Master the HKDSE Mathematics Compulsory Part with official examiner insights, precise time-management techniques, proven marking-scheme answer structures, and high-performance calculator strategies.
อ่าน 3 นาทีอัปเดตเมื่อ: 21 มิ.ย. 2569
ภาพรวมข้อสอบ
จำนวนฉบับ
2
คะแนนเต็ม
150
เวลาสอบ
3ชม. 30นาที
ประเภทคำถาม
4
ฉบับ
เวลา
คะแนน
จำนวนข้อ
น้ำหนักคะแนน
ประเภทคำถาม
Paper 1 (Conventional Questions)
2ชม. 15นาที
105
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Paper 2 (Multiple Choice)
1ชม. 15นาที
45
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เกณฑ์เกรด
5**5*54321U
ข้อกำหนดเครื่องคิดเลข
Use only calculators on the HKEAA Approved List, bearing the 'H.K.E.A.A. APPROVED' (or the older 'H.K.E.A. APPROVED') label. The approved list includes programmable scientific models such as the Casio fx-50FH II and fx-3650P II, and you MAY keep your own formulas and programs stored in the calculator's memory — HKDSE does not require you to clear it. Graphic-display (graphing) calculators and calculators with symbolic algebra (CAS) are not on the approved list and must not be used.
AO1: AO1: Mathematical Knowledge and Skills (60%)
AO2: AO2: Mathematical Application and Problem Solving (40%)
Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)
วัตถุประสงค์: Finds the discriminant \(\Delta=b^2-4ac\) and the two real roots of \(ax^2+bx+c=0\).
ใช้เมื่อใด: Any quadratic equation, or when a question asks you to test the nature of the roots.
ขั้นตอน
Prompts the coefficients a, b, c, then displays \(\Delta\) followed by the two roots.
โปรแกรม
?→A:?→B:?→C:B²-4AC→D:D◢(-B+√D)÷(2A)◢(-B-√D)÷(2A)
ข้อควรระวังในการสอบ: If \(\Delta<0\) there are no real roots (the \(\sqrt{D}\) step will error) — that itself tells you the nature of the roots.
Distance & Midpoint
Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)
วัตถุประสงค์: For points \((x_1,y_1),(x_2,y_2)\): the distance \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\) and the midpoint.
ใช้เมื่อใด: Coordinate geometry: length of a segment, checking midpoints, or perpendicular bisectors.
ขั้นตอน
Prompts \(x_1,y_1,x_2,y_2\) (A,B,C,D), then displays the distance, then the midpoint coordinates.
โปรแกรม
?→A:?→B:?→C:?→D:√((C-A)²+(D-B)²)◢(A+C)÷2◢(B+D)÷2
ข้อควรระวังในการสอบ: Enter coordinates in the order asked; mixing up the order swaps the points (distance is unaffected, midpoint is not).
Circle: Centre & Radius (general form)
Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)
วัตถุประสงค์: From \(x^2+y^2+Dx+Ey+F=0\): centre \((-\tfrac{D}{2},-\tfrac{E}{2})\) and radius \(\sqrt{(\tfrac{D}{2})^2+(\tfrac{E}{2})^2-F}\).
ใช้เมื่อใด: Any circle given in general form in coordinate geometry.
ขั้นตอน
Prompts \(D,E,F\), then displays the centre coordinates and the radius.
โปรแกรม
?→D:?→E:?→F:-D÷2◢-E÷2◢√((D÷2)²+(E÷2)²-F)
ข้อควรระวังในการสอบ: A negative value under the root means the equation is not a real circle.
Heron's Formula (triangle area)
Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)
วัตถุประสงค์: Area of a triangle from three sides \(a,b,c\): \(s=\tfrac{a+b+c}{2}\), area \(=\sqrt{s(s-a)(s-b)(s-c)}\).
ใช้เมื่อใด: Mensuration / trigonometry when all three sides are known but no height is given.
ขั้นตอน
Prompts \(a,b,c\), then displays the area.
โปรแกรม
?→A:?→B:?→C:(A+B+C)÷2→S:√(S(S-A)(S-B)(S-C))
ข้อควรระวังในการสอบ: Only valid if the three lengths can actually form a triangle (each side < sum of the other two).
Cosine Rule (angle from 3 sides)
Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)
วัตถุประสงค์: Angle \(C\) opposite side \(c\): \(C=\cos^{-1}\!\big(\tfrac{a^2+b^2-c^2}{2ab}\big)\).
ใช้เมื่อใด: Non-right-angled triangles where all three sides are known.
ขั้นตอน
Set the calculator to Degree mode, prompt sides \(a,b,c\), then display angle \(C\).
โปรแกรม
?→A:?→B:?→C:cos⁻¹((A²+B²-C²)÷(2AB))
ข้อควรระวังในการสอบ: Must be in Degree mode for HKDSE; Radian mode gives a wrong angle.
ข้อผิดพลาดที่พบบ่อย
1highคะแนนที่เกี่ยวข้อง: 2More about Trigonometry
Premature rounding of intermediate trigonometric or logarithmic values in Section B questions.
วิธีหลีกเลี่ยง: Keep all intermediate values as exact fractions, surds, or stored in calculator memories (A, B, C, D, X, Y), and round only the final answer to 3 significant figures or exact values as requested.
2mediumคะแนนที่เกี่ยวข้อง: 3Basic properties of circles
Assuming two solids are mathematically similar based solely on matching a single ratio (e.g., base radius ratio) without verifying both matching linear scale factors (height and radius).
วิธีหลีกเลี่ยง: To prove mathematical similarity, show that the ratio of heights equals the ratio of base radii, and that area scales as \(k^2\) and volume scales as \(k^3\).
3mediumคะแนนที่เกี่ยวข้อง: 2Quadratic equations in one unknown
Confusing the condition for rational roots in quadratic equations with merely having real roots (checking only if \(\Delta \ge 0\)).
วิธีหลีกเลี่ยง: For rational roots, the coefficients must be rational and the discriminant \(\Delta = b^2 - 4ac\) must be a perfect square. Always verify both conditions before drawing conclusions.
4highคะแนนที่เกี่ยวข้อง: 2Basic properties of circles
Omitting essential geometric reasons in geometry proofs (e.g., writing congruent triangles without stating 'AAS', 'SAS', or omitting parallel line reasons).
วิธีหลีกเลี่ยง: Every statement in a geometric proof must be backed by an approved shorthand abbreviation (e.g., 'alt. angles, AB//CD', 'vert. opp. angles', 'corr. angles') in brackets.
5mediumคะแนนที่เกี่ยวข้อง: 3Equations of straight lines
Incorrectly identifying the orthocentre of a right-angled triangle by setting up long equations of altitudes.
วิธีหลีกเลี่ยง: Recognise that the orthocentre of any right-angled triangle lies exactly on the vertex containing the 90-degree right angle. No calculation is needed if the right angle vertex is known.
6lowคะแนนที่เกี่ยวข้อง: 1More about Trigonometry
Failing to discard impossible or extraneous angles in 3D trigonometry questions (e.g., keeping an angle that violates basic plane geometry constraints).
วิธีหลีกเลี่ยง: Always check if your calculated angle makes geometric sense within the triangle or tetrahedron. Verify that sum of angles on a straight line, triangle angle sum, or inequality theorems are satisfied.