HKDSE-MATH - 2023 - Paper 1

2023-I-01

Ans: $h=\dfrac{15+k^2}{5-k}$

$\begin{array}{rcl}
\dfr

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2023-I-02

Ans: $x^{34}y^{55}$

$\begin{array}{cl}
& \dfrac{x

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2023-I-03

Ans: No

The maximum absolute error correct to the nearest $1

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2023-I-04

Ans: (a) $\dfrac{-9}{2} < x < 3$ (b) $4$

Consider the first inequality, we

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2023-I-05

Ans: $35$

Let $x$ and $y$ be the number of male and female pass

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2023-I-06

Ans: (a) $6:7:17$ (b) $\dfrac{43}{50}$

Consider the equat

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2023-I-07

Ans: $\angle RQS=27^\circ$, $\angle PQS=63^\circ$

In $\D

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2023-I-08

Ans: (b) No

In $\Delta ACE$ and $\Delta BDE$,
$\begin{array

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2023-I-09

Ans: (a) Mean $=36$, mode $=33$ (b) $\dfrac{7}{12}$

Since t

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2023-I-10

Ans: (a) $\Gamma$ is the perpendicular bisector of $AB$. (b

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2023-I-11

Ans: (a) Median $=2$, inter-quartile range $=2$, variance

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2023-I-12

Ans: (a) $26$ (b) $13\pi$

Let $f(x) = k_1 +k_2x^2$, where $k_

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2023-I-13

Ans: (a) $3x+4$ (b) $2$

Let $px+q$ be the quotient, where $p$

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2023-I-14

Ans: (a) $48\text{ cm}$ (b) (i) $3087\pi\text{ cm}^3$ (ii)

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2023-I-15

Ans: (a) $\dfrac{5}{18}$ (b) $\dfrac{67}{90}$

The requir

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2023-I-16

Ans: (b) $\dfrac{3}{4}$

Since $p$ and $5p$ are the roots of t

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2023-I-17

Ans: (a) $51.5^\circ$ (b) No

By applying the sine law to $\De

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2023-I-18

Ans: (a) $\log_7 \alpha = 2-\log_7 \beta$ (b) $1$

Since $\al

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2023-I-19

Ans: (a) $G=\left(25,\dfrac{t^2-126}{t}\right)$, $H=\

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