 香港新高中文憑試(改編)試題
 High School Exam paper
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Question 1 of 14
1. Question
$ \mbox{If } \dfrac{a}{x} + \dfrac{b}{y} = 2, \mbox{ then } x = $
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Question 2 of 14
2. Question
In the figure, $ \, {ABCD} \, $ is a parallelogram. $E \,$ is a point lying on $\,CD\,$ such that $\ BE=CE\, .$
If $\ \angle ADC=120°, \ $ then $\ \angle ABE= $
CorrectIncorrect 
Question 3 of 14
3. Question
According to the figure, which of the following must be true?
$ \begin{array}{ll}\textrm{I.} & a + c = b \\
\textrm{II.} &a + b = 180° + c \\
\textrm{III.} &b + c =3 60° \end{array} $CorrectIncorrect 
Question 4 of 14
4. Question
In the figure, the 1st pattern consists of 11 dots.
For any positive integer $n\,$, the $\,(n+1)$th pattern is
formed by adding 6 dots to the $\,n$th pattern.
Find the number of dots in the 7th pattern.
CorrectIncorrect 
Question 5 of 14
5. Question
If $ x \mbox{ and } \ y$ are nonzero numbers such that
$\ (4y – 3x):(2x + y) = 5:6, \, $ then $\ x:y= $CorrectIncorrect 
Question 6 of 14
6. Question
The monthly salary of Danny is \( 25\%\,\) higher than that of Paul while
the monthly salary of Paul is \(\ 25\%\, \) lower than that of Tracy.
It is given that the monthly salary of Donald is \(\ $37\,800 \, . \)
The monthly salary of Tracy is:CorrectIncorrect 
Question 7 of 14
7. Question
If $ –2 \lt a \lt 0 $, which of the following may represent the graph of $ y=(ax+2)^2+a \; ?$
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Question 8 of 14
8. Question
If \(\ k \) is a constant such that the quadratic equation \(\ x^2+kx + 6k + 64 = 0 \ \) has equal roots, then \(\ k =\)
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Question 9 of 14
9. Question
Let $ f(x) = 8x^3 + kx + 2 \;, $ where $ k $ is a constant. If $f(x) \, $ is divisible by $ 2x+1,$ find the remainder when $ f(x) \ $ is divided by $x + 1.$
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Question 10 of 14
10. Question
\( 0.0865423 = \)
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Question 11 of 14
11. Question
\( 25 – (2x3y)^2 = \)
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Question 12 of 14
12. Question
$ 27^{222} \cdot 5^{666} = $
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Question 13 of 14
13. Question
$ \mbox{If } \: 3\alpha + \beta = 7\alpha + 3\beta = 4 \mbox {, find } \: \beta. $
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Question 14 of 14
14. Question
The solution of $ \ {7x} \gt 20 – 2x \ $ and $ \ 6x – 18 \lt 0 \ $ is
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