 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= $
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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.
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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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初中模擬試題
For Form 3 (junior secondary) in HK or Year 9 (International Schools, or UK).
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Question 1 of 21
1. Question
$ 8(2)1 = $
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Question 2 of 21
2. Question
A pie chart showing the expenditure of Paul and Molly in Jan 2015. Which statement below must be correct?
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Question 3 of 21
3. Question
Which of the following is correct?
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Question 4 of 21
4. Question
Sean is \(x\) years old. Alice is 3 times as old as Sean. 5 years later, Alice will be of age
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Question 5 of 21
5. Question
Identify whether each of the following is factorization or expansion. \[\begin{array}{rcl} \text{(i)} && (x+1)(x+3) \\[0.5em] &=&x^2+4x+3 \\[0.4em] \text{(ii)}& & x^2 + 5x + 6 \\[0.5em] &=&(x+2)(x+3) \end{array}\]
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Question 6 of 21
6. Question
Solve graphically \[\left\{\begin{array}{rcl}x1&=&2y\\3x+y&=&10\end{array}\right.\]
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Question 7 of 21
7. Question
Find the length of AB in the diagram below:
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Question 8 of 21
8. Question
The weight of Mike is measured to be 30 kg correct to the nearest kg. Which of the following could be Mike's actual weight?
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Question 9 of 21
9. Question
A straight line L of slope 3/2. Find the straight line parallel to line L.
Line \( L_1 \) \( L_2 \) \(L_3 \) \( L_4 \) Slope \( \frac{3}{2} \) \( \frac{2}{3} \) \( \frac{3}{2} \) \( \frac{2}{3} \) CorrectIncorrect 
Question 10 of 21
10. Question
In the diagram below, which of the following is an obtuse angle?
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Question 11 of 21
11. Question
Provided that \( \enspace x \geq y \, , \ \) which of the following is true?
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Question 12 of 21
12. Question
In the diagram, AB \(\parallel\) CD. Find the corresponding angles.
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Question 13 of 21
13. Question
The cumulative frequency polygon below shows the lecture hours provided by 500 university professors. Extra annual leave will be given to those professors who have lectured 600 or more hours. How many professors will have extra annual leave?
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Question 14 of 21
14. Question
A sphere has diameter 12 cm. Find its surface area correct to 1 decimal place.
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Question 15 of 21
15. Question
After enlargement of the map below, any change in the (i) size and (ii) shape?
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Question 16 of 21
16. Question
Find out the pair of congruent triangles.
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Question 17 of 21
17. Question
In triangle ∆ABC below, D is the midpoint of BC. What is AD?
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Question 18 of 21
18. Question
A cylinder of base radius 10 cm and height 12 cm. Find its surface area.
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Question 19 of 21
19. Question
Tom walks through route AB of length \(5m\). The vertical distance BC is \(3m\) and the horizontal distance AC is \(4m\). Find the gradient of the route AB.
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Question 20 of 21
20. Question
Two similar cones having heights 4 cm and 2 cm respectively. If the volume of the large cone is V \(\rm cm^3\), then the volume of the small one is:
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Question 21 of 21
21. Question
$ \textrm{If } \dfrac{a}{x} + \dfrac{b}{y} = 5, \textrm{ then } x = $
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Modified Exam. questions for High School Algebra & Numbers
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Question 1 of 11
1. Question
$(ab)\left(a^{2}+a bb^{2}\right)=$
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Question 2 of 11
2. Question
If $3 x7 y=20=x+11 y \ ,$ then $\ y=$
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Question 3 of 11
3. Question
Which of the following statements about the graph of $\ y=(3x)(x+2)+6 \ $ is/are true?
$\begin{array}{ll} \text{I. } & \text{ The graph opens downwards.} \\
\text{II.} & \text{ The graph passes through the point (1,10) . } \\
\text{III.} & \text{ The } x \text{intercepts of the graph are } 3 \text{ and } 4 . \end{array}$CorrectIncorrect 
Question 4 of 11
4. Question
Let $k$ be a constant such that $2 x^{4}+k x^{3}4 x20\,$ is divisible by $\ 2 x+k .$ Find $k.$
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Question 5 of 11
5. Question
Let $k$ be a constant. If $f(x)=x^{3}+ kx^{2}+k,$ then $f(k)+f(k)=$
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Question 6 of 11
6. Question
The least integer satisfying the compound inequality $2(x5)+5<21$ or $\dfrac{3 x5}{4}>1 \ $ is
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Question 7 of 11
7. Question
If $0.08957<x<0.08964$, which of the following is true?
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Question 8 of 11
8. Question
$ h =5\dfrac{3}{k+4} $
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Question 9 of 11
9. Question
If $\alpha$ and $\beta$ are constants such that $(x6)(x+\alpha)3 \equiv(x8)^{2}+\beta \ , \ $ then $\ \beta=$
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Question 10 of 11
10. Question
$\dfrac{\left(6 x^{7}\right)^{2}}{4 x^{5}}=$
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Question 11 of 11
11. Question
The solution of $ \ {7x} \gt 20  2x \ $ and $ \ 6x  18 \lt 0 \ $ is
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完成答題後按 FINISH QUIZ，稍等幾秒會看到得分。最後別忘記按 VIEW QUESTIONS 得出正確答案。