# Time: 3 to 3 ½ hours M.M.:90

## Transcription

Time: 3 to 3 ½ hours M.M.:90

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. 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 Solution: Ans : (D) Q. 2 Solution: Ans : (B) Q. 3 Zero of the polynomial Solution: Ans: (D) Q. 4 The coefficient of y in the expansion of Solution: Ans: (C) Q. 5 . If each one is the supplement of the other, then the value of a is : Solution: Ans : (C) Q. 6 Solution: 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 Solution: Let the third side of the triangle be x cm Ans : (D) (D) 9 cm 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 Solution: 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 Solution: It is given that Q. 10 Solution: Q. 11 Using suitable identity evaluate : Solution: 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 Solution: AB = 2AC XY = 2 XD Also, AC = XD AB = XY [ C is the midpoint of AB] [ D is the midpoint of XY] [Given] [ Things which are double of the same thing are equal to one another] 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. Solution: In Δ OAC and Δ OBD OA = OB AOC = DOB OC = OD AC = BD OR [O is the midpoint of AB] [Vertically opposite angles] [O is the midpoint of CD] [ SAS rule] [ CPCT] Q. 14 Which of the following points do not lie in any quadrant? Where do those points lie? Solution: 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. Section – C Question numbers 15 to 24 carry 3 marks each Q. 15 Represent on the number line. OR Solution: 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 Q. 16 Solution: Q. 17 OR Solution: OR Q. 18 Determine the value of a for which the polynomial Solution: Q. 19 In the given figure, lines AB and CD intersect at O. If OR In the following figure, Find the value of x Solution: OR Q. 20 In the given figure, ABC is a triangle with BC produced to D. Also bisectors of Solution: Q. 21 The degree measure of three angles of a triangle are x, y and z. If z = Solution: , then find the value of z Q. 22 In the given figure, sides AB and AC of . Show that AC > AB are extended to points P and Q respectively. Also Solution: Q. 23 ABCD is a field in the form of a quadrilateral whose sides are indicated in the figure. If Solution: Q. 24 In the given figure, AC = BC, Solution: SECTION – D Question numbers 25 to 34 carry four marks each. Q. 25 OR Evaluate after rationalising the denominator of Solution: . It is being given that OR Q. 26 Prove that : Solution: Q. 27. Solution: 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 Solution: Coordinates of the vertices of the rectangle are Q. 29 Without actual division, prove that OR Solution: OR is exactly divisible by \ Q.30 Solution: Q. 31 Prove that if two lines intersect each other, then the vertically opposite angles are equal Solution: 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 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. Solution: 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] Q. 33 In the given figure, the sides AB and AC of are produced to points P and Q respectively. If bisectors BO and CO of respectively, meet at point O, prove that (i) (ii) Solution: (i) In the given figure, Q. 34 In the given figure, S is any point in the interior of . Show that SQ + SR < PQ + PR Solution: . Construction: Extend QS up to point T such that T lies on PR