9th maths sample paper sa-1-2011!13!3

7/30/2019 9th Maths Sample Paper Sa-1-2011!13!3

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Class - IX

MATHEMATICS

Time : 3 to 3 hours Maximum Marks : 80

: 3 3 : 80

Total No. of Pages : 15

c : 15

General Instructions :

1. All questions are compulsory.

2. The question paper consists of 34 questions divided into four sections A, B, C and D.Section - A comprises of 10 questions of 1 mark each, Section - B comprises of 8 questions of2 marks each, Section - C comprises of 10 questions of 3 marks each and Section - D comprisesof 6 questions of 4 marks each.

3 . Question numbers 1 to 10 in Section - A are multiple choice questions where you are to selectone correct option out of the given four.

4. There is no overall choice. However, internal choice has been provided in 1 question of twomarks, 3 questions of three marks each and 2 questions of four marks each. You have toattempt only one of the alternatives in all such questions.

5. Use of calculator is not permitted.

6. An additional 15 minutes time has been allotted to read this question paper only.

1.

2. - 34 , UU , , U - 10 1 ,U - 8 2 ,U - 10 3 ,U - 6 4

3. 1 10 4. , 1 2 , 3 3 2

4

5.

6. - 15 - -S

940109 - A2

1 P.T.O.


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SECTION - A

Question numbers 1 to 10 carry 1 mark each. Out of four given options choose the correctone.

1. The value of

1 1

2 27 8 is :

(A)

1

228 (B)

1

256 (C)

1

214 (D)

1

242

2. p is :

(A) a rational number (B) an integer

(C) an irrational number (D) a whole number

3. If (x21) is a factor of p (x)5x21x1k, then value of k is :

(A) 3 (B) 2 (C) 22 (D) 1

4. Zero of the polynomial p (x)5cx1d is :

(A) 2d (B) 2c (C)d

c(D)

d

c

5. If the point P lies in between M and N, C is the midpoint of MP then :

(A) MC1PN5MN (B) MP1CP5MN (C) MC1CN5MN (D) CP1CN5MN

6. In figure 1, if OA5OB, OD5OC then DAOD!DBOC by congruence rule :

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

7. In DABC if AB5BC then :

(A) B > C (B) A5C (C) A5B (D) A < C


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8. If two supplementary angles are in the ratio 2 : 7, then the angles are :

(A) 358, 1458 (B) 708, 1108 (C) 408, 1408 (D) 508, 1308

9. In right triangle DEF if E5908, then :

(A) DF is the shortest side (B) DF is the longest side

(C) EF is the longest side (D) DE is the longest side

10. In the given figure if PQ??RS then the measure of m is :

(A) 1108 (B) 1008 (C) 908 (D) 1378

SECTION - B

Question numbers 11 to 18 carry 2 marks each.

11. Evaluate

7 9

2 2

5

2

36 36

36

.

12. Simplify : 2

3 3 2 2 .

13. Evaluate (104)3 using suitable identity.

14. If a point C lies between two points A and B such that AC5BC, then prove that AC51

2AB.

Explain by drawing the figure.


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15. If the angles of a triangle are in the ratio 2 : 3 : 4, find the angles of the triangle.

16. In figure 3, X and Y are two points on equal sides AB and AC of a DABC such that AX5AY.Prove that XC5YB.

OR

In figure 4, ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively

are equal. Show that DABE!DACF.

17. Name the quadrant in which the following point lie (23, 2), (4, 23), (25, 24) and (3, 2).

18. In figure 5, if POR and QOR form a linear pair and a2b5808 then find the value ofa and b.


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SECTION - C


19. Simplify3 3 3

4 281 25 516 9 2

- - - - - - - - -

.

20. Simplify the following by rationalising the denominator.

7 3 5 2

48 18

OR

If3 1

a b 33 1

, find the value of a and b.

21. If1

7xx

then find the value of 33

1x

x .

OR

If1

3xx

then find the value of 33

1x

x .

22. Express 3.425 in the formpq where p and q are integers, qv 0.

23. If a21b21c25250 and ab1bc1ca53 find a1b1c.

24. In figure 6, DLMN is an isosceles triangle with LM5LN, and LP bisects NLQ, Prove thatLP??MN.


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25. In figure 7, find the value of x.

OR

In figure 8, if AB??CD then find the value of y.

26. A triangular park in a city has dimensions 30m326m328m. A gardner has to plant grassinside the park at Rs. 1.50 per m2. Find the amount to be paid to the gardner.

27. Show that in a right angled triangle the hypotenuse is the longest side.

28. Plot the points (x, y) given in the following table on the plane, choosing suitable units ofdistance on the axes.

x 2 1 1 3 0 3

y 8 7 3 1 2 0


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SECTION - D


29. Simplify

3 3 32 2 2 2 2 2

3 3 3

a b b c c a

a b b c c a

.

30. For what value of the polynomial 2x31ax2111x1a13 is exactly divisible by 2x21.

OR

Without actual division prove that x412x322x212x23 is exactly divisible by x212x23.

31. In figure 9, if AC5BC, DCA5ECB and DBC5EAC then Prove that BD5AE.

32. Factorise x3223x21142x2120.

33. In figure 10, if AD is the bisector of BAC then prove that :

(i) AB > BD (ii) AC > CD


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34. Prove that two triangles are congruent if any two angles and the included side of one triangleis equal to any two angles and the included side of the other triangle.

OR

In figure 11, OP bisects AOC, OQ bisects BOC and OP?OQ. Show that pointsA, O and B are collinear.

- o 0 o -


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U -

1 10 1 4

1.

1 1

2 27 8

(A)

1

228 (B)

1

256 (C)

1

214 (D)

1

242

2. p

(A) (B) Z

(C) (D)

3. (x21)p (x)5x21x1k k

(A) 3 (B) 2 (C) 22 (D) 1

4. p (x)5cx1d

(A) 2d (B) 2c (C)d

c(D)

d

c

5. PM N S MP C

(A) MC1PN5MN (B) MP1CP5MN (C) MC1CN5MN (D) CP1CN5MN

6. 1, OA5OB, OD5OCDAOD!DBOCZ

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


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7. DABC AB5BC

(A) B > C (B) A5C (C) A5B (D) A < C

8. 2 : 7

(A) 358, 1458 (B) 708, 1108 (C) 408, 1408 (D) 508, 1308

9. DDEF E5908

(A) DF U (B) DF

(C) EF (D) DE

10. PQ??RS m

(A) 1108 (B) 1008 (C) 908 (D) 1378

U -

11 18 2

11.

7 92 2

5

2

36 36

36

.

12. 2

3 3 2 2 .


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13. (104)3

14. A B C S AC5BC, h AC51

2AB,

Sc

15. 2 : 3 : 4

16. 3, DABC AB AC X Y S AX5AYh XC5YB.

, ABC AC AB BE CF , DABE!DACF

17. Z S (23, 2), (4, 23), (25, 24)(3, 2).


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18. 5, POR QOR a2b5808 ab

U -

19 28 3

19.

3 33

4 281 25 516 9 2

- - - - - - - - -

.

20.

7 3 5 2

48 18

3 1

a b 33 1

ab

21. 1

7xx

33

1x

x

1 3xx

33

1x

x

22. 3.425 p

q M p qZ qv 0


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23. a21b21c25250 ab1bc1ca53 a1b1c

24. 6,DLMN m LM5LN,LPNLQ m

h LP??MN

25. 7,x

8, AB??CD, y

26. 30m326m328m 1.50L , L

27.


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28.

x 2 1 1 3 0 3

y 8 7 3 1 2 0

U -

29 34 4

29.

3 3 32 2 2 2 2 2

3 3 3

a b b c c a

a b b c c a

.

30. a 2x31ax2111x1a13, (2x21)

h S x412x322x212x23x212x23

31. 9, AC5BC, DCA5ECB DBC5EAC h BD5AE.

32. U x3223x21142x2120.


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33. 10, ADBAC m h

(i) AB > BD (ii) AC > CD

34. h Z ,

11, OPAOC m OQBOC m OP?OQ

A, O B

- o 0 o -

9th maths sample paper sa-1-2011!13!3

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