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I, 0 SUMMATIVE ASSESSMENT I, 0 MA-09 / MATHEMATICS IX / Class IX 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 8 6 0 0 (iii) 8 (iv) (v) General Instructions: (i) All questions are compulsory. (ii) The question paper consists of questions divided into four sections A, B, C and D. Section-A comprises of 8 questions of mark each; Section-B comprises of 6 questions of marks each; Section-C comprises of 0 questions of marks each and Section-D comprises of 0 questions of marks each. (iii) Question numbers to 8 in Section-A are multiple choice questions where you are required to select one correct option out of the given four. (iv) There is no overall choice. However, internal choices have been provided in question of two marks, questions of three marks each and questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. Page of 0
SECTION A 8 Question numbers to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.. 6 6 79 (A) (B) The simplest form of the expression 6 6 79 (C) is : (D) 9 (A) (B) (C) (D) 9. (A) (B) 0 (C) (D) is a polynomial of degree : (A) (B) 0 (C) (D). y 7y 5 0 (y 6 ) y (A) 5 (B) 6 (C) (D) The degree of the polynomial y 7y 5 0 (y 6 ) y is : (A) 5 (B) 6 (C) (D). x x xk k (A) (B) (C) 9 (D) 9 The value of k, for which the polynomial x x xk has as its zero, is : (A) (B) (C) 9 (D) 9 5. 7 (A) 7 (B) 5 (C) 60 (D) 70 The exterior angle of a triangle whose interior opposite angles are and 7 is : (A) 7 (B) 5 (C) 60 (D) 70 Page of 0
6. PQR QR E PE, QPR, (A) QEER (B) QP > QE (C) QE > QP (D) ER > RP If E is a point on side QR of PQR such that PE bisects QPR, then : (A) QEER (B) QP > QE (C) QE > QP (D) ER > RP 7. (, ) y (A) (B) (C) 7 (D) The perpendicular distance of the point P (, ) from the y-axis is : (A) (B) (C) 7 (D) 8. x y (A) I II (B) II III (C) III I (D) II IV The points in which abscissa and ordinate have different sign will lie in : (A) I and II quadrants (B) II and III quadrants (C) III and I quadrants (D) II and IV quadrants 9 / SECTION-B Question numbers 9 to carry two marks each. 9. ( ) Simplify the product ( ) : 0. (x) bx x xb9 b If (x) is a factor of bx x xb9, find the value of b?. x x Factorise : x x :. (a) (b) Page of 0
How many planes can be made to pass through (a) three collinear points (b) three non-collinear points. x A0 BED0 Find the value of x in the given figure where A0 and BED0 Prove that if one angle of a triangle is equal to the sum of the other two angles, then the triangle is right angled.. 5 Find the area of a triangle of sides 5 cm, cm and cm. 5 / SECTION-C Question numbers 5 to carry three marks each. 5. 0 5 5 Rationalise the denominator of 0 5 5 6. Show that 0. 8 a b b c c a x x x ab bc c a.. a b b c c a x x x p q ab bc c a.. p, q q 0. Page 5 of 0
Express 0. 8 in the form of p, where p, q are integers and q 0. q 7. p x px xp (x) For what value of p, the polynomial x px xp is exactly divisible by (x). 6x 5y 6z 0xyz Factorise : 6x 5y 6z 0xyz 8. p(x)x bx x5 q (x)x x xb x b If the polynomials p(x)x bx x5 and q (x)x x xb leave the same remainder when divided by x, prove that b. 9. ABCD, BPQ(5x0) PQD(x0) y z In the given figure, if ABCD, BPQ(5x0) and PQD(x0), find the value of y and z. ABC65 BCE0, DCE5 CEF5 ABEF. Page 6 of 0
In the given figure, ABC65 BCE0, DCE5 and CEF5, show that ABEF. 0. ABC AB C > 60. In ABC, if AB is the greatest side, then prove that C > 60.. AD, BAC CPDBPD CAP BAP CPBP. In the given figure AD is bisector of BAC and CPDBPD. CAP BAP and CPBP. Prove that. ABCD AD BC X Y AYBX. XAYYBX ABCD is a square. X and Y are points on the sides AD and BC such that AYBX. Prove that XAYYBX Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one-half of the vertical angle Page 7 of 0
(see figure). 60 The unequal side of an isosceles triangle measures cm and its area is 60 cm. Find the perimeter of the given isosceles triangle. 5 / SECTION-D Question numbers 5 to carry four marks each. 5. a 5 b 5 5 5 a b If a 5 5 and b 5 5 find a b 5 0 0 0 5 80 5. 0. Evaluate 0.. 5 0 0 0 5 80 is being given that 5. and 6. 5 Represent 5 on the number line. 7. x x px 5xr pr If both x and x are factors of px 5xr, show that pr 8. xyz xyz xyyzzx x y z If xyz, xyz and xyyzzx find the value of x y z. 9. a b b c c a a b b c c a Page 8 of 0
a b b c c a Simplify a b b c c a 0. (, ) ; (, ) ; (, 0) (, 5) In which quadrant or on which axis do each of the points (, ) (, ), (, 0), and (, 5) lie? Verify your answer by locating them on the Cartesian plane?. DEAF, ADFG x, y In the given figure DEAF, ADFG, find x, y. PQR QR S PQQRRP > PS Page 9 of 0
In the given figure, S is any point on the side QR of PQR. PQQRRP > PS Prove that ABC AC D BD AC. If D is the midpoint of the hypotenuse AC of a right triangle ABC, prove that BD. AC. ABC AC AB BE CF (a) ABE ACF (b) ABAC (c) ABC ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that : (a) ABE ACF (b) ABAC (c) ABC is an isosceles triangle.. If two lines intersect, the vertically opposite angles are equal. Prove it. - o O o - Page 0 of 0