Exercise 1 Number and Algebra Question Booklet - · PDF fileNumber and Algebra Question Booklet. 3 Exercise 1 ... 6. Write your Name, Class and Class Number in the spaces below

1

Exercise 1

© Hong Kong Educational Publishing Company

Hong Kong Educational Publishing Co.

Exercise 1Number and Algebra

Question Booklet

3

Exercise 1


SECTION A: Choose the best answer for each question. You should mark all your answers in the ANSWER BOOKLET.

1. Factorize 121x2 - 25y2. A. (11x - 5y)(11x + 5y) B. 121(x + 5y)(x - 5y) C. 25(11x + y)(11x - y) D. (5y - 11x)(5y + 11x)

2. Factorize (x + y)2 - (x - y)2. A. 2x(x + y) B. 0 C. 4xy D. 2y(x - y)

3. Factorize 9a2 + 4(1 - 3a). A. (3a + 2)2 B. (3a - 2)2 C. (3a + 2)(3a - 2) D. Cannot be factorized

4. Factorize k2 - 7k + 12. A. (k - 3)(k - 4) B. (k + 3)(k - 4) C. (k - 3)(k + 4) D. (k - 2)(k - 6)

5. Factorize c2 - 2(3c - 4). A. (c + 2)(c + 4) B. (c + 4)(c - 2) C. (c - 2)(c - 4) D. (c - 4)(c + 2)

6. Mrs. Wong deposits $4000 into a bank for one year at an interest rate of 3% p.a. compounded yearly. What is the total amount after one year?

A. $60 B. $120 C. $4060 D. $4120

7. Thevalueofacardecreasesby8%eachyear.Ifthepresentvalueofthecaris$120000,finditsvalueafter two years.

A. $101 570 B. $101 568 C. $101 580 D. $101 600

KS3-NA11-3 factorize simple polynomials by using the difference of two squares

KS3-NA11-3 factorize simple polynomials by using the difference of two squares

KS3-NA11-3 factorize simple polynomials by using the perfect square expressions

KS3-NA11-4 use the cross method to factorize expressions of the form ax2 + bx + c

KS3-NA11-4 use the cross method to factorize expressions of the form ax2 + bx + c

KS3-NA5-3 solve simple problems on compound interest, compounded yearly

KS3-NA5-4 solve simple problems on growths and depreciations

10© Hong Kong Educational Publishing Company

TSA Assorted Exercises and Mock Practices Mathematics S3

SECTION B: Write ALL the answers in the ANSWER BOOKLET.

Working need not be shown.

26. Considerthefigureandcompletethefollowingquestions.

9πa2b is a *linear/quadratic/cubicmeasurement.(*Circlethecorrectanswer.)

Its dimension is .

27. Inthefigure,thevolumeofthesphereis11 498 23

cm3 .Findthevalueofr. (Take π as 227.)

28. Thefollowingaretwosimilarfigures.TheratiooftheperimeterofAtothatof Bis7:5.IftheareaofB is 125 cm2,findtheareaofA.

29. Thefollowingfigureshowsacuboid.WritedowntheanglebetweentheplanesABCD and ADHG.

KS3-MS3-6 distinguish among formulasfor lengths, areas, volumesby consideringdimensions

KS3-MS3-3calculatevolumesofspheres

KS3-MS3-5usetherelationshipsbetweensidesandsurfaceareasof similarfigurestosolverelatedproblems

KS3-MS8-5name the anglebetween2 planes, one of the planes beinghorizontal/vertical

Theexpressionisusedtocalculatethevolumeofthecylinder.



SECTION C: All working must be clearly shown. Write the mathematical expressions, answers and statements/conclusions in the

spaces provided in the ANSWER BOOKLET.

17. The following are the prices of 6 pairs of trousers in a shop.

$50, $450, $65, $78, $50, $72

A customer claims the average price of the trousers is $127.5. Do you think his claim is reasonable? Explain your answer briefly.

18. The following cumulative frequency polygon shows the weights of 50 students.

(a) Find the median of the weights.

(b) What is the percentage of students that are heavier than 45 kg?

19. An investment fund is made up of 3 different stocks. The following table shows the unit prices and weights of different stocks in the fund.

Stock A Stock B Stock C

Unit price $3 $2.5 $13.8

Weight 2 1 2

Find the weighted mean of the unit prices of the fund.

KS3-DH3-4 identify sources of deception in cases of misuse of averages

KS3-DH3-2 find median (from cumulative frequency polygons/curves only) from a set of grouped data

Determine whether the customer referred to the mean, median or mode.

KS3-DH3-3 calculate the weighted mean of a set of data

1

Mock Practice 1


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9 M E 1 ( Q )

Instructions:

1. There are 50 questions in this test.

2. The time allowed is 65 minutes.

3. Answer ALL questions in the separate ANSWER BOOKLET.

4. The use of HKEAA approved calculators is permitted.

5. Rough work should be done on the rough work sheet provided.

6. The diagrams in this paper are not necessarily drawn to scale.

TSA Assorted Exercises and Mock Practices Mathematics

Secondary 3Mock Practice 1

Question Booklet



7. Determine whether each of the following is factorization or expansion.

(i) 4x + 6x2 = 2x(2 + 3x)

(ii) x2 + 4x + 4 = (x + 2)2

(i) (ii)

A. Expansion Factorization

B. Expansion Expansion

C. Factorization Factorization

D. Factorization Expansion

8. Which of the following is correct?

A. 80 9> B. 100 10>

C. 120 11> D. 145 12>

9. Which of the following is an obtuse angle?

A. B.

C. D.

10. Five square plates are assembled to form an open box, of which the capacity is 64 cm3. Find the total area of the square plates.

A. 64 cm2

B. 66 cm2

C. 80 cm2

D. 96 cm2

KS3-MS4-3 identify types of angles with respect to their sizes

KS3-MS2-2 use the formulas for surface areas of cubes

KS3-NA11-1 demonstrate recognition of factorization as a reverse process of expansion

KS3-NA4-1 demonstrate, without using calculators, recognition of the integral part of a, where a is a

positive integer not greater than 200

11

Mock Practice 1



34. Inthefigure, AQB,CRD and PQRS arestraightlines.AB // CD. Find x.

35. Inthefigure,findthesumofthemarkedangles.

36. Inthefigure,ifa + b =180°,thenwhichofthefollowingmustbetrue?(Theremaybemorethanoneanswer.)

I. b + c = 180°

II. b + d = 180°

III. c + d = 180°

KS3-MS7-2 use the angle proper t iesassociatedwith intersecting lines/parallellinestosolvesimplegeometricproblems

KS3-MS7-5usetheformulasforthesumsoftheexterioranglesofconvexpolygons

Eachmarked angle is oneof the exterioranglesofthepentagon.

KS3-MS9-1present proofs of simplegeometric problems relatedwith anglesand lines

1 © Hong Kong Educational Publishing Company


Mock Practice 6

TSA Assorted Exercises and Mock Practices Mathematics

Secondary 3Mock Practice 6Answer Booklet

Marker’s Use OnlyDimension Question ScoreNumber and

Algebra 1 – 9, 22 – 32, 45 – 47 /28

Measures, Shape and Space 10 – 19, 33 – 41, 48 – 50 /32

Data Handling 20 – 21, 42 – 44, 51 – 52 /12

Total /72

9 M E 6 ( A )

Instructions: 1. The time allowed is 65 minutes.

2. Write ALL your answers in the spaces provided in this ANSWER

BOOKLET.

3. Do not write in the margins.

4. The use of HKEAA approved calculators is permitted.

5. Rough work should be done on the rough work sheet provided.

6. Write your Name, Class and Class Number in the spaces below.

Name Class Class No.



Plea

se d

o no

t writ

e in

the

mar

gin.

Plea

se d

o no

t writ

e in

the

mar

gin.

SECTION B: Write your answers in the spaces provided. Working need not be shown.

22. ( ) ( )− + × − =6 6 23

23. 3, -9, , -81, 243, , ...

24.

25. x =

26. (a - 4b2) - (-3a + 7b2) =

27. (6y - 5z)(9z + 4y) =

28. x2y3 - xy + xy2 - 1 =

29. (3x - 2y)2 =

30. Answer:

31. V =

32. (a) 4 15

4.2 (b) -9 -9.6

33. Answer:

24y2 + 34yz - 45z2

4a - 11b2

-6

A, C and D

27 -729

=

∠ACB or ∠BCA

-40

(xy2 - 1)(xy + 1)

9x2 - 12xy + 4y2

176

>

1

Answer Key


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Answer Key

5

Answer Key



(a) Corresponding cumulative frequency of the median = 25 From the graph, the median is 43 kg. 1* + 1** (b) From the graph, there are (50 - 30) = 20 students heavier than 45 kg. 1**

Percentage = ×2050

100% 1**

= 40% 1*

19. Weighted mean = × + × + ×+ +

$ . .3 2 2 5 1 13 8 22 1 2

1**

= $ .7 22 1*

20. (a)

C L E V E RM M, C M, L M, E M, V M, E M, RE E, C E, L E, E E, V E, E E, RE E, C E, L E, E E, V E, E E, RT T, C T, L T, E T, V T, E T, R 4*

(b) P(getting two identical letters) = 424

1**

= 16 1*

21. (a) P(having one pet)

=+ + + +

410365 410 102 56 17

1**

= 410950

= 4195 1**

(b) Estimated number of households

= ×10 200 4195

1**

= 4402 (cor. to the nearest integer) 1*

Mock Practice 1

Section A1. C 2. A3. D 4. C5. D 6. A7. C 8. D9. A 10. C11. D 12. A13. B 14. A15. B 16. B17. B 18. A19. B 20. C Section B21. (a) -4000 (b) +700 1*

22. 365- x 1*

23. 12 : 15 : 14 1*24. x5y4 1*25. 1.035 × 10-3 1*26. (6x + 1)2 1*27. 243 1*

28. y xx y

=+ =

5228 2*

29. –3 –2 –1 0– 2.25

1*30. B, D 1*31. 1200 1*32.

1*

33. (2, 300°) 1*34. 90° 1*35. 720° 1*36. III 1*37. II 1*38. 163.4 1*

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Exercise 1 Number and Algebra Question Booklet - · PDF fileNumber and Algebra Question Booklet. 3 Exercise 1 ... 6. Write your Name, Class and Class Number in the spaces below