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 semiperimeter The sides of the new triangle are 2a, 2b and 2c. Let s be its semiperimeter. 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 xaxis and point (0, 7) lies on yaxis.
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 yaxis. 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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