Contents sample

Primary 6

Essential Formulae 84 Shortcuts for Solving MC

Estimation 3

Elimination 4

Substitution 5

Assumption 6

Illustration 7

Second Term

7 Applications of percentages and Discount

56

8 Circles 60

9 Speed and Travel graphs 64

10 Circumference 68

11 Simple equations 72

12 Broken line graphs 76

Timed Drill 2 80

Primary 6

First Term

1 Division and Mixed operations of decimals 28

2 3-D shapes 32

3 Averages 36

4 Bar charts 40

5 Fractions, Decimals and Percentages 44

6 Volume 48

Timed Drill 1 52

Contents

Revision

1 Multiples and Factors P4 8 2 Fractions and Decimals P3 _ P5 10

3 Large numbers ^P5 12

4 Operations of whole numbers ^{P3 _ P4} 14

5 2-D shapes ^{P1 _ P4} 16

6 Directions ^P5 18

7 Perimeter and Area ^{P4 _ P5} 20

8 Volume P5 22

9 Symmetrical shapes P4 24

10 Pictograms ^P5 26

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Shortcuts for Solving MC Shortcuts for Solving MC

Addition and Subtraction of decimals Example 1

Victor is 0.18 m taller than Tony.

The difference in height between Chris and Victor is 0.25 m. What is the largest difference in height between Tony and Chris?

A. 0.07 m B. 0.36 m C. 0.43 m D. 0.5 m Answer:

2-D shapes Example 2

How many trapeziums are there in the figure on the right?

A. 3 B. 8

C. 9 D. 11

Answer:

Draw several figures of the above and shade the trapeziums to avoid mistakes when counting.

Individual Formed by 2 Formed by 3 Formed by 4 Formed by 6 Quick Approach

Directions Example 3

Cindy is 500 m north-east of Eva. Leo is 500 m south-east of Eva. In which direction is Leo from Cindy?

A. north-west B. south-west C. north D. south Answer:

Draw bars to show the relationship between their heights.

Case 1 Case 2

Tony Tony

Chris Chris

Victor Victor

0.18 0.18

0.25

0.25

0.25 － 0.18 ＝ 0.07 0.18 ＋ 0.25 ＝ 0.43 The difference is 0.07 m. The difference is 0.43 m.

Quick Approach

Draw everyone’s position according to the question.

N South Eva

Cindy

Leo 500 m 500 m

Quick Approach

When a question involves complicated settings, we can draw a diagram to represent the question.

Illustration

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Revision

Date:

Score:

Keypoint Express

7

/22

Measures

• Use the dissection method or filling method to find the area of a polygon.

E.g. What is the area of the figure on the right?

➔ Dissect the figure into a rectangle and a square.

➔ 8×4 ＋ 4×4 ＝ 48 The area is 48 cm².

Section A

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

1.

5 cm

8 cm 2 cm

2 cm

Two squares of side 2 cm each are cut out from a rectangle, as shown above. What is the perimeter of the remaining figure?

A. 22 cm B. 26 cm C. 30 cm D. 32 cm

2. Calvin has a wire of 1 m long. He used part of the wire to make a square of side 12 cm. Then he used the wire left to make a rectangle of width 6 cm.

What is the length of this rectangle?

A. 20 cm B. 23 cm C. 34 cm D. 40 cm

3.

3 cm 6 cm

14 cm 6 cm 10 cm

What is the area of the shaded part?

A. 168 cm² B. 105 cm² C. 84 cm² D. 36 cm² 4.

The above figure is formed by six squares of perimeter 60 cm each.

What is the area of the shaded part?

A. 900 cm² B. 450 cm² C. 225 cm² D. 120 cm²

2013

Substitution Find the length of the remaining wire first. Then substitute to check.

Perimeter and Area

4 cm 8 cm

Perimeter Square Side length×4 Rectangle (Length ＋ Width)×2

Area

Square Side length×Side length

Rectangle Length×Width

Parallelogram Base×Height

Triangle Base×Height

2

Trapezium （Upper base ＋ Lower base）× Height 2

•

•

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5.

24 cm

6 cm

There are three rectangular cards of the same size. Each card is 24 cm long and 6 cm wide. The cards are overlapped as shown above. What is the area of the figure formed?

A. 324 cm² B. 360 cm² C. 396 cm² D. 432 cm²

2011

6.

The above figure is formed by two squares of the same size and an equilateral triangle. The area of a square is 64 cm². What is the perimeter of the figure?

A. 48 cm B. 64 cm C. 80 cm D. 112 cm

Challenge

Section B

Working steps must be shown in answering questions in this section unless specified otherwise. (Total 10 marks)

7. The figure on the right is the layout of a small field in Green Farm.

(a) What is the area of the small field? (Give the answer only) ^{2 marks}

Answer: The area of the small field is m².

(b) The farm has another rectangular field of width 18 m. The area of this field is the same as that of the small field. What is the length of this field? (Give the answer only) ^{2 marks}

Answer: The length of this field is m.

8. My brother uses several equilateral triangles of the same size to form figures.

(a) How many equilateral triangles does my brother need at least to form a trapezium? (Give the answer only) ^{2 marks}

Answer: He needs at least triangles.

(b) The perimeter of the smallest parallelogram formed is 96 cm. What is the perimeter of an equilateral triangle? ^{4 marks}

18 m

9 m 12 m

9 m 18 m

Challenge

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Look for the solution here

Cracking Past Challenges

2012

Date:

Score:

Plastic stick X Plastic stick Y Plastic ball There are 7 plastic sticks X, 4 plastic

sticks Y and 8 plastic balls. How many more of each type will be needed at least to make a pentagonal prism?

Plastic stick X Plastic stick Y Plastic ball

A. 2 2 3

B. 3 1 2

C. 3 3 2

D. 3 6 2

Shape and Space

2

Term1st

3-D Shapes

Section A

Choose the correct answer. You only need to write down the letter preceding the selected answer. (Total 24 marks, 2 marks each)

1. In which of the following solids is the difference in number between vertices and edges the largest?

A. triangular pyramid B. quadrilateral prism C. pentagonal pyramid D. hexagonal prism 2.

What kind of solid can be formed by folding the above net?

A. triangular prism B. cuboid

C. pentagonal prism D. hexagonal prism

3. Which of the following is the net of a pentagonal prism?

A.

B.

C.

D.

Elimination

There are at least 7 faces in the net of a pentagonal prism. Eliminate options that have less than 7 faces.

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4. To make a prism with 8 vertices using plastic sticks and plastic balls, how many plastic sticks are used at least?

A. 8 B. 9 C. 12 D. 24 5.

The above figure is a triangular prism made of plastic sticks and plastic balls. Jack wants to change it into a hexagonal prism. How many more plastic sticks and plastic balls are needed at least?

No. of No. of

plastic sticks plastic balls

A. 9 6

B. 9 1

C. 3 6

D. 3 1

6. Plastic stick A Plastic stick B Plastic ball

There are 5 plastic sticks A, 4 plastic sticks B and 4 plastic balls. How many more materials are needed at least to make a cuboid with a square base?

Plastic Plastic Plastic stick A stick B balls

A. 0 3 4

B. 1 2 4

C. 2 1 8

D. 3 0 4

Challenge

7.

How many edges are there in the solid formed by the above net?

A. 6 B. 8 C. 9 D. 12

8. There are 10 sticks and 6 plastic balls. If they are used to make the framework of a solid with the smallest number of sticks and plastic balls left, what kind of solid can be formed?

A. triangular prism B. triangular pyramid C. quadrilateral prism D. pentagonal pyramid

9. Which of the following solids has the same shape of cut section no matter how the solid is cut once?

A. B.

C. D.

2006

2014

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Section B

Working steps must be shown in answering questions in this section unless specified otherwise. (Total 18 marks)

13. Peggy made some specific solids using plastic sticks and plastic balls.

?

Solid 1 Solid 2 Solid 3 Solid 4

(a) According to the pattern, by which two solids is solid 4 formed? (Give the answer only) ^{2 marks}

Answer: It is formed by a/an and a/an .

(b) To make a solid 4, how many plastic sticks and plastic balls are needed at least?

(Give the answer only) ^{2 marks}

Answer: At least plastic sticks and plastic balls are needed.

(c) According to the pattern, how many faces should solid n have? (Give the answer only and express the answer in terms of n) ^{2 marks}

Answer: Solid n should have faces.

2010

10. Which of the following figures

cannot be a cut section of a cylinder?

A. circle B. ellipse C. triangle D. rectangle

11. My sister makes a solid so that the difference in number between the sides of the base and vertices is 1. Which of the following solids can be made?

A. triangular prism B. quadrilateral pyramid C. pentagonal prism D. hexagonal prism

Challenge

12.

Which of the following solids has the above cut section when it is cut along the dotted line?

A. B.

C. D.

Elimination If the answer cannot be confirmed, first eliminate options that are sure to be cut sections of a cylinder.

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14. The net below is formed by six squares. Charles uses it to fold a solid.

36 cm

(a) What is the solid folded by Charles? How many edges does it have? (Give the answer only) ^{2 marks}

Answer: The solid is a/an . It has edges.

(b) What is the volume of the solid folded? (Give the answer only) ^{2 marks} Answer: The volume is . (Give your answer with a unit)

(c) A plastic stick costs $1.2. It is $0.7 more expensive than a plastic ball. Charles wants to make a framework of the solid folded using plastic sticks and plastic balls. How much does he need to pay at least for the material? ^{4 marks}

15. (a) The figure on the right is a cuboid. It is cut vertically along the dotted line into two equal halves. Write down the name of the shape of the cut section and draw the shape. (Give the answer only) ^{2 marks}

Answer: The shape of the cut section is a/an .

1 cm 1 cm

(b) What is the area of the cut section in part (a)?

(Give the answer only) ^{2 marks}

Answer: The area is . (Give your answer with a unit)

2016

4 cm

5 cm

3 cm _{5 cm}

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Timed Drill

Score:

2

Time: 25 mins /50

Term2nd

Section A (30 marks)

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

1. Which of the following numbers has the smallest value?

A. 1 38 B. 1.38

C. 140%

D. 1 720 2.

20 cm

The above is a rectangle of length 120 cm and width 40 cm. Four

right-angled triangles of the same size are shaded. What percentage of the figure is shaded?

A. 25%

B. 33%

C. 33 13 % D. 50%

3. A can of orange juice has 600 mL.

A promotion package has a volume of 20% more. Mike bought a promotion package of orange juice and drank 25%. How much orange juice was left?

A. 180 mL B. 450 mL C. 465 mL D. 540 mL

4. A pair of socks costs $30. It is sold at 5% off. Any purchase of 5 pairs or more have a discount of 15%. How much cheaper is it to buy 6 pairs?

A. $153 B. $27 C. $9

D. $4.5 5.

2 circles of diameters 8 cm and 2 circles of diameters 4 cm are put together. The centres are joined to form a trapezium, as shown above. What is the perimeter of the trapezium?

A. 24 cm B. 32 cm C. 48 cm D. 64 cm 6.

How many line(s) of symmetry is/are there in the above figure?

A. 0

B. 1

C. 3

D. 5

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14. Jim, Alvin and Ann needed to finish 10 questions. Jim took k seconds.

Alvin took 6 seconds more than half of Jim did and 3 seconds less than Ann did. Ann took 54 seconds. Which of the following equations should be used to find the time Jim took to finish the questions?

A. k

2 ＋3 ＝ 54 B. k2 － 3 ＝ 54

C. k

2 ＋9 ＝ 54 D. 2k＋9 ＝ 54

15. If 8 ＋ h5 ＝10.5, then 2h ＝ ? A. 20.2

B. 25 C. 44.5 D. 89

End of Section A

Section B (20 marks)

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

16. The following is the route map of the area near Mr Chan’s company.

Mr Chan’s Company 500 m 500 m 750 m

Convenience Store

MTR station Restaurant B

Restaurant A

(a) Today, Mr Chan walked from the company to Restaurant B to have lunch at an average speed of 2.5 m/s for 8 13 minutes. What was the distance between the Convenience Store and the MTR station? ^{4 marks}

(b) After lunch, Mr Chan went to the Convenience Store to buy chewing gum. The original price of chewing gum was $15.5 and now sold at a reduction of $9.3.

What was the percentage discount? (Give the answer only) ^{2 marks} Answer: The percentage discount was %.

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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. Use the above seven number cards to form the smallest even number.

What is this even number?

A. 1 035 789 B. 1 035 798 C. 1 357 908 D. 1 357 980

1. 用以上七張數字卡組成一個最小 的偶數，這個偶數是甚麼？

A. 1 035 789 B. 1 035 798 C. 1 357 908 D. 1 357 980

2. Which of the following options can make the above expression to be largest and odd?

A. ★ ＝ 4, ● ＝ 5

B. ★ ＝ 4, ● ＝ 1

C. ★ ＝ 5, ● ＝ 4

D. ★ ＝ 1, ● ＝ 4

2. 下列哪個選項能使以上算式得出 一個最大的奇數？

A. ★ ＝ 4，● ＝ 5

B. ★ ＝ 4，● ＝ 1

C. ★ ＝ 5，● ＝ 4

D. ★ ＝ 1，● ＝ 4

4

●

★ 3 1

×

0 5 7 9 3 1 8

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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。

31. Mrs Lam rented 660 m² of farmland to grow vegetables. 38 of the farmland was used to grow lettuce, 16 of it was used to grow broccoli. The rest was used to grow tomato.

(a) What fraction of the farmland was used to grow tomato? (Give the answer only)

[2 marks]

(b) If the monthly rent of the farmland was $12 per square metre, what was the monthly rent of the farmland used to grow tomato?

^{[4 marks]}

31. 林太太共租用 660 m² 的耕地來種 菜，其中 38 種植生菜， 1

6 種植西 蘭花，餘下的種植番茄。

(a) 種植番茄的耕地面積佔全幅耕 地的幾分之幾？（只須寫出答 案）

[2 分]

(b) 如果耕地每平方米的月租是

$12，那麼種植番茄的耕地的 月租共多少？

[4 分]

32. Jimmy is x years old this year. His grandmother is 66 years old this year.

His grandmother is 6 years old less than 4 times of the age of Jimmy.

How old is Jimmy this year? (Use an equation to solve the problem and show your working)

^{[4 marks]}

32. 子 明 今 年 x 歲， 他 的 祖 母 今 年 66 歲，她的年齡是子明的 4 倍小 6 歲。子明今年多少歲？（須用方 程列式計算）

[4 分]

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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.

Section

A

甲 部

Answer Sheet 答題紙

Name姓名： ⁽English⁾ (中文)

Class Class No.

班別： 班號：

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

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Teacher’s use only 供教師專用

31 (a).

The fraction was

佔全幅耕地的 。

31 (b). 2

32. 4

33 (a). 4

33 (b). 4

Kelvin should use the

家文應使用 。

Marks 佔分

Go On To Next Page 轉下頁續答

Section

B

乙 部

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