7 Basic Computation... 01-01

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7 Basic Computation... 01-01

2 Directed Numbers and Number Line... 02-01

3 Introduction to Algebra... 03-01

4 Using Algebra to Solve Problems ... 04-01

5 _Approxi roximation and Estimation... 05-01

6 Construction and Interpretation of Simple Statistical Diagrams (I)... 06-01 grated Assessment 1... IAl-01

7 Percentages... 07-01

8 Introduction to Geometry... 08-01

9 Areas and Volumes (I)... 09-01

10 Introduction to Coordinate Geometry... 10-01

11 Angles Related to Straight Lines... 11-01

12 Operations of Polynomials ... 12-01 grated Assessment 2... ... IA2-01

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Revision Test... RT-01 Road to HKDSE... 00-06

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Road to HKDSE - Junior Secondary

Mathematics Exercises (New Syllabus Edition) S1

1. Basic Computation

Name:

Class:

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1. Basic Computation

－（ Determine whether each of the following is correct or not.

1. 2 is a prime number.

2. For any two numbers, their H.C.F. must be less than their L.C.M.

3. 32 can be written as a product of its prime factors.

4. 25 733 is divisible by 9.

5. If the last 2 digits of a number is 32, then the number is divisible by 4.

6. 4 "'"" 2 X 32 = 4 "'"" (2 X 32)

Conventional Questions

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LevelO

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1. Find the H.C.F. of each of the following pairs of numbers.

(a) 2 x 2 x 3 and 2 x 3 x 5 (b) 2 x 3 x 3 x 5 and 2 x 2 x 3 x 3 x 3 x 7

2. Find the L.C.M. of each of the following pairs of numbers.

(a) 2 x 3 x 3 and 3 x 3 x 5 (b) 2 x 5 x 5 x 5 and 2 x 3 x 3 x 3 x 11

3. In each of the following, put a tick into the box if the number is divisible by 4, 6, 8 or 9.

(a) (b) (c) (d)

Number 328 810 1276 3234

Divisible by

4 6 8 ⁹

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;Cross-topics Challenge

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If A and Bare prime numbers and their L.C.M. is 35, find the value of （

_A 二） _B ^x

₂ ．

:Common ExamQuestions

1. Basic Computation

1. If a number is divided by 5, 6 and 8 respectively, the remainders are all 2. Find the smallest possible value of the number.

2. The L.C.M. of 18 and a prime number P is 1602. Find the value of P.

Hint

巨lPLC793-01-011-1

－

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[Conventional Questions

1. (a) Round up 842.9351 to the nearest hundred.

(b) Round down 842.9351 to 2 decimal places.

(c) Round off 842.9351 to 3 significant figures.

(3 marks) 2. In a room, the number of boys is 35% more than the number of girls. The sum of the numbers of boys and girls

is 94. Find the number of boys.

3. A handbag is sold at a discount of 20% on its marked price. The selling price of the handbag is $680.

(a) Find the marked price of the handbag.

(b) After selling the handbag, the profit percentage is 25%, find the cost of the handbag.

(4 marks)

(4 marks) 4. The marked price of a sofa is 25% above its cost. A profit of $150 is made by selling the sofa at a discount of

10% on its marked price. Find the marked price of the sofa.

(5 marks) 5. The price of a sport watch is $200 more than a classic watch. The price of 2 sport watches and 5 classic

watches is $7400. Find the price of a sport watch.

(4 marks)

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Road to HKDSE

—

= $3250

25. (a) Marked price= $250 x (1 + 40%)

＝＄纈 Profit = $(3250 -2500)

＝＄唧

(b) Total income= $[140(350) + 60(350) x (1-40%)]

= ＄61 6OO

$750 (b) Profit percentage = � x 100%

$2500

＝罈

21. (a) Total cost= $(60 + 140)

=$200

Total income= $(120 + 120)

=$240 Profit = $(240 -200)

＝＄

(b) Profit percentage=^—$40 x100%

$200

＝筮 Level 2

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，

22. (a) Income in last month = $5000 x 200

= ＄1 OOO OOO Income in this month

= $[5000(1 -10%) X 200(1 + 15%)]

= ＄1 O35 OOO (b) Percentage change

＝

$1 000 000

= +3.5%

23. Let $x be the cost of the jacket.

Marked price =$x(1 + 60%)

= $1紅

Selling price = $1紅(1-30%)

= $1.12x l.l2x-x = 30

X=25Q

Marked price of the jacket= $1.6(250)

＝磾 (S) Analysis

Express the marked price and the selling price in terms of the cost.

24. Let x be the number of candies Windy has.

••

Then Paul has (1 + 25%)x = l.25x.

X + l.25X = 144 X=64

Windy has 64 candies and Paul has 1.25(64) = 80 candies.

Their difference = 80 -64

＝垃

(c) Profit percentage= $(61 6OO-2OO x 25O)

$200 X 250

= 23.2%

26. (a) Price of 3 pairs of socks before discount

= $60 X 3

= $180

Selling price= $180 x (1 -10%)

＝醞 (b) Price before discount

= $(120 + 150 + 130 + 190)

= $590

Price Eric needs to pay

= $590 X (1 -20%)

＝醞

(c) Price before discount

= $(120 + 150 + 130 + 190 + 60)

= $650

Price Eric needs to pay

= $650 X (1 -40%)

= $390

< $472 It is agreed.

Multiple-choice Questions

甲1. Percentage increase (24-2O) °C x100%

＝

= 20%

The answer is C.

2. Weight of Fanny

= 72 7 (1 -20%) kg

= 90 kg The answer is A.

3. Profit percentage

＝ $（52-4O) x100%

= 30%$40

The answer is C.

4. Profit percentage

= ＄25 x 1OO%

$(125 -25)

= 25%

The answer is D.

x100%

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