Teknik Menjawab Soalan Matematik PMR

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Text of Teknik Menjawab Soalan Matematik PMR

BENGKEL MATEMATIK ( PMR )A

F GE

DC B

A E

EC

B F A O D E

TEKNIK MENJAWAB SOALAN DALAM KERTAS 2

Oleh LAI JUN SIEW SMK SUNGAI MAONG 2008

Teknik Menjawab Soalan Kertas 2 matematik PMR

Format Pentaksiran Matematik Baru PMR (2004)

Bil

Perkara

Kertas 1 ( 50/1 )

Kertas 2 ( 50/2 )

1

Jenis Instrumen

Ujian Objektif

Ujian Subjektif

2

Jenis Item

Aneka Pilihan dan Gabungan

Respons Terhad ( TunjukkanLangkah Kerja dan jawapan )

3

Bilangan Soalan

40 soalan ( Jawab semua)

20 soalan ( Jawab semua)

4

Jumlah Markah

40

60

5

Tempoh Ujian

1 jam 15 minit

1 jam 45 minat

6

Wajaran Konstruk

Pengetahuan - 40% Kemahiran - 60%

Pengetahuan - 30% Kemahiran - 65% Nilai - 05%

7

Cakupan Konteks

Semua bidang pembelajaran dari Tingkatan 1 hingga Tingkatan 3

Semua bidang pembelajaran dari Tingkatan 1 hingga Tingkatan 3

8

Aras Kesukuran Rendah -R Sederhana - S Tinggi -T

R:S:T=5:4:1

R:S:T=5:2:3 Keseluruhan R:S:T=5:3:2

9

Alatan Tambahan

a. Kalkulator Saintifik b. Buku Sifir Matematik c. Alatan Geometri

a. Buku Sifir Matematik b. Alatan Geometri

Lai J S , SMK Sg Maong, Kuching. 2009

1

Teknik Menjawab Soalan Kertas 2 matematik PMR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

ANALYSIS OF PMR MATHEMATICS PAPERS ( 2004 2008 ) Number of Questions Topics 2004 2005 2006 2007 P1 P2 P1 P2 P1 P2 P1 P2 Whole Numbers 0 0 1 1 1 0 1 0 Number Patterns and 3 0 3 0 2 0 2 0Sequences Fractions Decimals Percentages Integers and Directed Numbers Algebraic Expressions Basic Measurements Lines and Angles Polygons Perimeter and Area Solid Geometry Squares, Square Roots, Cubes and Cube Roots Linear Equations Ratios, Rates and Proportions Pythagoras Theorem Geometrical Constructions Coordinates Loci in Two Dimensions Circles ( Area and Angles) Transformations Statistics Indices Algebraic Formulae Scale Drawings Linear Inequalities Graphs of Functions Trigonometry

2008 P1 P2 1 1 2 1 1 3 3 1 4 2 3 1 1 2 1 2 1 5 1 4 1 1

1 1 1 1 0 3 1 2 1 2 0 0 3 3 0 2 1 6 1 5 0 0 1 1 1 0 40

1 0 0 1 3 0 0 0 0 1 1 1 0 0 1 0 1 0 2 2 2 1 0 1 1 1 20

0 0 1 1 0 0 1 5 0 3 0 1 4 3 0 2 1 6 1 4 0 0 0 1 2 0 40

0 0 0 1 3 0 0 0 0 0 1 1 0 0 1 0 1 0 2 1 2 1 1 1 1 2 20

2 0 1 0 0 1 2 3 2 4 0 1 3 1 0 3 1 5 1 4 0 0 0 1 2 0 40

1 0 0 1 3 0 0 0 0 0 1 1 0 0 1 0 1 0 2 2 2 1 1 1 1 1 20

1 1 1 1 0 1 0 4 3 4 0 1 3 1 0 2 1 5 1 4 0 0 0 1 2 40

0 1 0 1 3 0 0 0 0 1 1 1 0 0 1 0 1 0 3 2 1 1 0 1 1 1 20

1 1 4 2 1 1 1 1 1 1 20

1 2 40

Total

Lai J S , SMK Sg Maong, Kuching. 2009

2

Teknik Menjawab Soalan Kertas 2 matematik PMR

THE IMPORTANT TOPICS FOR PAPER 21. Fractions 2. Directed Numbers 3. Squares, Square Roots, Cubes and Cube Roots 4. Algebraic Expressions 5. Statistics 6. Linear Equations 7. Indices 8. Algebraic Formulae 9. Trigonometry 10. Transformations ( Reflections, Translations, Roations and Enlargements 11. Inequalities 12. Solid Geometry ( Net of Solids) 13. Congruency ( Transformations) 14. Graphs of Functions 15. Geometerical Constructions 16. Loci In Two Dimensions 17. Scale Drawing 18. Angles in Circles and Angles Between Parallel Lines 19. Coordinates

THE IMPORTANT TOPICS FOR PAPER 11. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Whole Numbers Number Patterns and Sequences Fractions Decimals Percenages Integers and Directed Numbers Algebraic Expressions Basic Measurements Lines and Angles Polygons Perimeter and Area Solid Geometry Volumes of Shapes Squares, squares Roots, Cubes and Cubes Roots Linear Equations Ratio, Rates and Proportions Pythagoras Theorem Scale Drawings Coordinates Loci in Two Dimensions Circles Angles , Area & Circumference Transformations Statistics Indices Algebraic Formulae Linear Inequalities Graphs of Functions Trigonometry

Lai J S , SMK Sg Maong, Kuching. 2009

3

Teknik Menjawab Soalan Kertas 2 matematik PMR

Guidelines For Answering Questions in Mathematics paper 2 ( PMR )1. 1. FRACTIONS. 2.3 1 1 5 ( + ) 3 2 63. (4 1 1 + 3 )7 2 5

1 1 1 (1 ) 12 4 2

1.

1 1 1 (1 ) 12 4 2 1 5 1 = ( ) 12 4 2 1 5 2 = ( ) 12 4 4 1 3 = 12 4 1 = 16

2.

3 = = = = =

1 1 5 ( + ) 3 2 6 10 3 5 ( + ) 3 6 6 10 8 3 6 10 6 3 8 5 2 1 2 2

2. DIRECTED NUMBERS. A. Calculate the following. Give your answers as decimals.1 0 . 45 ( 3 )+ 2 4

2

2

1 0 .4 ( 7 ) 2

3. 24 28 14 =

3 0.45 ( ) + 2 4 = 0.45 + 0.75 + 2 = 0.3 + 2 = 2.33. DECIMALS

1.

3 .2 5 = 0 .0 8

3.2 5 1. 0.08 16.0 = 0.08 1600 = 8 =200

2.

4 0 .1 8 0 .9

3. Squares and square roots, cubes and cube roots. Examples (Calculation can be carried out without using calculators): 12 = 1 92 = 81 172 = 289 22 = 4 102 = 100 18 = 324 32 = 9 112=121 19 = 361 42 = 16 122 = 144 202 = 400 52 = 25 132 = 169 252 = 625 62 = 36 142 = 196 72 = 49 152 = 225 82 = 64 16 = 256

Squares

1=1Square Roots 81 = 9 289 =17 1 =1 Cubes 93= 7293

4 =2100 = 10 324 =18 2 =8 103=10003

9=3121 =11

16 = 4144 =12

25 = 5169 =13 625 =25 53 = 125

36 = 6

49 = 7225 =15

64 = 8256 =16

196 =1463 = 216

361 =19 3 = 273

400 =20 4 = 643

73 = 343

83= 512

Lai J S , SMK Sg Maong, Kuching. 2009

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Teknik Menjawab Soalan Kertas 2 matematik PMR

Cube Roots

3

1 =1

3 8 =23 1000 =10

3 27 =3

3 64 =4

3 125 =5

3 216 =6

3 343 =7

3 512 =8

3 729 =9

A. Find the value of

1.

3

0.3433 3 3

2.

1.69

3.

3

0.729

343 = 7 0.343 = 0.7 0.343 = 0.7

B. Calculate the value of :1.

(7) 2 + 169

2.

( 121 4 2 ) 3 5 2

3.

62 3

64 729

( 7) 2 + 169 = 49 + 13 = 624. ALGEBRAIC EXPRESSIONS

1.

Simplify each of the expressions to its simplest form. (i) 10x 3y + ( 2x 3) (ii) ( y 5 ) 25 + 4y (iii) 5(xy 4 ) 8 ( xy 2 )

10x 3y + ( 2x 3) = 10x 3y + (2x 3) (2x 3 ) = 10x 3y + 4x 6x 6x + 9 = 4x 2x 3y + 92. Factorize each of the following expressions. (i) 4p 8pq (ii) y(2x y) + 5xy (iii) (m3) ( 6 2m)

4p 8pq = 4p(12q)

y(2x y) + 5xy = 2xy + y + 5xy = 3xy + y = y ( 3x + y )

3.

(i)

Express

2 x 3x 2 8 as a single fraction in its lowest ter m. y 5 xy

2x 3x 2 8 2x 5x (3x 2 8) = y 5xy y 5x 5xy = = = 10x 2 (3x 2 8) 5xy 10x 2 3x 2 + 8 5xy 7x 2 + 8 5xya s a s in g le fra c tio n in its lo w e s t te rm .

( ii)

E x p re s s

1 2n 5 5n 10n2

Lai J S , SMK Sg Maong, Kuching. 2009

5

Teknik Menjawab Soalan Kertas 2 matematik PMR 5. a. STATISTICS Construct or complete the pictogram, bar chart, line graph and pie chart base on the information given.

1. The table below shows the number of computers sold in a computer retail shop in the period of the first four months of 2004.Month January February March April Number of computers 10 20 12 1820

Draw a bar chart / pie chart to represent all the information in the table on a grid

February 120o 72 March o

January 60 o o 108 April

10 360 = 60o 60 20 360 = 120o 60 12 360 = 72o 60 18 360 = 108o 60

2. Day Number of watermelons Mon 100 Tue x Wed 90 Thurs 140 Fri 160

The table above shows the number of watermelons harvested in a farm from Monday to Friday. If the total number of watermelons harvested for five days is 610, (i) Find the value of x . (ii) Complete the pictogram by drawing the correct numbers of Monday Tuesday Wednesday Thursday Friday for Tuesday and Thursday.

3. The diagram below shows the scores obtained by 15 police cadets in a shooting competition.

1,2,4,3,1,2,4,1,3,2,1,3,1,1,3(a) Using the data, complete the frequency table . (b) State the mode. (c) State the median. Score 1 2 3 4 Frequency

Lai J S , SMK Sg Maong, Kuching. 2009

Number of Computers

6

Teknik Menjawab Soalan Kertas 2 matematik PMR 6. Linear Equations

1. Solve the equation 5k = 3k 8 5k = 3k 8 5k 3k = 8 2k = 8 k = 4

2. Solve the equation 6x 3 = 3(4+x)

3. Solve the equation k + 5 (8 3k) = - 19 2

4. Solve the equation 8y 2 = 3y + 8

6x 3 = 3(4 + x) 6x 3 = 12 + 3x 6x 3x = 12 + 3 3x = 15 15 x = 3 x =5

8. k +

5. Solve the equation7. Indices

x 7 = x + 23 4

5 (8 3k) = 19 2 15k k + 20 = 19 2 15k k = 19 20 2 2k - 15k = 39 2 - 13k = -78 - 78 k = - 13 k =64 6 8

1. Simplify (rs

5 3

) s

15

2

Simplify (3pq ) (q ) p q

3

2

3

(rs -5 ) 3 s 15 = r 3 s 15 +15 = r 3s 0 =r33. Simplify 2m 9m4 5

(3pq 3 ) 2 (q 3 ) 4 p 6 q 8 = 3 2 p 2 q 6 q 12 p 6 q 8 = 9p 2-6 q 6 +12 8 = 9p -4 q 103 2 3 814 4. Find the value of 95

2

5. Simplify

( 4m n )2 1

2

2m3n 4

6. Given that 3

x 4

= 81 , calculate the value of x.

8. Algebraic Formulae

1. Given that p

p 2 = , express p in terms of r. r r

2. Given that

k 2 = 4 , express k in terms of t. t

2 p = r r rp rp - 2 = r pr = 2 + p ppr - p = 2 p( r - 1) = 2 p= 2 ( r - 1)

k -2 =4 t k - 2 = 4t ( k - 2 )2 = ( 4t)2 k -