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Exercise 1
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Exercise 1Number and Algebra
Question Booklet
3
Exercise 1
© Hong Kong Educational Publishing Company
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
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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.
6© Hong Kong Educational Publishing Company
TSA Assorted Exercises and Mock Practices Mathematics S3
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
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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
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TSA Assorted Exercises and Mock Practices Mathematics S3
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
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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
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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.
4© Hong Kong Educational Publishing Company
TSA Assorted Exercises and Mock Practices Mathematics S3
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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
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Answer Key
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(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*