(Not to be printed with the question paper) · 2013-06-07 · (Not to be printed with the question...

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(Not to be printed with the question paper)

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I, 2012

SUMMATIVE ASSESSMENT – I, 2012

/ MATHEMATICS

IX / Class – IX

3 90

Time allowed : 3 hours Maximum Marks : 90

(i)

(ii) 34 8

1 6 2 10

3 10 4

(iii) 1 8

(iv) 2 3 3 4 2

(v)

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A, B, C and D.

Section-A comprises of 8 questions of 1 mark each; Section-B comprises of 6 questions of 2

marks each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises

of 10 questions of 4 marks each.

(iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are required

to select one correct option out of the given four.

(iv) There is no overall choice. However, internal choices have been provided in 1 question of

two marks, 3 questions of three marks each and 2 questions of four marks each. You have to

attempt only one of the alternatives in all such questions.

(v) Use of calculator is not permitted.

MA1-040

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SECTION–A

1 8 1

Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.

1. 0.777…..

pq p, q q 0

(A) 77

90 (B)

7

10 (C)

7

9 (D)

77

99

The p

q form of 0.777….. where p and q are integers, q 0 is :

(A) 77

90 (B)

7

10 (C)

7

9 (D)

77

99

1

2. a31

(A) (a1), (a2a1) (B) (a1), (a2

a1)

(C) (a1), (a2a1) (D) (a1), (a2

a1)

The factors of a31 are :

(A) (a1), (a2a1) (B) (a1), (a2

a1)

(C) (a1), (a2a1) (D) (a1), (a2

a1)

1

3. p(x)5x3

(A) 35 (B) 3 (C) 3

5 (D) 15

Zero of the polynomial p(x)5x3 is :

(A) 35 (B) 3 (C) 3

5 (D) 15

1

4. (5x3)(x23x2)

(A) 5 (B) 3 (C) 4 (D) 1

The degree of the polynomial (5x3)(x23x2) is :

(A) 5 (B) 3 (C) 4 (D) 1

1

5. 130

(A) 50 (B) 65 (C) 145 (D) 155

If one angle of a triangle is 130, then the angle between the bisectors of the other

two angles is :

(A) 50 (B) 65 (C) 145 (D) 155

1

6.

(A) SAS (B) ASA (C) SSA (D) SSS

Which of the following is not a criterion for congruence of triangles :

(A) SAS (B) ASA (C) SSA (D) SSS

1

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7. (2, 3)

(A) (B)

(C) (D)

Point (2, 3) lies in the : (A) I Quadrant (B) II Quadrant (C) III Quadrant (D) IV Quadrant

1

8. P(2, 3) Q(3, 5) P Q

(A) 1 (B) 1 (C) 2 (D) 5

If the coordinates of the points are P(2, 3) and Q(3, 5), then (abscissa of

P)(abscissa of Q) is :

(A) 1 (B) 1 (C) 2 (D) 5

1

/ SECTION-B

9 14 2

Question numbers 9 to 14 carry two marks each.

9. 2157

625

Express 2157

625 in decimal form and state whether it is terminating or not.

2

10. 10597

Find the product using identities : 10597.

2

11. 343p31331b3

Factorise : 343p31331b3

2

12. ADCB ACDB.

/

In the given figure ADCB. Prove that ACDB.

State the Euclid’s axiom/postulate used for the same.

2

13. OA OB

(i) x25 y

(ii) y35 x

2

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In the given figure OA and OB are opposite rays (i) If x25, find the value of y. (ii) If y35, what is the value of x.

/ OR

If a transversal intersects two parallel lines, then the bisectors of any pair of alternate angles are parallel. Prove it.

14. 5 cm 12 cm 13 cm 13 cm

The sides of a triangle are 5 cm, 12 cm and 13 cm. Find the length of perpendicular from the opposite vertex to the side whose length is 13 cm.

2

/ SECTION-C

15 24 3

Question numbers 15 to 24 carry three marks each.

15. 13

Represent 13 on the number line.

/ OR

2 5 7

a b 352 5 7

, a b

Find a and b if 2 5 7

a b 352 5 7

3

16.

142

1 13 31 1

5 8 27

Simplify :

142

1 13 31 1

5 8 27

3

17. 1 4x

x

33

1 x

x

If 1

4xx

, find the value of 33

1 x

x .

/ OR

3

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p(x)x33x2

2x4 p(2)p(1)p(0)

If p(x)x33x2

2x4, find the value of p(2)p(1)p(0)

18. 7(2xy)225(x2y)12

Factorise : 7(2xy)225(x2y)12

3

19. PQPS, PQSR, SQR28 QRT65 x, y z

In the given figure, PQPS, PQSR. SQR28 and QRT65. Find the

values of x, y and z.

/ OR

xADCABC

In the given figure, prove that xADCABC

3

20. ABC AB AC P Q PBC > QCB

AC > AB.

3

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Sides AB and AC of triangle ABC are extended to P and Q respectively.

If PBC > QCB, prove that AC > AB.

21. ABAC, BPPC ABPACP

In the given figure ABAC, BPPC. Prove that ABPACP

3

22. PQRS SRT PTQT

In the adjoining figure, PQRS is a square and SRT an equilateral triangle. Prove

that PTQT.

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23. xywz AOB

In the given figure xywz. Prove that AOB is a line.

3

24. 47 cm 60 cm

25 cm 26 cm

Find the area of a trapezium whose parallel sides are 47 cm and 60 cm and non parallel sides are 25 cm and 26 cm.

3

/ SECTION-D

25 34 4

Question numbers 25 to 34 carry four marks each.

25. 3 2

3 2x

3 2

3 2y

x2

y2

If 3 2

3 2

x

and 3 2

3 2

y

find x2y2.

/ OR

52x1(25)x1

2500, x

If 52x1(25)x1

2500, find the value of x.

4

26.

6 3 2 4 3

2 3 6 3 6 2

4

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Simplify by rationalising the denominator :

6 3 2 4 3

2 3 6 3 6 2

27. x3x2

4x4

By using factor theorem, factorise : x3x2

4x4

4

28. p(x)x42x3

3x29x73b x1 29 b

p(x) x2

If the polynomial p(x)x42x3

3x29x73b when divided by x1, leaves

the remainder 29, find the value of b. Also find the remainder when p(x) is

divided by x2.

4

29. abc5, abbcca10 a3b3

c33abc25

Given abc5, abbcca10, then prove that a3b3

c33abc25

4

30. (1, 1), (5, 1) (5, 3)

Three vertices of a rectangle are (1, 1), (5, 1) and (5, 3). Plot these points on a

graph paper and find the coordinates of the 4th vertex.

4

31. ABC AB AC E D CBE

BCD O BOC901

2A

In triangle ABC, the sides AB and AC are produced to points E and D

respectively. If the bisectors of CBE and BCD meet at O, then prove that

BOC901

2A

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32. ACAE, ABAD, BADEAC BCDE.

In the given figure ACAE, ABAD, BADEAC. Show that BCDE.

/ OR

ABAC, ADBC, BD E DC F

(i) ABE ACF (ii) BAECAF

In the given figure, ABAC, ADBC, E is the midpoint of BD and F is the midpoint of DC. Prove that

(i) ABE ACF (ii) BAECAF

4

33.

In an isosceles triangle, angles opposite to equal sides are equal. Prove this.

4

34. ABC ABAC BLAC CMAB BLCM

AMAL

In the given figure, ABC is a triangle. ABAC, BLAC and CMAB. Show that BLCM. Also prove AMAL.

4

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