Summative Assessment- I Guess Papers for Class-ix

Sample Test Paper (for Summative Assessment-1 Class - IX)

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SUMMATIVE ASSESSMENT-I 2014-15 Class-IX MATHEMATICS TIME : 3 Hrs

Maximum Marks : 90

Instructions:

General Instructions: Instructions: (i) All questions are compulsory. (ii) The question paper consists of 31 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 of 2 marks each. Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each. (iii) Use of calculator is not permitted.

SECTION - A Question numbers 1 to 10 carry 1 mark each. 1. If x2 + kx + 6 = (x + 2) (x + 3) for all x, the value of k is : (A) 1 (B) 21 (C) 5 (D) 3 2. Zero of the zero polynomial is : (A) 0 (B) 1 (C) any real number (D) not defined 3. In ΔABC and ΔDEF, AB A B = DF and ∠ A = ∠D. The two triangles will be congruent by SAS axiom if : (A) BC = EF (B) AC = DE (C) BC = DE (D) AC = EF 4. In ΔABC, if ∠ A = 35° and and ∠B = 65°, then the longest side of the triangle is : (A) AC (B) AB (C) BC (D) None of these 5. The 5. The points (25, 2) and (2, 25) lie in the : (A) same quadrants (C) II and IV quadrants respectively

(B) II and III quadrants respectively (D) IV and III quadrants respectively

6. The distance of a point (0, -3) from the origin is : (A) 0 units (B) -3 units (C) cannot be determined 7. Which of the following is a rational number ? (A) (B) π (C) 0.101001000100001.......

(D) 3 units

(D) 0.853853853.........

8. Which 8. Which of the following statements is incorrect ? (A) A line segment has definite length. (B) Three lines are concurrent if and only if they have a common point. (C) Two lines drawn in a plane always intersects at a point. (D) One and only one line can be drawn passing through a given point and parallel to a given line. 9. When 9. When p(x) is divided by ax-b then the remainder is : (A) p(a+b) (B) p(-b/a) (C) p(a/b) Class – X (MATHEMATICS) Sample Paper

Page 1 of 17

(D) p(b/a) Summative Assessment-I (2014-15)

10. Which 10. Which of the following points lie on the negative side of x-axis ? (A) (24, 0) (B) ( 23, 2) (C) (0, 24) (D) (5, 27) SECTION-B Question numbers 11 to 18 carry 2 marks each. 11. Evaluate 11. Evaluate : 12. In the fig. 1, sides QP and RQ of ΔPQR are produced to points S and T respectively. If 135° and ∠PQT = 110°, find ∠PRQ.

∠SPR

=

Fig. 1 13. If 13. If the complement of an angle is one – one –third third of its supplement, find the angle. 14.If 14.If a + b + c = 7 and ab + bc + ca = 20, find the value of a 2 + b2 + c2. 15. Find two rational numbers in the form 0.363663666366663.......

between 0.343443444344443...... and

16. In 16. In fig. 2, if AB||CD then find the value of x.

Fig. 2 17. In 17. In fig. 3,

∠PQR

= ∠PRQ, then prove that

∠PQS

= ∠PRT.

Fig. 3 18. . Factorise : SECTION - C

Class – X (MATHEMATICS) Sample Paper

Page 2 of 17

Summative Assessment-I (2014-15)

Question numbers 19 to 28 carry 3 marks each. 19. Locate

on the number line

20. Express

in the form

where P and Q are integers and Q ≠ 0.

21. Find 21. Find the value of x 3 – 8y – 8y3 – 36xy – 36xy – – 216 216 when x = 2y + 6. 22. Factorise 22. Factorise : (ax + by) 2 + (ay – (ay – bx) bx) 2 23. In fig. 5, ΔABC, is an isosceles triangle in which AB = AC, side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle.

Fig. 5 24. In figure 6, D is a point on side BC of ΔABC such that AD = AC. Show that AB > AD.

Fig. 6 25. A 25. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the base 15 cm, find the height of parallelogram. 26. Find 26. Find the value of 64x 3 + 125z 3, if 4x + 5z = 19 and xz = 5. 27. In 27. In the fig. 8, AD and CE are the angle bisectors of ∠ AOC.


∠ A

and ∠C respectively. If ∠ ABC = 90° 90° then find

Page 3 of 17


28. In ΔABC, BE and CF are altitudes on the sides AC and AB respectively such that BE = CF. Using RHS congruency rule, prove that AB = AC. SECTION - D Question numbers 29 to 34 carry 4 marks each.

29. If

, find the value of

30. The 30. The polynomial p( x ) = x4 – 2x – 2x3 + 3x2 – ax – ax + 3a - 7 when divided by (x+1) leaves the remainder 19. Find the value of a. Also find the remainder, when p(x) is divided by x+2. 31. Prove “If two lines intersect each other, then the vertically opposite angles are equal”. 32. In the fig. 9, the sides AB and AC of ΔABC are produced to points E and D respectively. If bisectors BO and CO of CBE and BCD respectively meet at point O, then prove that

∠BOC

= 90° -

∠BAC.

Fig. 9 33. (i) Multiply 9x2 + 25y2 + 15xy + 12x – 12x – 20y 20y + 16 by 3x – 3x – 5y 5y - 4 using suitable identity. 2 2 (ii) Factorise : a + b – 2(ab – 2(ab – – ac ac + bc). 34. In the fig. 10, D and E are points on the base BC of a ΔABC such that AD = AE and Prove that AB = AC.


Page 4 of 17

∠BAD

= ∠CAE.



Maximum Marks : 90

Instructions:

General Instructions: Instructions: (i) All questions are compulsory. (ii) The question paper consists of 31 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 of 2 marks each. Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each. (iii) Use of calculator is not permitted. SECTION - A Question numbers 1 to 10 carry 1 mark each. Out of four given options choose the correct one. 1. π is : (A) a rational number (B) an integer (C) an irrational number (D) a whole number 2. The decimal form of (A) 0.56 (B) 0.056

is : (C) 0.0056

(D) 5.6

3. Zero 3. Zero of the polynomial p (x) = cx + d is : (A) -d

(B) -c

(C)

(D)

4. Degree 4. Degree of the polynomial p(x) = 4x 4 + 2x3 + x5 + 2x + 7 is : (A) 7 (B) 4 (C) 5 (D) 3 5. If 5. If the point P lies in between M and N and C is midpoint of MP then : (A) MC + PN = MN (B) MP + CP = MN (C) MC + CN = MN

(D) CP + CN = MN

6. If 6. If the measure of an angle is twice the measure of its supplementary angle then the measure of the angle is : (A) 60° (B) 90° (C) 120° (D) 130° 7. In 7. In figure 1, if PQ||RS then the measure of m is : (A) 110° (B) 100° (C) 90°


(D) 137°

Page 5 of 17


Fig. 1 8. In ΔABC if AB = BC then : (A) ∠B > ∠C (B) ∠ A = ∠C

(C) ∠ A = ∠B

(D) ∠ A < ∠C

9. If ΔABC ≅ ΔDEF by SSS SSS congruence congruence rule then : (A) AB = EF, BC = FD, CA = DE (B) AB = FD, BC = DE, CA = EF (C) AB = DE, BC = EF, CA = FD (D) AB = DE, BC = EF, C F 10. The 10. The complement of an angle m is : (A) m (B) 90° + m (C) 90° - m

(D) m x 90°

SECTION-B Question numbers 11 to 18 carry 2 marks each. 11. Simplify : 12. Simplify

. and express the result in the exponential form of x.

13. Find the value of the polynomial

when z = 3.

14. In 14. In figure 2, X and Y are t wo points on equal sides AB and AC of a ΔABC such that AX = AY. Prove that XC = YB.

Fig. 2 15. If a point C lies between two points A and B such that AC = BC, then prove that

.

16. In 16. In figure 3, find the value of x.


Page 6 of 17


Fig. 3 OR In figure 4, if x ≠ y = w + z, then prove that AOB is a line.

Fig. 4 17. In 17. In figure 5, if

∠POR

and

∠QOR

form a linear pair and a - b = 80° then find the value of a and b.

Fig. 5 18. Name 18. Name the quadrants in which the following points lie (-5, -4), (2, -4), (-7, 6) and (2, 3). SECTION - C Question numbers 19 to 28 carry 3 marks each. 19. Simplify 19. Simplify the following by rationalising the denominator.

OR

If

, find the value of a and b.


Page 7 of 17


20. Express

in the form

where p and q are integers and q ≠ 0.

21. If a2 + b2 + c2 = 250 and ab + bc + ca = 3 find a + b + c.

22. If

then find the value of

.

OR

If


.

23. Find the value of ‘p’ if 5 p-3 x 32p-8 = 225. 24. In 24. In figure 6, find the value of x.

Fig. 6 OR In figure 7, if AB||CD then find the value of y.

Fig. 7 25. In 25. In figure 8, if QT

⊥ PR, ∠TQR

= 40° and

∠SPR

= 30° find the value of x and y.

Fig. 8


Page 8 of 17


26. Show 26. Show that in a right angled triangle the hypotenuse is the longest side. 27. Sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area. 28. Plot 28. Plot the points (3, 2), (-2, 2), (-2, -2) and (3, -2) in the cartesian plane. Join these points and name the figure so formed. SECTION-D Question numbers 29 to 34 carry 4 marks each. 29. For 29. For what value of the polynomial 2x 3 + ax2 + 11x + a + 3 is exactly divisible by 2 x - 1. OR Without actual division prove that x 4 + 2x3 – 2x – 2x2 + 2x - 3 is exactly divisible by x 2 + 2x - 3. 30. Prove 30. Prove that 31. Factorise 31. Factorise a 7 + ab6. 32. In 32. In figure 9, if AC = BC,

∠DCA

= ∠ECB and

∠DBC

= ∠EAC then Prove that BD = AE.

Fig. 9 33. In figure 10, D is a point on side BC of ΔABC such that AD = AC. Show that AB > AD.

Fig. 10 34. Prove 34. Prove that two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle. OR


Page 9 of 17


In figure 11, OP bisects ∠ AOC, OQ bisects bisects ∠BOC and OP collinear.

⊥ OQ.

Show that points A, O and B are

Fig. 11


Maximum Marks : 90

Instructions:

General Instructions: 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 10 questions of 1 mark each. Section B comprises of 8 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each. (iii) Use of calculator is not permitted. Class – X (MATHEMATICS) Sample Paper

SECTION - A

Page 10 of 17


SECTION - A Question numbers 1 to 10 carry 1 mark each. Out of four given options choose the correct one.

1. The value of

.

(A) (B) (C) (D) 2. π is : (A) a rational number (B) an integer (C) an irrational number (D) a whole number 3. If 3. If (x - 1) is a factor of p(x) = x 2 + x + k, then value of k is : (A) 3 (B) 2 (C) -2 (D) 1 4. Zero 4. Zero of the polynomial p (x) = cx + d is : (A) -d (B) -c (C) (D) 5. If 5. If the point P lies in between M and N and C is midpoint of MP then : (A) MC + PN = MN (B) MP + CP = MN (C) MC + CN = MN (D) CP + CN = MN 6. In figure 1, if OA = OB, OD = OC then ΔAOD


≅ ΔBOC

Page 11 of 17

by congruenc congruence e rule :


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

Fig. 1 7. In ΔABC if AB = BC then : (A) ∠B > ∠C (B) ∠ A = ∠C (C) ∠ A =

∠B

(D) ∠ A < ∠C 8. If 8. If two supplementary angles are in the ratio 2 : 7, then the angles are : (A) 35°, 145° (B) 70°, 110° (C) 40°, 140° (D) 50°, 130°

9. In right triangle ΔEF if

∠E

= 90°, then :

(A) DF is the shortest side (C) EF is the longest side (B) DF is the longest side (D) DE is the longest side

10. In 10. In the given figure if PQ||RS then the measure of m is : (A) 110° (B) 100° (C) 90° (D) 137°


Page 12 of 17


Fig. 2 SECTION-B Question numbers 11 to 18 carry 2 marks each.

11. Evaluate

.

12. Simplify : 13. Evaluate 13. Evaluate (104) 3 using suitable identity.

14. If a point C lies between two points A and B such that AC = BC, then prove that

.

Explain by drawing the figure. 15. If 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 ΔABC such that AX = AY. Prove that XC = YB.

Fig. 3 OR In figure 4, ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that ΔABE

≅ ΔACF.


Page 13 of 17


Fig. 4 17. Name 17. Name the quadrant in which the following point lie (-3, 2), (4, -3), (-5, -4) and (3, 2).

18. In 18. In figure 5, if

∠POR

and

∠QOR

form a linear pair and a - b = 80° then find the value of a and b.

Fig. 5 SECTION-C Question numbers 19 to 28 carry 3 marks each.

19. Simplify 19. Simplify

20. Simplify 20. Simplify the following by rationalising the denominator.

OR If

then find the value of a and b.

21. If


.

OR If


22. Express

in the form

. where p and q are integers and q ≠ 0.

24. In figure 6, ΔLMN is an isosceles tria ngle with LM = LN, and LP bisects

∠NLQ,

Prove that

LP||MN.


Page 14 of 17


Fig. 6 25. In 25. In figure 7, find the value of x.

Fig. 7 OR In figure 8, if AB||CD then find the value of y.

Fig. 8 26. A 26. A triangular park in a city has dimensions 30m x 26m x 28m. A gardener has to plant grass inside the park at Rs. 1.50 per m 2. Find the amount to be paid to the gardener.

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

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

-2

-1


1

3

0

Page 15 of 17

-3


y

8

7

3

-1

2

0

SECTION-D Question numbers 29 to 34 carry 4 marks each.

29. Simplify 29. Simplify 30. For 30. For what value of the polynomial 2x 3 + ax2 + 11x + a + 3 is exactly divisible by 2 x - 1. OR Without actual division prove that x 4 + 2x3 – 2x – 2x2 + 2x - 3 is exactly divisible by x 2 + 2x - 3. 31. In 31. In figure 9, if AC = BC,

∠DCA

= ∠ECB and

∠DBC

= ∠EAC then Prove that BD = AE.

Fig. 9 32. Factorise 32. Factorise x 3 – 23x – 23x2 + 142x - 120. 33. In 33. In figure 10, if AD is the bisector of

∠BAC

then prove that :

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

Fig. 10 34. Prove 34. Prove that two triangles are congruent if any two angles and the included side of one triangle is 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 points A, O and B are

collinear.


Page 16 of 17


Fig. 11


Page 17 of 17


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Summative Assessment- I Guess Papers for Class-ix

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