Name : ___________________________________

Panitia Matematik Sekolah Menengah Atas Daerah Muar/Ledang

Program MAS Matematik Tingkatan 4 Tahun 2011

d/a SMK Pesisiran Perdana, Ledang

Nama : ______________________________________

Tingkatan : ___________________________________

Program MAS Mathematik Ledang Tingkatan 4 Set 1/2011

Topik No. soalanMuka surat

1. Simultaneous equations1 122 4

2. Mathematical reasoning13 235 7

3. Operation on sets24 358 10

4. Statistics36 4511 17

Cadangan pelaksanaan

1. Guru membuat 2 atau 3 soalan dengan langkah-langka yang tetap , langkah (,(,(,.....

2. Memasti murid membuat soalan berikutnya mengikut langkah (,(,(,....

3. Memastikan murid membuat soalan dengan diri sendiri atau dengan bimbingan rakan sebaya.

Penyedia soalan : Cik Yee Siew Ying SM Sains Muar,GC Matematik

Penyunting : Pn. Chiam Yean Jwee SMK Pesisiran Perdana, Guru MatematikName : _____________________________

Form : _____________________________

1. SIMULTANEOUS LINEAR EQUATIONS

Calculate the values of each unknown that satisfy the following simultaneous linear equations. 1.

[m = 2, n = 3]2.

[ m = 4 , n = 2 ]3.

[ m = 7/4 , n = 9/ 4 ] 4.

[ x = 3, y = 2 ]

5.

[ h = 6, k = ]6.

[ m = 9 , n = 7 ]

7.

[ p = 5, q = 1/3 ]

8.

[ a = 16, b = 9 ]

9.

[ h = 9/17 k = 2/51 ]

10.

[p = 3, q = 4 ]11.

[ m = 3 , n = 4 ]

12.

[ v = 6 w = 1 ]

Name : _____________________________________

Form : ______________________________________

2. MATHEMATICAL REASONING

13. (a) State whether each of the following statement is true or false.

(i) and

(ii) All squares have two diagonals of equal length

(i) .. (ii)

(b) Write down two implications from the following sentence.

.

.

(c) Complete the conclusion in the following argument.

Premise I : All regular pentagons have exterior angles .

Premise II : EFGHI is a regular pentagon.

Conclusion : ...

14. (a) Is the sentence below a statement or non- statement?

4 is a prime number

(b) Write down two implications based on the following sentence.

..

(c) Based on the information below, make a general conclusion by induction regarding the number of subsets in a set with k elements.

The number of subsets in a set with 2 elements is

The number of subsets in a set with 3 elements is

The number of subsets in a set with 4 elements is

.

15. (a) State whether each of the following statement is true or false.

(i)

(ii) Any quadratic equations can be factorised(i) .. (ii) (b) Write down two implications based on the following sentence.

.

..

(c) Complete the premise in the following argument.

Premise I :

.Premise II : PQRSTUVW is an octagon.

Conclusion : PQRSTUVW has eight sides.

16. (a) Combine the following pairs of statements by using operation to form a true statement.

Statement I : 9 is an even number.

Statement II : 9 is a perfect square.

..

(b) Complete the conclusion in the following argument.

Premise I : If n is an integer, then 3n is divisible by 3

Premise II : 3n is not divisible by 3Conclusion :

.

(c) Form a general conclusion by induction for the numbers -2, 7, 22, 43, which follows the pattern :

.. ..17. (a) Complete the following mathematical sentence using symbols > or < to satisfies each of following :

(i) A true statement : -6 -2

(ii) A false statement : 7

(b) Determine whether each of the following statements is true or false.

(i) All prime numbers are odd numbers

(ii) Some sets have at least two subsets(i) (ii) ..

(c) Form a general conclusion by induction for the number sequence : 0, 3, 8, 15,

..

..

18. (a) Determine whether each of the following statements is true or false.

(i)

(ii) 0 > 2 and 0.5 is an integer.

(i) .. (ii) (b) Complete the premise in the following argument.

Premise I : All squares have two diagonals of equal length

Premise II : ..

Conclusion : PQRS has two diagonals of equal length.

(c) Write two implications based on the following sentence.

..

..19. (a) State whether the following statement is true or false.

(i) = 0.5 or 51 is a prime number

(ii) All factors of 8 are factors of 6

(i) (ii) .

(b) Given the implication :

If 2x = 6 then 3x = 9

State the converse of the above implication and determine this converse is true or false.

(c) Complete the premise in the following argument.

Premise I :

Premise II : 25 is a perfect square

Conclusion : is an integer.20. (a) Is 2 + 6 = 7 a statement? Give your reason.

(b) Given polar number 14, 9, 4, -1 as below :

14 = 14 5(0)

9 = 14 5(1)

4 = 14 5(2)

-1 = 14 5(3)..

..(c) Complete the premise in the following argument.

Premise I : If Ali arrives late to school, then he does not take breakfast.Premise II :

..Conclusion : Ali takes breakfast.

21. (a) Given the following implication :

If x is a perfect square then is a whole number State the antecedent and the consequent.

Antecedent : .

Consequent : .

(b) Given the implication : If q > 7, then q > 4

State the converse of the above implication and determine this converse is true or false.

.

(c) Complete the premise in the following argument.

Premise I : .

Premise II : PQR is a triangle

Conclusion : PQR has three sides.

22. (a) Given the antecedent and the consequent Antecedent : m = 5

Consequent : 2m + 3 = 13

Construct a mathematical statement in the form of if p, then q

..

(b) State the quantifier all or some in each of the following statement to make a true

statement.(i) even numbers are perfect squares(ii) rhombuses have four equal sides

(c) Form a general conclusion by induction for the numbers which follows the pattern :

-5 = 3(1) 8

-2 = 3(2) 8

1 = 3(3) 8

4 = 3(4) 8

..

23. (a) State whether the following statements are true or false.

(i)

(ii) Number 5 is an odd number or number 2 is a prime number.

(i) ___________ (ii) ____________

(b) State the antecedent and consequent of the implication:

Antecedent : ______________________

Consequent : ______________________

(c) Complete the following argument.

Premise 1 : If y > 3, then 5y > 15.

Premise 2 : ___________________________

Conclusion : y < 3.

Name : ________________________________

Form : _________________________________3. OPERATION ON SETS24. The Venn diagram in the answer space shows sets P , Q and R such that the universal set,

On the diagrams in the answer space, shade

(a) the set P

EMBED Equation.3

(b) the set (

EMBED Equation.3 Answer:

(a) (b)

25.The Venn diagram in the answer space shows sets K, L and M such that the universal set, ( = K ( L ( M.

On the diagrams in the answer space, shade

(a) L M ,

(b) ( K ( M ) L.

Answer:

26The Venn diagrams in the answer space below shows the sets (, P, Q and R. Shade the regions in the diagram in the answer space for the following sets.

(a) (P ( Q) ( R (b) P ( (Q ( R)

Answer:

(a)

(b)

27The Venn diagram in the answer space shows sets A, B and C. On the diagram provided in the answer spaces, shade

(a)the set A ( B(b)the set (A ( B) ( C.

Answer:

(a) (b)

(b)28The Venn diagram in the answer space shows sets P, Q and R such that the universal set, ( = P ( Q ( R.

On the diagrams in the answer space, shade

(a)the set P ( Q,

(b)the set (P ( Q) ( RAnswer:

(a) (b)

29. The Venn diagram in the answer space shows the universal set (, sets P, Q and R. On the diagram in the answer space, shade the region for

(a) P ( Q ,

(b) ( P ( Q ) ( R.Answer: (a)

(b)30.The Venn diagram in the answer space shows sets P, Q and R with the universal set Shade

(a) the set

EMBED Equation.3

(b) the set (. Answer :

(a)

(b)

[JUNE 2005]

31. The Venn diagram in the answer space shows sets P, Q and R with the universal set Shade

(a) the set Q (b) the set P (Q. Answer(a)

(b)

[JUNE 2003]

32. The Venn diagram shows sets (, P, Q dan R. Shade

(a)

(b) )

Answer :

(a)

(b)

[TRIAL SBP 2004]

33. The Venn diagram in the answer space shows sets P, Q and R such that the universal set, ( = P ( Q ( R.

On the diagrams in the answer space, shade

(a) P( ( R(

(b) Q ( R ( P

Answer :

(b)

34. The Venn diagram in the answer space shows the universal set (, sets P, Q and R.

The universal set ( = P ( Q ( R. On the diagram in the answer space, shade the region for

(a) P ( Q

(b) P ( ( Q ( R ) (. Answer:

(a)

(b)35. The Venn diagram in the answer space shows sets , and such that the universal set, = .

On the diagrams in the answer space, shade

(a) the set P ( ( Q ,

(b) the set ( P ( Q ( ) ( R .

Answer:

(a)

(b)Name : ________________________________________

Form : ________________________________________

4. STATISTICS

36.The ages of 30 people who visited a mobile library on a certain day are as follows

21232012142418241817

28302526152023281927

251722351715981317

(a)Construct a grouped frequency table for the above data using the classes 6 10, 11 15 and so on.

(b)Based on the frequency table, calculate the mean age of the 30 people.

(c ) Using a scale of 2 cm to represent 5 years on the x-axis and 2 cm represent 2 people on y-axis, draw a histogram based on the above frequency table.37.The data following shows the marks for participants for the colouring contests.

243539412632332526

303634403555233438

413245252133283722

294638274943334844

524028314424362732

(a) Using data in the diagram and a class interval of 5 marks, complete the following table.

MarksMidpointFrequency

21 25

26 30

(b) Based on your table in (a),

i) state the modal class.

ii) Calculate the mean mark for the contest and give your answer correct to 2 decimal places.(c) By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 participant on the vertical axis, draw a frequency polygon for the data.

38.The height, in cm, of 50 plants are distributed as shown in the following table.

(a)

Height (cm)MidpointFrequency

40 443

45 495

50 5410

55 5916

60 648

65 696

70 742

(i) Copy and complete the above table.

(ii) Hence, calculate the mean height of the plants.

(b) Using a scale of 2 cm to represent 5 cm on the x-axis and 2 cm to represent 5 plants on the y-axis, draw an ogive for the distribution.

From the ogive, find

i) the median

ii) the upper quartile

39.The data in Diagram 94(a) show the marks of 40 students for the Mathematics monthly test.

4653446042383155

3537543246564060

5240344552355036

4738404845425344

5044585136485632

a)Using data in the diagram 94(a) and class interval of 5 marks, complete table 94(b)

in the answer space.MarksMidpointFrequency

31 35

36 - 40

b)Base on your table in (a)

i)state the modal class

ii)calculate the mean mark of the Mathematics monthly test and give your answer

correct to 2 decimal places.

c)By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the

vertical axis, draw a histogram for the data.

40.The data in Diagram 95(a) shows the time, in minute, taken by 30 students to solve some trigonometry problems.

435049546065

473556616656

475551584148

625240575863

725253366754

(a)

Using data in Diagram 95(a) and a class interval of 5 minutes, complete Table 95(b) in the

answer space.

Time(minutes)FrequencyMidpoint

35 39

40 44

Table 95(b)(b) Based on table 95(b),(i) find the modal class,

(ii) calculate the mean time taken by the students.

(c)By using a scale of 2 cm to 10 minutes on the horizontal axis and 2 cm to 1 students on the vertical axis, draw a histogram based on Table 3.

41.Table 96 shows the distribution of the ages of 200 participants in a big walk event.

Age (years)FrequencyCumulative

FrequencyUpper

Boundary

15 ( 1910

20 ( 2420

25 ( 2950

30 ( 3460

35 ( 3936

40 ( 4418

45 ( 496

Table 96

(a) Using the data in Table 96, complete the table provided.

[4 marks]

(b) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 20 participants on

the y-axis , draw an ogive for the data.

[5 marks]

(c) Based on your ogive in (b),

(i) find the inter quartile,

(ii) explain briefly the meaning of the third quartile.

[3 marks]

42. The data below shows the Chemistry test marks scored by a group of 40 students in Form 4 Wawasan.

68406566604653564958

78577353695170645862

47656766713656533837

7561377448417563 3377

((a)Using the given data and a class interval of 10 marks, complete the frequency table in the answer space.

[4 marks]Answer: (b)From the table in (a),

(i)state the modal class,

(ii)calculate the mean mark.

[4 marks]

(c)By using a scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 2 students on the vertical axis, draw a frequency polygon for the data.

[4 marks]43.The table shows the time taken ( in minutes ) by a group of 100 tourists in visiting an art gallery.

(a)Based on the above data,

(i)determine the range.

(ii)complete the cumulative frequency table given below.

[5 marks]

Time taken (minutes)FrequencyCumulative FrequencyUpper boundary

15 190

20 2414

25 2931

30 3424

35 3913

40 4410

45 496

50 542

(b)By using a scale of 2 cm to 5 minutes the horizontal axis and 2 cm to 10 visitors

on the vertical axis, draw an ogive.

[4 marks]

(c)From your ogive, estimate

(i)the median,

(ii)the interquartile range.

[3 marks]

44. The data in Diagram 99(a) shows the ages of 50 runners who took part in a charity run event.14361216273127283028

16182318243223141831

22302320253031222037

12263623283034383336

11232727343825121729

DIAGRAM 99(a)(a)Based on the data in Diagram 99(a) and by using a class interval of 5, complete Table 99(b) in the answer space.

[4 marks]

Age (years)MidpointFrequency

11 15

Table 99(b)

(b)Based on Table 99(b) in (a), calculate the estimated mean of the age of the runners.

[3 marks]

(c)By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1 runner on the vertical axis, draw a frequency polygon for the data.

[5 marks]45.The data in Diagram 100(a) shows the marks obtained by 40 pupils in a quiz.

6776917981828771

7982888372847189

8086708662838380

7584847784868576

8075957773867768

DIAGRAM 100(a)

(a)Using the data in Diagram 100(a), and a class interval of 5, complete Table 100(b)

in the answer space.

MarksFrequencyCumulative FrequencyUpper Boundary

61 65

TABLE 100(b)[6 marks]

(b)By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the

y-axis, draw an ogive based on the data.

[5 marks]

(c)From your ogive in (b), find the third quartile.

[1 mark]

EMBED Equation.3 is positive if and only if k is positive

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EMBED FXDraw200.Document

DIAGRAM 94(a)

Diagram 95(a)

Marks scoredMidpointFrequency20 29 30 39

Time taken (minutes)20 2425 2930 3435 3940 4445 4950 54Frequency143124131062

PAGE 17

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