A comprehensive study and exam preparation guide for the OCR GCSE (9-1) Mathematics J560 Higher Tier, incorporating structural insights, common mistakes from examiner reports, and tactical calculator advice.
อ่าน 4 นาทีอัปเดตเมื่อ: 21 มิ.ย. 2569
ภาพรวมข้อสอบ
จำนวนฉบับ
3
คะแนนเต็ม
300
เวลาสอบ
4ชม. 30นาที
ประเภทคำถาม
3
ฉบับ
เวลา
คะแนน
จำนวนข้อ
น้ำหนักคะแนน
ประเภทคำถาม
Paper 4 (J560/04) Higher Tier - Calculator
1ชม. 30นาที
100
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Paper 5 (J560/05) Higher Tier - Non-Calculator
1ชม. 30นาที
100
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Paper 6 (J560/06) Higher Tier - Calculator
1ชม. 30นาที
100
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เกณฑ์เกรด
9876543U
ข้อกำหนดเครื่องคิดเลข
A scientific or graphical calculator that meets JCQ regulations may be used (some GCSE Mathematics and Science papers are non-calculator). Graphical calculators must be set to exam mode; you must clear any stored programs, notes or data before the exam, and the calculator must not be able to retrieve stored text or formulae.
AO1: AO1: Use and apply standard techniques (50%)
AO2: AO2: Reason, interpret and communicate mathematically (25%)
AO3: AO3: Solve problems within mathematics and in other contexts (25%)
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 under JCQ rules, but you must still show your method — an unsupported calculator answer earns no method marks. Clear all stored programs, notes and data (graphical calculators in exam mode) before the exam.
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 under JCQ rules, but you must still show your method — an unsupported calculator answer earns no method marks. Clear all stored programs, notes and data (graphical calculators in exam mode) before the exam.
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 under JCQ rules, but you must still show your method — an unsupported calculator answer earns no method marks. Clear all stored programs, notes and data (graphical calculators in exam mode) before the exam.
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 under JCQ rules, but you must still show your method — an unsupported calculator answer earns no method marks. Clear all stored programs, notes and data (graphical calculators in exam mode) before the exam.
ข้อผิดพลาดที่พบบ่อย
1highคะแนนที่เกี่ยวข้อง: 3Similarity
Failing to square the linear scale factor when working with surface areas, or to cube it for volume scaling on mathematically similar models.
วิธีหลีกเลี่ยง: Always identify the linear scale factor first, then explicitly calculate and write down the area scale factor \( k^2 \) and volume scale factor \( k^3 \) before doing any multiplication.
2highคะแนนที่เกี่ยวข้อง: 2Triangle mensuration
Losing final accuracy marks due to premature rounding of intermediate values during multi-step trigonometry calculations.
วิธีหลีกเลี่ยง: Keep the full decimal expansions on your calculator screen or store intermediate steps to at least 5 significant figures on paper.
3highคะแนนที่เกี่ยวข้อง: 2Circles
Omitting explicit geometric reasons in circle theorems and parallel line angle proofs.
วิธีหลีกเลี่ยง: Write down the exact mathematical name of the rule (e.g., 'alternate segment theorem' or 'angles subtended by the same arc are equal') alongside your angle calculations.
4mediumคะแนนที่เกี่ยวข้อง: 3Discrete growth and decay
Applying a simple interest calculation to a multi-year investment or savings account instead of compound interest.
วิธีหลีกเลี่ยง: Always verify if the question states 'simple' or 'compound'. For compound interest, use the exponential multiplier formula: \( \text{Initial} \times (\text{multiplier})^n \).
5mediumคะแนนที่เกี่ยวข้อง: 2Combined events and probability diagrams
Failing to subtract the intersection 'x' from the individual totals of a Venn diagram when calculating conditional probabilities or ratios.
วิธีหลีกเลี่ยง: Always construct the Venn Diagram from the middle outwards, subtracting overlapping regions from individual category totals before completing the outer elements.
6mediumคะแนนที่เกี่ยวข้อง: 1Interpreting and representing data
Plotting points at the group midpoints instead of the upper boundaries on a cumulative frequency curve.
วิธีหลีกเลี่ยง: Always plot the cumulative frequency against the upper class boundary of each interval.
7mediumคะแนนที่เกี่ยวข้อง: 2Ruler and compass constructions
Failing to draw supportive construction arcs when performing perpendicular bisectors or angle bisectors.
วิธีหลีกเลี่ยง: Never draw boundary lines freehand or erase your compass construction marks; examiners require visible intersecting arcs to award full marks.