2025 DSE 数学-Mathematics 真题 答案 详解

答案(英文)

2025 HKDSE Mathematics Compulsory Part Examination Paper I Suggested Solutions by Jacky Chan

1
[ \frac{\left(x^4 y^{-5}\right)^3}{xy^2} = x^{4 \times 3 - 1} y^{-5 \times 3 - 2} = x^{11} y^{-17} = \frac{x^{11}}{y^{17}} ]

2
[ \frac{1}{3d-4} - \frac{2}{6d+5} = \frac{(6d + 5) - 2(3d - 4)}{(3d - 4)(6d + 5)} = \frac{13}{(3d - 4)(6d + 5)} ]

3
Since (m:n=8:7), let (\begin{cases} m = 8k \ n = 7k \end{cases}), where (k) is a non-zero constant. [ 2m + 3n = 999 \ 2(8k) + 3(7k) = 999 \ k = 27 \ n = 7(27) = 189 ]

4a
((-2,-4))

b
(C=(-2,-4+t)) Since A, O and C are collinear, The slope of OC = The slope of OA [ \frac{(-4+t)-0}{-2-0}=\frac{-2-0}{4-0} ] (t = 5)

P.1 (17) © Jacky Chan Yui Him (2025) All rights reserved.