symbolically are banned for this specification. This numeric solver only confirms a number, it does not replace the written method.
Table mode for sign checks
Casio fx-991EX ClassWiz (or equivalent with a table function)
วัตถุประสงค์: Spot the sign of a function around a suspected root or turning point before committing to a full algebraic argument.
ใช้เมื่อใด: Cubic and quartic root questions, and checking cofactor or cross-product signs before writing a final matrix or vector.
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 works only on the function typed in during the exam, it stores nothing between questions and clears when you exit the mode.
ข้อผิดพลาดที่พบบ่อย
1highคะแนนที่เกี่ยวข้อง: 2Complex numbers, loci
Treating a half-line locus in the Argand diagram as a full infinite line when finding where two loci meet.
วิธีหลีกเลี่ยง: Sketch the locus first and mark which half of the line is actually included, then check the intersection point sits on that half before using its coordinates.
2mediumคะแนนที่เกี่ยวข้อง: 3Matrices, linear systems
Finding a zero determinant for a 3 by 3 system and stopping there, without establishing whether the planes form a line of intersection or are simply inconsistent.
วิธีหลีกเลี่ยง: After a zero determinant, substitute back or reduce the system, then state in words whether the geometry is a sheaf of planes meeting in a line or a triangular prism with no common point.
3mediumคะแนนที่เกี่ยวข้อง: 1Vectors
Leaving out the factor of one half in the vector triangle area formula, writing the area as the full magnitude of the cross product instead of half of it.
วิธีหลีกเลี่ยง: Write the formula with the half already in it before substituting any numbers, so it cannot get dropped at the final line.
4highคะแนนที่เกี่ยวข้อง: 2Vectors, planes
Using the angle between a line's direction vector and a plane's normal as the line-plane angle itself.
วิธีหลีกเลี่ยง: Find the angle to the normal with the dot product, then subtract it from 90 degrees to get the angle between the line and the plane.
5highคะแนนที่เกี่ยวข้อง: 3Matrices, inverses
Sign slips in the alternating grid of cofactors before transposing to find a matrix's adjugate, especially in the middle entries of a 3 by 3 matrix.
วิธีหลีกเลี่ยง: Write the sign grid, plus minus plus, minus plus minus, plus minus plus, next to the matrix before calculating a single cofactor, then apply it as you go rather than at the end.
Reversing the order of subtraction in relative velocity, computing the reference object's velocity minus the target's instead of target minus reference, which flips the bearing of the resulting path.
วิธีหลีกเลี่ยง: Write the relative velocity formula out with subscripts before substituting: target relative to reference is always the target's velocity minus the reference's velocity.
Multiplying two transformation matrices in the wrong order when one transformation follows another, computing MR when the question needs RM or the reverse.
วิธีหลีกเลี่ยง: Write the composite explicitly as the second transformation times the first before multiplying, and check it by testing the composite on a simple point such as (1, 0).
Treating a high PMCC value on its own as proof that one variable causes changes in the other.
วิธีหลีกเลี่ยง: State that correlation shows association only, and that any causal claim needs reasoning independent of the correlation coefficient itself.