# Sample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours

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1 Sample Question Paper Mathematics First Term (SA - I) Class IX Time: 3 to 3 ½ hours M.M.:90 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 have to select one correct option out of the given four. (iv) There is no overall choice. However, internal choice has 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.

2 SECTION A Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice Q. 1 Ans : (D) Q. 2 Ans : (B) Q. 3 Zero of the polynomial Ans: (D)

3 Q. 4 The coefficient of y in the expansion of Ans: (C) Q. 5 value of a is :. If each one is the supplement of the other, then the Ans : (C)

4 Q. 6 Ans : (C) Q. 7 Two sides of a triangle are 13 cm and 14 cm and its semiperimeter is 18 cm. Then third side of the triangle is : (A) 12 cm (B) 11 cm (C) 10 cm (D) 9 cm Let the third side of the triangle be x cm Ans : (D)

5 Q. 8 If the sides of a triangle are doubled, then its area: (A) remains the same (B) is doubled (C) becomes three times (D) becomes four times Let a, b and c be the sides of the original triangle and s be its semi-perimeter The sides of the new triangle are 2a, 2b and 2c. Let s be its semi-perimeter. SECTION B Question numbers 9 to 14 carry 2 marks each Q. 9 Find an irrational number between It is given that

6 Q. 10 Q. 11 Using suitable identity evaluate : Q. 12 In the adjoining figure, AC = XD, C is the midpoint of AB and D is the midpoint of XY. Using an Euclid s axiom show that AB = XY AB = 2AC [ C is the midpoint of AB] XY = 2 XD [ D is the midpoint of XY] Also, AC = XD [Given] AB = XY [ Things which are double of the same thing are equal to one another]

7 Q. 13 In the given figure, O is the midpoint of AB and CD. Prove that AC = BD OR. Find the shortest and longest side of the triangle. In Δ OAC and Δ OBD OA = OB [O is the midpoint of AB] AOC = DOB [Vertically opposite angles] OC = OD [O is the midpoint of CD] [ SAS rule] AC = BD [ CPCT] OR

8 Q. 14 Which of the following points do not lie in any quadrant? Where do those points lie? Points ( 3, 0) and (0, 7) do not lie in any quadrant. Point ( 3, 0) lies on x-axis and point (0, 7) lies on y-axis.

9 Section C Question numbers 15 to 24 carry 3 marks each Q. 15 Represent on the number line. OR Steps of construction : 1. Take OA = 2 units, on the number line. 2. Draw BA = 1 unit, perpendicular to OA. Join OB 3. Taking O as centre and OB as radius, draw an arc intersecting the number line at C. 4. Hence, point C represents OR

10 Q. 16

11 Q. 17 OR OR

12 Q. 18 Determine the value of a for which the polynomial

13 Q. 19 In the given figure, lines AB and CD intersect at O. If In the following figure, Find the value of x OR

14 OR

15 Q. 20 In the given figure, ABC is a triangle with BC produced to D. Also bisectors of

16 Q. 21 The degree measure of three angles of a triangle are x, y and z. If z =, then find the value of z

17 Q. 22 In the given figure, sides AB and AC of. Show that AC > AB are extended to points P and Q respectively. Also Q. 23 ABCD is a field in the form of a quadrilateral whose sides are indicated in the figure. If

18

19 Q. 24 In the given figure, AC = BC,

20 SECTION D Question numbers 25 to 34 carry four marks each. Q. 25 OR Evaluate after rationalising the denominator of. It is being given that

21 OR Q. 26 Prove that :

22 Q. 27.

23 Q. 28 Write the coordinates of the vertices of a rectangle in III quadrant whose length and breadth are 5 and 2 units respectively, one vertex is at the origin and the shorter side is on y-axis. Also, plot the points on the graph Coordinates of the vertices of the rectangle are

24 Q. 29 Without actual division, prove that is exactly divisible by OR OR

25 \ Q.30

26 Q. 31 Prove that if two lines intersect each other, then the vertically opposite angles are equal Given : Two lines AB and CD intersect each other at the point O To prove: Proof : Ray OA stands on the line CD at O

27 Q. 32 ABC and DBC are two triangles on the same base BC. Such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC. are on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Let AD intersects BC at O To prove : AB = AC AD = AD [Given] [Common side]

28 Q. 33 In the given figure, the sides AB and AC of bisectors BO and CO of (i) are produced to points P and Q respectively. If respectively, meet at point O, prove that (ii) (i) In the given figure,

29 Q. 34 In the given figure, S is any point in the interior of. Show that SQ + SR < PQ + PR. Construction: Extend QS up to point T such that T lies on PR

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