# Revision on Operation on Sets, SPM maths

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Fokus Jaya Set 1

PROGRAM PENINGKATAN 2Q NEGERI SELANGOR MATEMATIK SPM 2010 FOKUS JAYA SET 1 BAHAGIAN A 1 The Venn diagram in the answer space shows sets P, Q and R such that the universal set = P Q R . On the diagram in the answer space, shade (a) the set P Q, (b) the set P ' Q R .

(

)

[3 marks] (b) P Q

Answers : (a) P R Q

R

2. Diagram below is a Venn diagram which shows the sets X, Y and Z such that the universal set = X Y Z. On a separate diagram, shade the region that represents (a) X ' Z (b) (Y Z ') X

3.

The Venn diagram in the answer space shows sets A, B and C. Given the universal set = AA' B

B

C. On the diagram provided in the answer spaces, shadeA ( B C)

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Fokus Jaya Set 1

4.

Calculate the value of x and of y that satisfy the following simultaneous linear equations:4x + y= 1 2 x += 3y 8

[4 marks]

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4

Solve the following quadratic equation: x 2 + 4 x 9 = 2( x 3) [4 marks]

5.

4m 2 2 Solve the quadratic equation =1 7m

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(a)

State whether the following statement is true or false. Some even numbers are divisible by 3.

(b)

Write down the converse of the following implication. Hence, state whether the converse is true or false. If x is a multiple of 12, then x is a multiple of 3.

(c)

Write down Premise 2 to complete the following argument: Premise 1 : If the radius of a circle is 14 cm, then the circumference of the circle is 28 cm. Premise 2 : Conclusion : The radius of the circle is not 14 cm.

(d) Make a general conclusion by induction for the sequence of numbers 7, 14, 27, which follows the following pattern.1 4 =3(2 )2 + 21 7 = 3( 2) + 1

2 1 = 3(2 )3 + 3 .... = .......... ...

[6 marks] Answers : (a) (b) (c) (d) 4

Fokus Jaya Set 1

7(a)Combine the following statements to form a true statement. Statement 1: < Statement 2: 92 = 81 Answer: (b) Write a conclusion based on the following premises. Premise 1: If a right prism has a cross-sectional area of 75 cm2 and a height of 35 cm, then the volume of the prism is 2 625 cm3. Premise 2: The volume of a right prism is not 2 625 cm3. Conclusion: _________________________________________ (c) Make a conclusion by induction for the number sequence 4, 7, 12, 19, ..., according to the pattern below. 4 = 12 + 3 7 = 22 + 3 12 = 32 + 3 19 = 42 + 3 ... = ..........

Answer:

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8

2 3 It is given that matrix A = . 4 5 (a) (b) Find the inverse matrix of A. Write the following simultaneous linear equations as matrix equation: 2x 3y = 7 4 x 5 y = 13 Hence, using matrix method, calculate the value of x and of y [6 marks]

9. It is given that X = and Y = p such that XY = . (a) Find the values of p and q.

(b) Write the following simultaneous linear equations as matrix equation: 5x 9y = 6 3x + 5y = 4 Hence, using matrix method, calculate the value of x and y.

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Diagram 1 shows five cards labelled with letters. 6

Fokus Jaya Set 1

S

MDIAGRAM 1

I

L

E

All these cards are put into a box. A two-letter code is to be formed by using any two of these cards. Two cards are picked at random, one after another, without replacement. (a) List the sample space.

(b) List all the outcomes of the events and find the probability that (i) the code begins with the letter M, (ii) the code consists of two vowels or two consonants.

[6 marks] 11. Diagram 2 shows four cards labeled with letters.

All these cards are put into a box. A two-letter code is to be formed by using two different cards from the box. The two cards are picked at random. (a) List the sample space.

(b) List all the outcomes of the events and find the probability that (i) the code begins with letter T. (ii) the code consists of one vowel and one consonant. [5 marks]

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Fokus Jaya Set 1

BAHAGIAN B 12 (a) Complete Table 12 in the answer space for the equation y = down the values of y when x = -3 and x = 1.5. 24 x by writing [2 marks]

(j) For this part of the question, use the graph paper provided. You may use a flexible curve rule. By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units 24 on the y-axis, draw the graph of y = . [4 marks] x (c) By using the graph drawn in 12(b), find i. the value of y when x = 2.9, (ii) .the value of x when y = -13. [2 marks] (d ) Draw a suitable line on your graph to find the values of x which satisfy the equation 2 x 2 + 2 = 24 for 4 x 4 . State these values of x.

4 marks]

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Fokus Jaya Set 1

(b) For this part of the question, use the graph paper provided. You may use a flexible curve rule. Of (c) By using a scale of 2 cm to 1 unit of the x-axis and 2 cm to 2 units on the y-axis, draw the graph y = x3 + 7x 9 for 3 x 2. From your graph, find

(i) the value of y when x = 1.2, (ii) the value of x when y = 5.6 [2 marks] (d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x3 + 12x 17 = 0 for 3 x 2. State the values of x. [4 marks] Answer: Jawapan: (a) x y 3 3 2.5 2 15 1 15 Table 1 Jadual 1 (b) refer graph (c) (i) 0 0.5 5.6 1 3 1.5 1.9 2 3

(ii)

(d)

14. The data in Diagram 15 shows the marks for a Mathematics monthly test for 40 students.

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Fokus Jaya Set 1

(a) Using data in Diagram 15 and a class interval of 5 marks, complete Table 14 in the answer space.

[4 marks]

(b) For this part of the question, use the graph paper provided. By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 5 students on the vertical axis, draw an ogive based on Table 15. [5 marks] (c) Find the interquartile range from your ogive in (b), [3 marks]

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You are not allowed to use graph paper to answer this question. (a) Diagram 15(i) shows a solid right prism with rectangular base ABHG on a horizontal plane. The surface ABCDE is the uniform cross-section of the prism. AE and BC are vertical edges. Rectangle DEFK is an inclined plane and rectangle CDKJ is a horizontal plane. K 3 cm F 5 cm G H J

E 4 cm A

D

C

8 cm

DIAGRAM 15(i)

6 cm

B

X Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X. [3 marks] Answer: (a)

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Fokus Jaya Set 1

(b)

A solid cuboid is cut and removed from the solid in Diagram 15(i). The remaining solid is shown in Diagram 15(ii). Rectangle QRST is a horizontal plane. SB = 2 cm, UT = 3 cm and ST = 4 cm. K F W G Q D E 4 cm A R 6 cm S BDIAGRAM 15(ii)

3 cm

J 5 cm

U H T 8 cm Y

Draw to full scale, (i) the plan of the remaining solid, [4 marks] (ii) the elevation of the remaining solid on a vertical plane parallel to BH as viewed from Y. [5 marks]

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Fokus Jaya Set 1

15

a) x y 3 3 2.5 10.9 2 15 1 15 0 9 0.5 5.6 1 3 1.5 1.9 2 3

Fokus Jaya Set 1

(b)

(c)

(c)(i) y = 15.6 (ii) x = 2.9, 0.5 (d) y = x3 + 7x 9 ---- (1) x3 + 12x 17 = 0 ---- (2) (1) + (2): y = 5x 8 x = 1.6, 0.6

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(a)

Class Frequency Midpoint interval 35 42 3 38.5 43 50 8 46.5 51 58 7 54.5 59 66 2 62.5 67 74 8 70.5 75 82 9 78.5 83 90 3 86.5 (b) Total (midpoint of class frequency) = 38.5(3) + 46.5(8) + 54.5(7) + 62.5(2) + 70.5(8) + 78.5(9) + 86.5(3) = 2 524 Total frequency =3+8+7+2+8+9+3 = 40 Estimated mean of money = = RM63.10

(c)

(d) Modal class of the expenditure is 75 82.

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