Master the HKDSE Mathematics Compulsory Part with official examiner insights, precise time-management techniques, proven marking-scheme answer structures, and high-performance calculator strategies.
読了時間 3 分更新日: 2026年6月21日
試験の概要
試験数
2
満点
150
制限時間
3時間 30分
出題形式
4
試験
時間
配点
問題数
配点比率
出題形式
Paper 1 (Conventional Questions)
2時間 15分
105
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—
—
Paper 2 (Multiple Choice)
1時間 15分
45
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—
—
評価段階
5**5*54321U
電卓の規定
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%)
過去問と採点基準にもとづいて作成（2021–2025）。
電卓プログラム
Quadratic Roots & Discriminant
Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)
目的: Finds the discriminant \(\Delta=b^2-4ac\) and the two real roots of \(ax^2+bx+c=0\).
使う場面: Any quadratic equation, or when a question asks you to test the nature of the roots.
手順
Prompts the coefficients a, b, c, then displays \(\Delta\) followed by the two roots.
プログラム
?→A:?→B:?→C:B²-4AC→D:D◢(-B+√D)÷(2A)◢(-B-√D)÷(2A)
試験での注意: 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)
目的: 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.
使う場面: Coordinate geometry: length of a segment, checking midpoints, or perpendicular bisectors.
手順
Prompts \(x_1,y_1,x_2,y_2\) (A,B,C,D), then displays the distance, then the midpoint coordinates.
プログラム
?→A:?→B:?→C:?→D:√((C-A)²+(D-B)²)◢(A+C)÷2◢(B+D)÷2
試験での注意: 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)
目的: From \(x^2+y^2+Dx+Ey+F=0\): centre \((-\tfrac{D}{2},-\tfrac{E}{2})\) and radius \(\sqrt{(\tfrac{D}{2})^2+(\tfrac{E}{2})^2-F}\).
使う場面: Any circle given in general form in coordinate geometry.
手順
Prompts \(D,E,F\), then displays the centre coordinates and the radius.
プログラム
?→D:?→E:?→F:-D÷2◢-E÷2◢√((D÷2)²+(E÷2)²-F)
試験での注意: 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)
目的: Area of a triangle from three sides \(a,b,c\): \(s=\tfrac{a+b+c}{2}\), area \(=\sqrt{s(s-a)(s-b)(s-c)}\).
使う場面: Mensuration / trigonometry when all three sides are known but no height is given.
手順
Prompts \(a,b,c\), then displays the area.
プログラム
?→A:?→B:?→C:(A+B+C)÷2→S:√(S(S-A)(S-B)(S-C))
試験での注意: 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)
目的: Angle \(C\) opposite side \(c\): \(C=\cos^{-1}\!\big(\tfrac{a^2+b^2-c^2}{2ab}\big)\).
使う場面: Non-right-angled triangles where all three sides are known.
手順
Set the calculator to Degree mode, prompt sides \(a,b,c\), then display angle \(C\).
プログラム
?→A:?→B:?→C:cos⁻¹((A²+B²-C²)÷(2AB))
試験での注意: Must be in Degree mode for HKDSE; Radian mode gives a wrong angle.
よくあるミス
1high影響する配点: 2More about Trigonometry
Premature rounding of intermediate trigonometric or logarithmic values in Section B questions.
回避方法: 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.
2medium影響する配点: 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).
回避方法: 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 \(k^3\).
3medium影響する配点: 2Quadratic equations in one unknown
Confusing the condition for rational roots in quadratic equations with merely having real roots (checking only if \(\Delta \ge 0\)).
回避方法: 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.
4high影響する配点: 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).
回避方法: 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.
5medium影響する配点: 3Equations of straight lines
Incorrectly identifying the orthocentre of a right-angled triangle by setting up long equations of altitudes.
回避方法: 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.
6low影響する配点: 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).
回避方法: 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.