Contents
1 Directed Numbers ... 1
2 Estimation ... 7
3 Using Algebra to Solve Problems ... 14
4 Operations of Polynomials ... 21
5 Percentages ... 27
6 Construction and Interpretation of Simple Statistical Diagrams (I) ... 34
7 Introduction to Geometry ... 42
8 Areas and Volumes (I) ... 49
9 Symmetry and Transformation ... 56
10 Introduction to Coordinate Geometry ... 63
11 Congruence and Similarity ... 70
12 Angles Related to Straight Lines ... 77
Revision Test ... 84
Preparing for the New School Year ... 91
... 94
... 95
Sample
Place Hong Kong Paris Chicago Tokyo Sydney
Time zone GMT GMT GMT GMT GMT
Knowledge Reminder
1. Operations of Directed Numbers
(a) Addition (b) Subtraction
(+a) + (+b) = +a + b (+a) – (+b) = +a – b (–a) + (+b) = –a + b (–a) – (+b) = –a – b (+a) + (–b) = +a – b (+a) – (–b) = +a + b (–a) + (–b) = –a – b (–a) – (–b) = –a + b
(c) Multiplication (d) Division
(+a)(+b) = +ab (–a)(+b) = –ab (+a)(–b) = –ab (–a)(–b) = +ab
b a +
+ = +b a b a + - = –b
a b a - + = –b
a a - = +a
Daily Life Mathematics
A time zone is a region on Earth that has uniform standard time. There are 24 time zones on Earth. The definition of a time zone can be written in short form as GMT ± n, where GMT stands for the Greenwich Mean Time and n is a positive number.
For example, the time zone of Los Angeles is GMT – 8.
That means the time in Los Angeles is 8 hours later than that in Greenwich.
Can you find out the time zone of the following cities?
Unit 1
Directed Numbers
Exercise
Level 1
Calculate each of the following expressions (1 – 12).
1. (–3) – (–5) + (–4) 2. 4 – (–3) – (+6) 3. (–3)(–4)(+8)
= + – = 4 + –
= =
4. ( ) ( ) 15 5 9 - -
5. (+9)(–4) – (–12) 6. (+7) + (–2)(–3) 2. Number Line
Number line is a straight line with points representing numbers in an order. Positive numbers are on the right hand
side of 0 and negative numbers are on the left hand side of 0. –3 –2 –1 0 1 2 3
Negative Positive
Common Mistakes
Calculate (+60) ÷ (–5) × (+3).
Solution:
(+60) ÷ (–5) × (+3) = (+60) ÷ (–15)
= –4
i When performing multiplication and division in an expression, the order of operations is from the left to the right:
(+60) ÷ (–5) × (+3) = (–12) × (+3)
= –36
C oncept Builder
C oncept Builder
Determine whether each of the following statements is correct or not.
1. –3 + 7 = –4 Correct Incorrect
2. +6 – 2 = (+6)(–2) Correct Incorrect
3. (+4)(+8) = (–4)(–8) Correct Incorrect
4. For any integers a and b, a + b is always positive. Correct Incorrect 5. For any non-zero integers a and b, a × b and a ÷ b always have the
same sign. Correct Incorrect
Pan Lloyds Mathematics Study Pack — Summer Revision (Latest Upgraded Edition) S.1 – S.2
2
Sample
7. 2(–5) + (–3)(–7) 8. (+27) ÷ (–9) – (+3)(2)
9. (–2)(–8) + (–16) ÷ (+4) 10. (–1)(–2)(–3) – (+1)(+2)(+3)
11. 11 55 - ]+ ] gg –
6 4
36 - + +
] ]- ]
g g g
6 @ 12. (–5) + (+7)(–2) – ( )
( ) 5 25 - +
13. A submarine is 250 m below the sea level. Later it ascends 120 m. Using positive and negative numbers to represent the positions above and below the sea level respectively, what is the new position of the submarine now?
Level 2
Calculate each of the following expressions (14 – 17).
14. 2 5 9 16
# ' 6
- + - - -
] g ] g ] g b l
6 @
Hint
Convert the division of fraction into multiplication of its reciprocal.
15. 0. 1 5+4
b l × (–8) ÷ 3 4
b l- 16. (–2) + ((-+23)) ×
27
7 9
- - - +
] ] ]
g g g
6 @
17. 8
3 1
12 8 3
'
#
- -
+
- + - -
] c
] ] ]
g m
g g g
6 @
18. Calculate (–1) × (–1) × …× (–1) (n + 1) terms (a) n is odd, if
(b) n is even.
19. Mary joined a TV game show. She had 0 mark at the beginning. She would get 20 marks for each correct answer and lose 10 marks for each incorrect answer. If she got 6 questions correct and 9 questions incorrect, find her final marks.
20. Can you find the value of the expression (+1) + (–2) + (+3) + (–4) + … + (+99) + (–100) without using a calculator? Briefly explain how you can do it.
Hint
Represent the marks rewarded and the marks deducted by directed numbers.
r Fo
HKDSE
Pan Lloyds Mathematics Study Pack — Summer Revision (Latest Upgraded Edition) S.1 – S.2
2
Sample
21. From the given number line, find the value of x – y.
A. 7 B. 1 C. –1
D. –7 22. Calculate (–1) + (–2) – (–3) + (–4).
A. –10 B. –4 C. 4 D. 10
23. Calculate [(–3) – (–6)] × (+5).
A. –45 B. –15 C. 15 D. 40
24. 2 7 9
2 7 9 - + - + - +
] ] ]
] ] ]
g g g
g g g =
A. –1 B. 1 C. –4 D. 4
Multiple-choice Questions
25. 4 2
5 7 -
- + × 0 3. 0 4. 2 5
- - + = A. 0.3
B. –0.3 C. 30 D. –30 26. Calculate
2 -1
b l× b-32l× ... × 9 -8
b l.
A. 92 B. 9 1 C. –1 D. –
9 1
27. Alice enters an elevator at the 30th floor of a building. The elevator first ascends 15 levels and then descends 37 levels before Alice leaves the elevator.
Using positive and negative numbers to represent the up and down of the elevator respectively, what is the overall change in the position of the elevator?
A. +22 levels B. –22 levels C. +52 levels D. –52 levels
0
–1 2 y
x
M ake Yourself Smarter
M ake Yourself Smarter
In the following figure, make the sum of each circle as 0 by the given numbers on the right.
–1 5
–5
6
–2
–4 –6
2 4
3 1
7 –3
r Fo
HKDSE
Enrichment Corner
Referring to the question in Daily Life Mathematics, the answers are as follows:
Place Hong Kong Paris Chicago Tokyo Sydney
Time Zone GMT + 8 GMT + 1 GMT – 6 GMT + 9 GMT + 10
If the time in Greenwich is now 10:00 a.m., we can find the time at any places by using the time zone.
For example, the time in Chicago is 10 – 6 = 4 4:00 a.m., and the time in Sydney is 10 + 10 = 20
8:00 p.m.
(a) If the time in Greenwich is now 1:00 p.m., what is the time in Hong Kong?
(b) (i) Find the difference in time zone between Hong Kong and Chicago.
(ii) If the time in Hong Kong now is 9:30 p.m., find the time in Chicago without finding the time in Greenwich.
Open-ended Question
Given that a – b = –9, where a and b are integers. Give TWO possible sets of a and b for each of the following cases:
(a) Both a and b are positive.
(b) Both a and b are negative.
(c) One of them is positive while the other is negative.
G lossary G lossary G lossary
directed number 有向數 negative number 負數 number line 數線 positive number 正數
Pan Lloyds Mathematics Study Pack — Summer Revision (Latest Upgraded Edition) S.1 – S.2
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