Master the Pearson Edexcel International GCSE Further Pure Mathematics (4PM1) with our examiner-backed guide. Learn how to manage the 120-minute papers, prevent accuracy loss through proper exact-value working, score maximum marks on 'Show That' proofs, and implement strategic checks using substitution and numerical methods.
อ่าน 4 นาทีอัปเดตเมื่อ: 21 มิ.ย. 2569
ภาพรวมข้อสอบ
จำนวนฉบับ
2
คะแนนเต็ม
200
เวลาสอบ
4ชม.
ประเภทคำถาม
4
ฉบับ
เวลา
คะแนน
จำนวนข้อ
น้ำหนักคะแนน
ประเภทคำถาม
Paper 1 (4PM1/01)
2ชม.
100
11
50%
Short Answer (Algebra & Series), Medium Structured (Calculus & Coordinate Geometry), Long Applied (Trig & Coordinate Proof)
Paper 2 (4PM1/02)
2ชม.
100
11
50%
Short Answer (Trig & Inequalities), Medium Structured (Graphs, Logs & Series), Long Applied (Vectors & 3D Geometry)
เกณฑ์เกรด
9876543U
ข้อกำหนดเครื่องคิดเลข
A scientific or graphical calculator is permitted. Graphical calculators must be in exam mode with all stored programs and data cleared before the exam; the calculator must not be able to retrieve stored text or formulae.
AO1: AO1: Demonstrate knowledge and understanding of mathematical techniques (55%)
AO2: AO2: Apply mathematical techniques to solve problems and prove identities (45%)
วัตถุประสงค์: Tabulate \(y\) across a range of \(x\) to locate sign changes (roots) and approximate maxima/minima.
ใช้เมื่อใด: Solving or sketching a function when you want to find where its graph crosses or turns.
ขั้นตอน
Enter the function in TABLE mode, set the start, end and step, then read where the sign of \(y\) changes or where it peaks.
ข้อควรระวังในการสอบ: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
Statistics mode (mean, SD & regression)
Scientific calculator (e.g. Casio fx-991 series)
วัตถุประสงค์: Read the mean \(\bar{x}\) and standard deviation directly, and the gradient/intercept (and \(r\)) of a linear regression for bivariate data.
ใช้เมื่อใด: Any data-handling, statistics, or required-practical analysis question.
ขั้นตอน
Enter the data in STAT mode (1-VAR or A+BX), then recall \(\bar{x}\), \(\sigma\) or the regression coefficients.
ข้อควรระวังในการสอบ: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
Carry exact values with Ans & memory
Scientific calculator (e.g. Casio fx-991 series)
วัตถุประสงค์: Keep full-precision intermediate values to avoid rounding errors.
ใช้เมื่อใด: Multi-step calculations where premature rounding loses the final accuracy mark.
ขั้นตอน
Use Ans, STO/RCL or the M+ memory to reuse the unrounded result of each step; round only the final answer.
ข้อควรระวังในการสอบ: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
Equation solver — to CHECK your working
Scientific calculator (e.g. Casio fx-991 series)
วัตถุประสงค์: Use the built-in EQN/SOLVE mode to verify roots of quadratics or simultaneous equations you have already solved by algebra.
ใช้เมื่อใด: As a check only, after solving by hand.
ขั้นตอน
Enter the coefficients in EQN mode (or use SOLVE) and confirm they match your worked solution.
ข้อควรระวังในการสอบ: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
ข้อผิดพลาดที่พบบ่อย
1highคะแนนที่เกี่ยวข้อง: 3Trigonometry
Premature rounding of intermediate surd and trigonometric values in multi-step questions.
วิธีหลีกเลี่ยง: Store exact intermediate values in calculator variables (A, B, C, D) instead of writing down and working with truncated decimals.
2highคะแนนที่เกี่ยวข้อง: 4Trigonometry
Cancelling out trigonometric terms by dividing both sides of an equation (e.g. dividing by sin A) instead of factorising.
วิธีหลีกเลี่ยง: Collect all terms on one side of the equation and factorise (e.g. sin A(2cos A - 1) = 0) to avoid losing valid roots in the given interval.
3highคะแนนที่เกี่ยวข้อง: 5Calculus
Skipping explicit algebraic integration steps and limit substitutions, presenting only the final numerical value computed by a calculator.
วิธีหลีกเลี่ยง: Always write down the integrated algebraic expression in square brackets, show the substituted upper and lower limits explicitly as a subtraction, and then solve.
4mediumคะแนนที่เกี่ยวข้อง: 1The quadratic function
Forgetting to write final formulated quadratic equations with '= 0', leaving only a quadratic expression.
วิธีหลีกเลี่ยง: Double-check that any final quadratic equation requested contains the equality sign and zero (e.g., 3x^2 - 12x - 81 = 0) to secure the final accuracy mark.
5mediumคะแนนที่เกี่ยวข้อง: 2Logarithmic functions and indices
Failing to check and reject invalid roots in logarithmic equations.
วิธีหลีกเลี่ยง: Substitute all calculated x-values back into the original logarithmic arguments; if an argument becomes negative or zero, explicitly state that the root is rejected.