Contents sample

Primary 4

Essential Formulae 76 Shortcuts for Solving MC

Estimation 3

Elimination 4

Substitution 5

Assumption 6

Illustration 7

Second Term

7 Mixed operations 48

8 Fitting and Dissecting shapes and Symmetrical shapes

52

9 Fractions and Decimals 56

10 Addition and Subtraction of fractions 60

11 Bar charts 64

12 Area 68

Timed Drill 2 72

Primary 4

First Term

1 Multiples and Factors 20

2 Quadrilaterals 24

3 Multiplication 28

4 Division 32

5 Perimeter (1) 36

6 Perimeter (2) 40

Timed Drill 1 44

Contents

Revision

1 5-digit numbers ^P3 8

2 Time ^{P2 _ P3} 10

3 3-D shapes and 2-D shapes ^{P1 _ P3} 12

4 Fractions P3 14

5 Pictograms P2 16

6 Directions ^P2 18

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Shortcuts for Solving MC Shortcuts for Solving MC

Estimation

Multiplication Example 1

Which of the following has the smallest value?

A. 297 × 8 B. 424 × 5 C. 596 × 4 D. 685 × 2 Answer:

Mixed operations of addition and subtraction Example 2

My brother had $2958. My sister had $1087.

They jointly bought a bookshelf and $1999 was left. How much did the bookshelf cost?

A. $912 B. $959

C. $2046 D. $3870

Answer:

Division Example 3

Which of the following brands of lotion for 1 bottle is the cheapest?

Brand Price

M $484 for 4 bottles

N $324 for 2 bottles

O $396 for 3 bottles and buy 3 get 1 free

P $120 for 1 bottle

A. Brand M B. Brand N C. Brand O D. Brand P Answer:

Round off the multiplicand in each option to the nearest hundred to get the approximation. Then compare.

Option A: 300 × 8 ＝ 2400 Option B: 400 × 5 ＝ 2000 Option C: 600 × 4 ＝ 2400 Option D: 700 × 2 ＝ 1400

Option has the smallest value.

Quick Approach

First write down the expression. Then do the estimation.

Expression: 2958 ＋ 1087 － 1999

Estimation: 3000 ＋ 1000 － 2000 ＝ 2000 Option is closest to $2000.

Quick Approach

First write down the expression.

Then round off the dividend to the nearest hundred.

Brand M: 500 ÷ 4 ＝ $ Brand N: 300 ÷ 2 ＝ $ Brand O: 400 ÷ 4 ＝ $ Brand P: $120

Brand is the cheapest.

Quick Approach

Some problems with the four operations may involve complicated calculations. If the numbers in the options differ by a lot, then the answer can be got quickly by estimation.

To do this, round off each number in the expression to the nearest whole number, ten or hundred ... Then do the calculation, compare the results with that in the options to find the answer.

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Revision

Date:

Score:

Keypoint Express

5

/16

Data handling

Section A

Choose the correct answer. You only need to write down the letter preceding the selected answer. (Total 12 marks, 2 marks each)

Amount of Fruit Juice Bought by Miss Chan Each stands for 1 cup

Orange Papaya Apple Melon Pear Juice Juice Juice Juice Juice

According to the above graph, answer questions 1 to 3.

1. During a sale, each cup of juice was sold at $9. Miss Chan bought the juice with $180. When she made the pictogram, she recorded the amount of orange juice wrongly, as shown above. How many more should she add to the column for orange juice?

A. 3 B. 8 C. 15 D. 20

2014

2. Mr Wong bought 2 cups of melon juice and 1 cup of pear juice. What fraction of the fruit juice Miss Chan bought was that Mr Wong bought?

A. 3

7

B. 2

3

C. 3

17 D. 320

3. Miss Chan bought 15 cups of grape juice and mango juice altogether. If the grape juice is 5 cups more than apple juice, what is the difference between the amount of mango juice and that of pear juice?

A. 2 B. 5 C. 6 D. 9

Challenge

Pictograms

Favourite Ball Games of P.4A Boys

Football Basketball

Volleyball Badminton

Each stands for 1 person

Title

Items

State the quantity that each picture stands for.

Use pictures to represent each item.

E.g. There are 7 ’s in the row for Football. That means there are 7 people like football.

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Fund Raised by Carmen in Flag Selling Day Each stands for 1 coin

$10 $5 $2 $1

According to the above graph, answer questions 4 to 6.

4. How many times of the value of $1 coins was that of $10 coins collected by Carmen?

A. 2 B. 4 C. 5 D. 10

5. The total value of $5 coins and $2 coins collected by Carmen was $23.

The number of $5 coins and the number of $2 coins differed by 1.

How many are there in the column for $2 coins?

A. 1 B. 2 C. 3 D. 4

6. How much did Carmen raise?

A. $14 B. $25 C. $48 D. $58

Challenge

Section B

Working steps must be shown in answering questions in this section unless specified otherwise. (Total 4 marks)

7. Number of sushi eaten by Mr Lam today Each stands for 1 dish Yellow dish

Green dish Red dish Gold dish

(a) Mr Lam went to a Japanese restaurant to eat sushi. There were 2 pieces of sushi per dish. How many pieces of yellow dish sushi did Mr Lam eat? (Give the answer only) ^{2 marks}

Answer: Mr Lam ate pieces of yellow dish sushi.

(b) The price of a dish of gold dish sushi is 3 times that of a dish of yellow dish sushi.

How many times of the amount Mr Lam paid for gold dish sushi is that he paid for yellow dish sushi? (Give the answer only) ^{2 marks}

Answer: The amount he paid is times that for gold dish sushi.

Challenge

Substitution Substitute each option to see which gives a total value of $5 coins and $2 coins $23.

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Date:

Score:

Look for the solution here

1

Term1st

Section A

Choose the correct answer. You only need to write down the letter preceding the selected answer. (Total 34 marks, 2 marks each)

1. Find the H.C.F. of 11 and 17.

A. 0

B. 1 C. 17 D. 187

Elimination

The common factors of two numbers must lie between 1 and the smaller number.

Eliminate options that lie outside this range.

2. Henry has two number cards. The common factors of numbers on these two number cards are 1, 2, 3, 4, 6 and 12 only. Which of the following could be his number cards?

A.

12

30

B.

36

60

C.

24

48

D.

42

72

3. The first seven multiples of R are:

R, 12, 18, 24, 30, 36, 42

Which of the following is not a factor of R?

A. 1 B. 2 C. 3 D. 4

4. The first 6 multiples of S:

12, 24, 36, 48, 60, 72 The first 7 multiples of T:

18, 36, 54, 72, 90, 108, 126

What is the L.C.M. of S and T?

A. 72 B. 48 C. 36 D. 24

2017

Multiples and Factors

Number

Cracking Past Challenges

2014

If M is divisible by 2 and N is divisible by 7, which of the following expressions must be divisible by 14?

I. M×N II. M ＋ N III. 8×N

A. I and II only B. I and III only C. II and III only D. I, II and III

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5. How many common factors are there for 15 and 25?

A. 5 B. 3 C. 2 D. 1

6. What is the greatest common multiple of 9 and 21 within 300?

A. 3 B. 63 C. 126 D. 252

7. If 180 is a common multiple of 15 and

△, which of the following numbers can be △?

A. 16 B. 20 C. 42 D. 50

Substitution

Substitute each option into △ to see which has a common multiple of 180 with 15.

8. If P＝Q×3, which of the following is not always correct?

A. 3 is a multiple of Q.

B. Q is a factor of P.

C. P is a multiple of 3.

D. The factors of Q are also the factors of P.

9. What is the sum of the second and third common multiples of 8 and 12?

A. 72 B. 96 C. 120 D. 144

10. Carmen has 16 bookmarks. The number of bookmarks she has is a multiple of that Cindy has. It is known that they have different number of bookmarks. List all the possible numbers of bookmarks Cindy has.

A. 1, 2, 4 B. 1, 4, 8 C. 1, 2, 4, 8 D. 1, 2, 4, 8, 16

11. What is the L.C.M. of the fifth and seventh multiples of 3?

A. 3 B. 36 C. 105 D. 315

12. The fifth common multiple of M and N is 220. What is the L.C.M. of M and N?

A. 44 B. 55 C. 88 D. 110

13. Which of the following sets of

numbers has 750 as their L.C.M. and 75 as their H.C.F.?

A. 2 × 3 × 5 × 7, 3 × 3 × 5 × 7 B. 2 × 2 × 5 × 5,

3 × 3 × 5 × 5 C. 2 × 5 × 5 × 7,

2 × 2 × 7

D. 3 × 5 × 5 × 5, 2 × 3 × 5 × 5

2013

Assumption Assign a value to P and Q, then examine the options.

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Section B

Working steps must be shown in answering questions in this section unless specified otherwise. (Total 16 marks)

18. A community centre holds a charity dinner. There are 219 families taking part.

(a) Each family gets a charity ticket. There are 219 charity tickets and the number on the tickets are from 001 to 219. Holders of ticket number being a multiple of 30 get a prize. How many families get a prize? (Give the answer only) ^{2 marks} Answer: families get a prize.

(b) The following three families sit at table 7. There are 12 people at the table.

Family Wong’s family Lee’s family Fong’s family

Number of people ? ? 2

The numbers of people of all three families are factors of the number of people at the table. Wong’s family has the largest number of people. How many people are there in Wong’s family and Lee’s family? (Give the answer only) ^{2 marks}

Answer: There are people in Wong’s family and people in Lee’s family.

2007

Challenge

14. Which of the following pairs of number cards has the product as their L.C.M.?

A.

4

10

B.

6

15

C.

9

21

D.

12

13

15. The first multiple of X is X. How many times of X is the sum of the second, third and fifth multiples of X?

A. 3 B. 5 C. 10 D. 30

Challenge

2014

16. Which of the following is not a factor of the result of ★×6?

A. 1 B. 6

C. ★× 2 D. ★× 12

17. If 18 is a factor of □ and 18 is a multiple of ○, which of the following must be correct?

I. ○ is a factor of □.

II. 6 is a factor of □.

III. 9 is a multiple of ○.

A. I and II only B. I and III only C. II and III only D. I, II and III

ChallengeChallenge

Assumption Assume ★ to be a number, then examine each option to see if it is a factor of ★ × 6.

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19. Class 4A

Boys 16

Girls 14

The above table shows the numbers of boys and girls in Class 4A. Miss Lam is preparing for their Christmas party.

(a) Miss Lam prepared some hats and hair accessories. The number of boys is a multiple of the number of hats. It is known that there are not enough hats for every boy. List all possible numbers of hats. (Give the answer only) ^{2 marks} Answer: The possible numbers of hats are . (b) Miss Lam gives every student a present that is worth $8. How much do these

presents cost? ^{4 marks}

20. The figure below shows some of the house numbers on Liberty Street.

No. 31 No. 33 No. 35

No. 30 No. 32

Liberty Street Park

(a) The building in which Winnie lives is shown on the above street map. Her house number is the difference of two numbers. The H.C.F. of these two numbers is 10.

What is her house number? (Give the answer only) ^{2 marks} Answer: Winnie’s house number is .

(b) If Winnie’s home is to the west of the Park, in which direction is building No. 33 from the Park? (Give the answer only) ^{2 marks}

Answer: Building No. 33 is to the of the Park.

(c) There are 30 people living on the same floor as Winnie. The number of her family member is a factor of this number. Her family members are more than 3 and less than 6. How many neighbours does Winnie have? (Give the answer only) ^{2 marks} Answer: Winnie has neighbours.

ChallengeChallenge

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Date:

Score:

Timed Drill 1

Time: 25 mins /50

Term1st

Section A (30 marks)

Choose the correct answer. You only need to write down the letter preceding the selected answer. (2 marks each)

1. There are 205 L of water. How many kettles of capacity 18 L each can be fully filled at most?

A. 10 B. 11 C. 12 D. 13

2. Our hall can accommodate up to 300 people.

Manager

The Beautiful Villa hosted an event in which 13 student groups took part in the hall. All student groups had the same number of students. Finally, one of the groups was absent. How many students attended the event at most?

A. 276 B. 277 C. 299 D. 300

3. 34 67Y is a 5-digit number. The least number added to make it divisible by both 2 and 5 is 6. What digit does Y stand for?

A. 1

B. 4

C. 6

D. 9

4. Which of the following groups of numbers has the product 2 times of their L.C.M.?

A. 6, 14 B. 8, 12 C. 14, 21 D. 10, 15

5. The first multiple of M is M. How many times of M is the sum of the first five multiples of M?

A. 5

B. 6

C. 15 D. 120 6.

6-bed room $60 per day for a bed⁺ 8-bed room $45 per day for a bed⁺

+ Check-in after 12：00 and check-out before 14：00 the next day will be counted as a day

* Check-in before 12：00 or check-out after 14：00 will be charged for 1 extra day

Youth Hostel Prices

Tony checked in a 8-bed room of the youth hostel at 10：34 a.m. on

12 February and checked out at 12：43 on 25 February. How much should he pay?

A. $585 B. $630 C. $780 D. $840

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End of Section A

Section B (20 marks)

Working steps must be shown in answering questions in this section unless specified otherwise.

16. The shopkeeper of a gift shop is packing all types of goods.

(a) There are 13 photo frames in the shop. The total weight is 975 g. The weight of a photo frame is 3 times of that of a card box. What is the weight of a card box?

(Give the answer only) ^{2 marks}

Answer: The weight of a card box is g.

(b) The shopkeeper evenly distributes 229 key rings into 19 boxes and then put the remaining key rings into one of the boxes. How many key rings are there in this box? (Give the answer only) ^{2 marks}

Answer: There are key rings in this box.

13. _P

Q R

The above regular hexagon is cut along the dotted line and divided into three parts. If the curves are equal in length, which of the following is correct?

A. P has the shortest perimeter.

B. Q has a longer perimeter than R.

C. The three parts have the same perimeter.

D. The perimeters of the three parts cannot be compared.

14. Use 6 squares each of perimeter 16 cm to form a rectangle. What is the

shortest perimeter of the rectangle?

A. 20 cm B. 40 cm C. 56 cm D. 96 cm

15.

The above graph shows the number of students in each level receiving Progress Awards in the 1^st Term.

There were 25 students receiving the awards. The number of Primary 5 students receiving the awards was 2 times of that of Primary 6 students.

How many should be in the row of Primary 6?

A. 1B. 3 C. 6D. 9

Primary 1 Primary 2 Primary 3 Primary 4 Primary 5 Primary 6

Each stands for 1 student Number of Students

Receiving Progress Awards in the 1^st Term

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Time allowed for the test: 50 minutes 測驗時間：50分鐘

Instructions:

1. This test contains two sections:

Section A: Questions 1 – 30 Section B: Questions 31 – 36 2. Answer ALL questions.

3. Write your answers on the answer sheet.

4. Write your Name, Class and Class Number on the answer sheet.

5. You may do your rough work in the blank space of this test booklet and there is no need to rub it out after the test.

6. The use of calculator is not allowed.

學生須知：

1. 本測驗卷共有兩部分：

甲部：第 1 至第 30 題

乙部：第 31 至第 36 題

2. 全部題目均須作答。

3. 把答案寫在答題紙上。

4. 在答題紙上填寫姓名、班別及班號。

5. 學生可利用本測驗卷的空白部分做算草，測驗完畢後無須將算草擦去。

6. 不准使用計算機。

Hong Kong Attainment Test 香港學科測驗

（Pre-Secondary 1 中一入學前）

Mathematics

數學

Mock Paper 模擬試卷

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Note:

Not all diagrams are drawn to scale.

Section

A

Choose the correct answer. You only need to write down the letter preceding the selected answer.

注意：

部分附圖不依比例繪畫。

甲 部

選出正確的答案。學生只須填上所選答案 前的英文字母。

1. What is the nearest place value of the money raised in the charity run that Mr Cheung has corrected to?

A. ten thousands place B. thousands place C. hundreds place D. tens place

1. 張先生把慈善跑籌得的款項取近 似值至哪個位？

A. 萬位

B. 千位

C. 百位

D. 十位

2. Which of the following has only 1, 3, 5 and 15 as their common factors?

A. 15 and 20 B. 15 and 40 C. 20 and 30 D. 30 and 45

2. 以下哪組數的公因數只有 1、3、5 和 15 ？

A. 15 和 20 B. 15 和 40 C. 20 和 30 D. 30 和 45

Money Raised in Charity Run 慈善跑籌得的款項

$30 925

The money raised in the charity run was about $31 000.

慈善跑籌得約 $31 000。

Mr Cheung 張先生

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31. 超 級 市 場 有 一 些 不 同 包 裝 的 雞 蛋，其中大盒裝有雞蛋一打，小 盒裝有雞蛋 8 隻。

(a) 店員把大盒裝和小盒裝雞蛋各 24 盒放上貨架，共有雞蛋多少 隻？

[4 分]

(b) 媽媽付 $150 購買 3 盒大盒裝 雞蛋，共找回 $42。每隻雞蛋 價值多少？（只須寫出答案）

[2 分]

(c) 媽媽用去其中 16 隻雞蛋，餘 下的雞蛋佔原有雞蛋的幾分之 幾？（只須寫出答案）

[2 分]

31. There are different types of packaging of eggs in the supermarket. The large box of eggs contains a dozen eggs and the small box of eggs contains 8 eggs.

(a) The shop assistant put 24 large boxes of eggs and 24 small boxes of eggs on a shelf. How many eggs were there?

^{[4 marks]}

(b) My mother bought 3 large boxes of eggs and paid $150. She got a change of $42. What was the price of each egg? (Give the answer only)

^{[2 marks]}

(c) My mother used 16 eggs of them.

What fraction of the eggs she bought is the remaining eggs?

(Give the answer only)

^{[2 marks]}

Section

B

Working steps must be shown in answering questions in this section unless specified otherwise.

乙 部

除特別指明外，在回答本部問題時，須列出計 算步驟。

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Answer Sheet 答題紙

Name姓名： ⁽English⁾ (中文)

Class Class No.

班別： 班號：

Total Marks 總分

1. 6. 11. 16. 21. 26.

2. 7. 12. 17. 22. 27.

3. 8. 13. 18. 23. 28.

4. 9. 14. 19. 24. 29.

5. 10. 15. 20. 25. 30.

Hong Kong Attainment Test 香港學科測驗

Pre-Secondary 1 Mathematics 中一入學前數學科

Mock Paper  模擬試卷

Section

A

甲 部

sample

Teacher’s use only 供教師專用

31 (a).

31 (b). 4

The price of each egg was

每隻雞蛋價值 $ 。

31 (c). 2

of the eggs she bought is the remaining eggs.

餘下的雞蛋佔原有雞蛋的 。

32 (a). 2

32 (b). 4

It will cost

費用是 $ 。

Marks 佔分

2

Go On To Next Page 轉下頁續答

Section

B

乙 部

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