summative assessment- i guess papers for class-ix

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

(Maths & Science)

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Class – X (MATHEMATICS) Sample Paper Page 1 of 17 Summative Assessment-I (2014-15)

Class-IX MATHEMATICS

TIME : 3 Hrs Maximum Marks : 90

Instructions:

General 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 = 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 ∠B = 65°, then the longest side of the triangle is : (A) AC (B) AB (C) BC (D) None of these

5. The points (25, 2) and (2, 25) lie in the : (A) same quadrants (B) II and III quadrants respectively (C) II and IV 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 (D) 3 units

7. Which of the following is a rational number ?

(A) (B) π (C) 0.101001000100001....... (D) 0.853853853.........

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 p(x) is divided by ax-b then the remainder is : (A) p(a+b) (B) p(-b/a) (C) p(a/b) (D) p(b/a)

SUMMATIVE ASSESSMENT-I 2014-15


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 :

12. In the fig. 1, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR =

135° and ∠PQT = 110°, find ∠PRQ.

Fig. 1

13. If the complement of an angle is one–third of its supplement, find the angle.

14.If a + b + c = 7 and ab + bc + ca = 20, find the value of a2 + b2 + c2.

15. Find two rational numbers in the form between 0.343443444344443...... and 0.363663666366663.......

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

Fig. 2

17. In fig. 3, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Fig. 3

18. . Factorise :

SECTION - C



19. Locate on the number line

20. Express in the form where P and Q are integers and Q ≠ 0.

21. Find the value of x3 – 8y3 – 36xy – 216 when x = 2y + 6.

22. Factorise : (ax + by) 2 + (ay – 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 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 the value of 64x3 + 125z3, if 4x + 5z = 19 and xz = 5.

27. In the fig. 8, AD and CE are the angle bisectors of ∠A and ∠C respectively. If ∠ABC = 90° then find

∠AOC.


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


29. If , find the value of

30. The polynomial p(x) = x4 – 2x3 + 3x2 – 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 – 20y + 16 by 3x – 5y - 4 using suitable identity. (ii) Factorise : a2 + b2 – 2(ab – ac + bc).

34. In the fig. 10, D and E are points on the base BC of a ΔABC such that AD = AE and ∠BAD = ∠CAE. Prove that AB = AC.




Instructions:


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 is : (A) 0.56 (B) 0.056 (C) 0.0056 (D) 5.6

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

(A) -d (B) -c (C) (D)

4. Degree of the polynomial p(x) = 4x4 + 2x3 + x5 + 2x + 7 is : (A) 7 (B) 4 (C) 5 (D) 3

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 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 figure 1, if PQ||RS then the measure of m is : (A) 110° (B) 100° (C) 90° (D) 137°



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 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 complement of an angle m is : (A) m (B) 90° + m (C) 90° - m (D) m x 90°

SECTION-B


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 figure 2, X and Y are two 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 figure 3, find the value of x.


Fig. 3

OR

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

Fig. 4

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 the quadrants in which the following points lie (-5, -4), (2, -4), (-7, 6) and (2, 3).

SECTION - C


19. Simplify the following by rationalising the denominator.

OR

If , find the value of a and b.


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 then find the value of .

23. Find the value of ‘p’ if 5p-3 x 32p-8 = 225.


Fig. 6

OR

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

Fig. 7

25. In figure 8, if QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30° find the value of x and y.

Fig. 8


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 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


29. For what value of the polynomial 2x3 + ax2 + 11x + a + 3 is exactly divisible by 2x - 1.

OR

Without actual division prove that x4 + 2x3 – 2x2 + 2x - 3 is exactly divisible by x2 + 2x - 3.

30. Prove that

31. Factorise a7 + ab6.

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 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.

Fig. 11



Instructions:




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 (x - 1) is a factor of p(x) = x2 + x + k, then value of k is :

(A) 3

(B) 2

(C) -2

(D) 1

4. Zero of the polynomial p (x) = cx + d is :

(A) -d

(B) -c

(C)

(D)

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 by congruence 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 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 the given figure if PQ||RS then the measure of m is :

(A) 110°

(B) 100°

(C) 90°

(D) 137°


Fig. 2

SECTION-B


11. Evaluate .

12. Simplify :

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 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.


Fig. 4

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

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


19. Simplify

20. Simplify the following by rationalising the denominator.

OR

If then find the value of a and b.

21. If then find the value of .

OR

If then find the value of .

22. Express in the form where p and q are integers and q ≠ 0.

24. In figure 6, ΔLMN is an isosceles triangle with LM = LN, and LP bisects ∠NLQ, Prove that

LP||MN.


Fig. 6


Fig. 7

OR

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

Fig. 8

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 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 -3


y 8 7 3 -1 2 0

SECTION-D


29. Simplify

30. For what value of the polynomial 2x3 + ax2 + 11x + a + 3 is exactly divisible by 2x - 1.

OR

Without actual division prove that x4 + 2x3 – 2x2 + 2x - 3 is exactly divisible by x2 + 2x - 3.

31. In figure 9, if AC = BC, ∠DCA = ∠ECB and ∠DBC = ∠EAC then Prove that BD = AE.

Fig. 9

32. Factorise x3 – 23x2 + 142x - 120.

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

(i) AB > BD

(ii) AC > CD

Fig. 10

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.


Fig. 11

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