# 9 th CBSE Mega Test - II

Size: px
Start display at page:

Transcription

1 9 th CBSE Mega Test - II Time: 3 hours Max. Marks: 90 General Instructions All questions are compulsory. 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 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 10 questions of 4 marks each. Question numbers 1 to 8 in Section A are multiple choice questions where you are to select one correct option out of the given four. There is no overall choice. However, internal choice has been provided in 1 question of two marks each, 3 questions of three marks each and questions of four marks each. You have to attempt only one of the alternatives in all such questions, Use of calculators is not permitted. NAME OF THE CANDIDATE CONTACT NUMBER PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

2 Solution Visits: Section-A [Question number 1 to 8 carries 1 mark each] 1. If x is irrational number, then x is : (a) rational (b) Irrational (c) 0 (d) real (D) real. One of the factors of (16y 1) + (1 4y) is : (a) (4 + y) (b) (4 y) (c) (4y + 1) (d) 8y (D) 8y [ (16y 1) + (1 4y) 16y y 8y 3y 8y 8y (4y 1)] 3. The value of 4 3 equal to: (a) 1/6 (b) 6 (c) 1/6 (d) 6 (C) 1/6 [ 4 3 {( ) 1/3 } 1/4 1/3 1/4 1/6 ] 4. In which of the following (x + ) is a factor? (a) 4x 3 13x + 6 (b) x 3 + x + x + 4 (c) 4x x 5 (d) x 3 + x x 9 (A) 4x 3 13x + 6 [ Let f(x) 4x 3 13x + 6 f( ) 4( ) 3 13 ( ) + 6] 4 ( 8) ] 5. An exterior angle of a triangle is 10 0 and the two interior opposite angles are equal. Each of these angle is : PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH

3 (a) 60 0 (b) (c) 10 0 (d) (A) 60 0 [ Let each interior opposite angle be x. We know that exterior angle of a triangle is equal to the sum of two its interior opposite angles. x + x 10 0 x 10 0 x 60 0 ] 6. Two sides of a triangle are 1 cm and 13 cm. The length of the third side cannot be: (a) 0.8 cm. (b) 5cm. (c) 4 cm. (d) 6cm. (A) 0.8 cm. [ The sum of any two side of a triangle is grater then its third side. Here, ( ) cm. 1.8 cm 13 cm] 7. In the given figure, if AB AC and AP AQ, then by which congruence criterion PBC QCB. (a) SSS (b) ASA (c) SAS (d) RHS (C) SAS [ AB AC and AP AQ AB AP AC AQ BP CQ Now, in PBC and QCB, we have AB AC B C BP CQ (proved above) PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 3

4 BC CB (common) By SAS congruency, we have PBC QCB 8. Heron s formula is : (a) s(s a)(s b)(s c) (b) (s a)(s b)(s c) (c) s(s a)(s b)(s c),s a + b + c (d) s s a s b s c, s a + b + c (D) s s a s b s c, s a + b +c Section-B [Question number 9 to 14 carries mark each] 9. Simplify: Factorise: x 4 + 4x + 3 x 4 + 4x + 3 y + 4y + 3 PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 4

5 y + 3y + y + 3 ( where x y) y(y + 3) +1 ( y + 3) ( y+ 3) ( y+ 1) (x + 3) (x +1) ( y x )] 11. Evaluate (104) 3 using suitable identity. (104) 3 ( ) (100+ 4) [ Using identity (a + b) 3 a 3 + b 3 + 3ab(a +b)] Define (a) a square (b) perpendicular lines. (a) A square: A square is a rectangle having same length and breadth, here, undefined terms are length, breadth and rectangle. (b) Perpendicular lines: Two coplanar (in a plane) lines are perpendicular, if the angle between them at the point of intersection is one right angle. Here, the term one right angle is undefined. 13. In the given figure, prove that AB EF OR In the given figure, lines l and m intersect each others at O. If x 40 0, Then find the value of y, z and w. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 5

6 Here, BCD BCE ECD Also, ABC BCD 0 ABC 50 But these are the alternate interior angles of AB and CD. Further AB CD.. (1) 0 0 CEF DCE But these are the interior angles on the same side of CD and EF. EF CD From (1) and (), we have AB CD and EF CD AB EF ( If two lines are parallel to the same line, they are parallel to each other) Lines l and m intersect at O x 0 + y y y Or z x 40 0 (vertically opposite angles) w y (vertically opposite angles) (Linear pair) PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 6

7 14. A point lies on the x-axis at a distance of 9 units from y-axis. What are its coordinates? What will be its coordinates if it lies on y-axis at a distance of 9 units from x-axis? 15. If x If a point lies on x-axis at a distance of 9 units from y-axis, then its abscissa is 9 and ordinate is 9. Coordinates of the point are (9, 0) If a point lies on y-axis at a distance of 9 units from x-axis, then its abscissa is 0 and ordinate is 0. Coordinates of the point are (0, 9) Section-C [Question number 15 to 4 carries 3 mark each] 3 3 and y 3 3, then find the value of x + y 10xy. OR Find the square root of 4.7 geometrically. x Similarly, we can find y 5 6 x + y 10xy (x + y xy) 8xy (x y) 8xy [(5 + 6) (5 6 )] 8(5 + 6) (5 6) [ ] 8(5 ( 6) ) PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 7

8 (4 6) 8(5 4) Or First of all draw a line of length 4.7 units such that AB 4.7 units. Now, from point B, mark a distance of 1 unit. Let this point be 'C. Let 'O' be the mid-point of the distance AC. Now, draw a semicircle with centre 'O' and radius OC. Let us draw a line perpendicular to AC passing through the point 'B' and intersecting the semicircle at point 'D'. The distance BD 4.7 Now, to represent 4.7 on the number line. Let us take the line BC as number line and point 'B' as zero, point 'C' as 1 and so on. Draw an arc with centre B and radius BD, which intersects the number line at point 'E'. Then, the point 'E' represents If x , find the value of x 3 1 x 3. OR If 5.36 and , find the value of x x PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 8

9 7 4 3 We have 1 x 14 x 1 x x On cubing both sides, we have x 3 x x 14 x x x x 3 x x 3 x If a + b + c 6, then find the value of ( a) 3 + ( b) 3 + ( c) 3 3( a) ( b) ( c). Sol. Let a x, b y and c z x + y+ z a + b + c 6 (a + b + c) Now, ( a) 3 + ( b) 3 + ( c) 3 3( a) ( b) ( c) x 3 + y 3 + z 3 3xyz (x + y + z) (x + y + z xy yz zx) 0 (x + y + z xy yz zx) 0 PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 9

10 18. Find the remainder when 3x 3 4x + 7x 5 is divided by (x-3) and (x + 3). Let f(x) 3x 3 4x +7x 5 When f(x) is divided by (x 3) Remainder f(3) 3(3) 3 4(3) 7(3) Also, when f(x) is divided by (x + 3) Remainder f( 3) 3( 3) 3 4( 3) + 7( 3) 5 3 ( 7) In the given figure, prove that x a + b + c. OR The sides BA and DC of a quadrilateral ABCD are produced as shown in figure. Show that x y a b. Sol. Let reflex ADC y Now, ADC + reflex ADC 360 PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

11 x + y (i) In quadrilateral ABCD, we have a + b + c + reflex ADC 360 a + b + c + y (ii) From (i) and {ii), we have x + y a + b + c + y x a + b + c Or Join BD a is the exterior angle of BDC D a CBD + CDB...(i) [ ext. sum of two interior opp. s] Also, b is the exterior angle of ABD b ABD ADB (ii) [ ext. sum of two interior opp. s] Adding (i) and (ii), we have a b CBD CBD ABD ADB CBD ABD CDB ADB x y 0. In the given figure, if AB CD, APQ 50 and PRD 17, find x and y. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

12 Sol. AB CD and PQ is a transversal PQR APQ (alternate interior angles) x 50 PRD is the exterior angle of PQR PRD PQR + QPR [ ext. sum of two interior 17 x + y opposite angles] y y Prove that the angles opposite to equal sides of an isosceles triangle are equal. Is the converse true? Given : A ABC in which AB AC To Prove : B C Construction : Draw the bisector of BAC which meets BC in D. Proof : In ABD and ACD, we have AB AC (given) BAD CAD (by construction) AD AD (common) So, by SAS congruence axiom, we have ABD ACD B C (c. p. c. t.) The converse of the above theorem is also true i.e., the sides opposite to equal angles of an isosceles triangle are equal. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

13 . In the given figure, D and E are points on the base BC of a ABC such that BD CE and AD AE. Prove that ABE ACD. BE BD + DE EC + DE ( BDCE) DC BE DC Also, AD AE AED ADE (angles opposite to equal sides are equal) In ABE and ACD, we have AD AE (given) AEB ADC ( AED ADE) BE CD (proved above) By SAS congruence axiom, we have ABE ACD 3. 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 O. To Prove : (i) AOD COB (ii) AOC BOD PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

14 Proof : Since, ray OA stands on the line CD at O. AOC + AOD 180 (i) Also, ray OC stands on the line AB at O. AOC + COB (ii) From (i) and(ii), we have AOC + AOD AOC + COB AOD COB Similarly, we can prove AOC BOD 4. Find the area of a triangular park, two sides of which are 18 cm and 10 cm and the perimeter is 4 cm. Sol. Let a, b and c be the sides of a triangular park. Let a 18 cm, b 10 cm Perimeter of the triangular park 4 cm a + b + c 4cm 18 cm + 10 cm + c 4 cm 8 cm + c 4 cm c 4 cm 8 cm c 14 cm a b c 4 s 1cm. Area of the triangular park by Heron's formula s(s a)(s b)(s c) PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

15 cm Section-D [Question number 5 to 34 carries 4 mark each] 5. Using factor theorem, factorise the polynomial: x 4 + 3x 3 + x 3x 3. OR Show that x 3 + y 3 + z 3 3xyz 1 (x + y + z) [(x y) + (y - z) + (z x) ] Sol : Let f(x) x 4 + 3x 3 + x 3x 3 Put x 1 in f(x), we have f(1) (1) 3 + (1) 3(1) By factor theorem, x - 1 is a factor of f(x). Again, put x 1 in f(x), we have f ( 1) ( 1) 4 + 3( 1) 3 + ( 1) 3( 1) By factor theorem, x + 1 is a factor of f(x) Thus, (x + 1) and (x 1) are both factors of f(x) (x + 1) (x 1) x 1 is a factor of f(x) Now, divide f(x) by x 1, we have PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

16 4 3 x 1 x 3x x 3x 3(x 3x 3 x x 4 3 3x 3x 3x 3 3x 3 3x 3x 3 3x 3 0 We have, f(x) (x 1) (x + 3x + 3) (x 1)(x + 1)(x + 3x + 3) Or Here, R.H.S. 1 (x + y + z) [(x y) + (y z) + (z x) ] 1 (x + y + z) (x xy + y + y yz + z + z +zx + x ) 1 x y z x y z xy yz zx (x + y + z) (x + y + z xy yz zx) x 3 + y 3 +z 3 3xyz L.H.S. 6. Simplify: OR If a and b , find a b. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

17 Or We have a Similarly, we have b PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

18 Now, a b And a b Hence, a b a b a b Find the value of a, if (x + a) is a factor of x 4 a x + 3x a. Let p(x) x 4 a x + 3x a (x + a) is a factor of polynomial p(x) By factor theorem, we have p( a) 0 ( a) 4 a ( a) + 3( a) a 0 a 4 a 4 3a a 0 4a 0 a 0 8. The polynomial ax 3 + 4x + 3x 4 and x 3 4x + a when divided by (x 3) leave the same remainder. Find the value of a. Let f(x) ax 3 + 4x + 3x 4 And g(x) x 3 4x + 4 When f(x) and g(x) are divided by (x 3) leave the same remainder PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

19 f(3) g(3) a(3) 3 +4(3) +3(3) (3) + a 7a a 7a a 7a a a 6 a 1 9. The polynomial p(x) x 4 x 3 + 3x ax + 3a 7 when divided by (x + 1) leaves the remainder19. Find the value of a. Also, find the remainder, when p(x) is divided by(x + ). We have p(x) x 4 x 3 + 3x ax + 3a 7..(1) When p(x) is divided by (x +1) leaves remainder 19 p( 1) 19 ( 1) 4 ( 1) 3 + 3( 1) a( 1) + 3a a + 3a a a 0 a 5 Putting the value of a in (1), we have p(x) x 4 x 3 + 3x 5x x 4 x 3 + 3x 5x + 8 Remainder p( ) ( ) 4 ( ) 3 + 3( ) 5( ) PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH 1

20 30. In the given figure, PQR is an equilateral triangle in the coordinate axes and coordinates of Q and R are (0, 4) and (0, 4). Find the coordinates of the vertex P. Here, Q is (0, 4) and R is (0, 4) QR QR 8 units PQR is an equilateral triangle PQ QR PR 8 units Now, in rt. OPQ, PQ 8 units and OQ 4 units OP PQ OQ units Abscissa of P is 4 3and it lies on x axis. It ordinate is 0. Hence, the coordinates of P are ( 4 3, 0). 31. In the given figure, AP and DP are bisectors of two adjacent angles A and D of a quadrilateral ABCD. Prove that APD B C. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH

21 In quadrilateral ABCD, we have 0 A B C D A B C D A D 180 B C As, AP and DP are the bisectors of A and D 0 And Now, In PAD PDA 1 1 APD, we have A D 0 1 PAD PDA 180 B C 0 APD PAD PDA APD 180 B C APD B C APD B C 0 0 (Using (1))..(1) 3. AD is an altitude of an isosceles triangle ABC in which AB AC. Show that (i) AD bisects BC (ii) AD bisects A. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH

23 Proof : In ABC, AB is the smallest side. BC AB 1...(i) ( angle opposite to longer side is greater) In ADC, CD is the longest side. CD > AD ii Adding (i) and (ii), we have A C Again, in ADB, AB is the smallest side. AD >AB iii In BCD, CD is the greatest side. CD > BC iv Adding (iii) and (iv), we have B D Hence, A C and B D. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH

24 34. AD, BE and CF, the altitudes of ABC are equal. Prove that ABC is an equilateral triangle. Consider right BCE and right CBF, we have Hyp. BC Hyp. BC (Common) CF BE (Given) By RHS congruence axiom, we have BCE CBF B C (by c. p. c. t.) AC BC (i) ( sides opposite to equal angles are equal) Similarly, ABD BAE B C (by c. p. c. t.) AC BC. (ii) ( sides opposite to equal angles are equal) From (i) and (ii), we have ABD BEA AB BC AC Hence, ABC is an equilateral triangle. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 30, SECTOR 40 D, CHANDIGARH

### SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)

1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x

### SUMMATIVE ASSESSMENT I, IX / Class IX

I, 0 SUMMATIVE ASSESSMENT I, 0 0 MATHEMATICS / MATHEMATICS MATHEMATICS CLASS CLASS - IX - IX IX / Class IX MA-0 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 8 6 0 0 (iii) 8 (iv) (v) General Instructions:

### Q4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and.

SUMMATIVE ASSESSMENT 1 (2013 2014) CLASS IX (SET I) SUBJECT : MATHEMATICS Time: 3 hours M.M. : 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions

### SOLUTIONS SECTION A SECTION B

SOLUTIONS SECTION A 1. C (1). A (1) 3. B (1) 4. B (1) 5. C (1) 6. B (1) 7. A (1) 8. D (1) SECTION B 9. 3 3 + 7 = 3 3 7 3 3 7 3 3 + 7 6 3 7 = 7 7 6 3 7 3 3 7 0 10 = = 10. To find: (-1)³ + (7)³ + (5)³ Since

### SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-) MATHEMATICS CLASS IX Time: 3 to 3 1 hours Maximum Marks: 80 GENERAL INSTRUCTIONS: 1. All questions are compulsory.. The question paper is divided into four sections

### Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.

Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?

### Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths

Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here

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

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

### TRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions

CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)

### Class IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).

Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects

### Class-IX CBSE Latest Pattern Sample Paper {Mathematics}

Class-IX CBSE Latest Pattern Sample Paper {Mathematics} Term-I Examination (SA I) Time: 3hours Max. Marks: 90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of

### Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?

Class IX - NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,

### Class IX Chapter 7 Triangles Maths

Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,

### 21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then

### 10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)

10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular

### 6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.

6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has

### CHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles

CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a

### CONGRUENCE OF TRIANGLES

Congruence of Triangles 11 CONGRUENCE OF TRIANGLES You might have observed that leaves of different trees have different shapes, but leaves of the same tree have almost the same shape. Although they may

### SUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX. Time allowed : 3 hours Maximum Marks :90

SUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX Time allowed : 3 hours Maximum Marks :90 General Instructions: i. All questions are compulsory. ii. The question paper consists of 34 questions divided

### Triangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance.

Triangles Chapter Flowchart The Chapter Flowcharts give you the gist of the chapter flow in a single glance. Triangle A plane figure bounded by three line segments is called a triangle. Types of Triangles

Geometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS

### 1 / 23

CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)

### Class 7 Lines and Angles

ID : in-7-lines-and-angles [1] Class 7 Lines and Angles For more such worksheets visit www.edugain.com Answer the questions (1) ABCD is a quadrilateral whose diagonals intersect each other at point O such

### Properties of the Circle

9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference

### Class : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system

Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following:. Insert rational numbers between. Epress 57 65 in the decimal form. 8 and.. Epress. as a fraction in the simplest

### TA0DV2S I, 2013 SUMMATIVE ASSESSMENT I, 2013 / MATHEMATICS IX / Class IX

TA0DVS I, 0 SUMMATIVE ASSESSMENT I, 0 / MATHEMATICS IX / Class IX 90 Time Allowed : hours Maximum Marks : 90 General Instructions: All questions are compulsory. 6 0 The question paper consists of questions

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F SESSING ENDING EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA

### Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between

### Class IX Chapter 8 Quadrilaterals Maths

1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles

### SHW 1-01 Total: 30 marks

SHW -0 Total: 30 marks 5. 5 PQR 80 (adj. s on st. line) PQR 55 x 55 40 x 85 6. In XYZ, a 90 40 80 a 50 In PXY, b 50 34 84 M+ 7. AB = AD and BC CD AC BD (prop. of isos. ) y 90 BD = ( + ) = AB BD DA x 60

### Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite

Fill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 FOR HALF YEARLY EXAM (017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX Chapter VSA (1 mark) SA I ( marks) SA II

### 8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral

### MATHEMATICS CLASS - IX MATHEMATICS CLASS - IX

I, 202 SUMMATIVE SUMMATIVE ASSESSMENT ASSESSMENT I, I, 20 20 SUMMATIVE MATHEMATICS SUMMATIVE ASSESSMENT CLASS - I, IX 202 I, 20 MATHEMATICS CLASS - IX / MATHEMATICS MATHEMATICS CLASS - IX IX / Class IX

### Similarity of Triangle

Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree

### EXERCISE 10.1 EXERCISE 10.2

NCERT Class 9 Solved Questions for Chapter: Circle 10 NCERT 10 Class CIRCLES 9 Solved Questions for Chapter: Circle EXERCISE 10.1 Q.1. Fill in the blanks : (i) The centre of a circle lies in of the circle.

### 1 / 23

CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper

### CLASS IX : CHAPTER - 1 NUMBER SYSTEM

MCQ WORKSHEET-I CLASS IX : CHAPTER - 1 NUMBER SYSTEM 1. Rational number 3 40 is equal to: (a) 0.75 (b) 0.1 (c) 0.01 (d) 0.075. A rational number between 3 and 4 is: (a) 3 (b) 4 3 (c) 7 (d) 7 4 3. A rational

### SUMMATIVE ASSESSMENT I, 2014

SUMMATIVE ASSESSMENT I (0) SUMMATIVE ASSESSMENT I, 04 MATHEMATICS Lakdfyr ijh{kk CLASS &I - IX MATHEMATICS / f.kr Class IX / & IX 4600 Time allowed: 3 hours Maimum Marks: 90 fu/kkzfjr le; % 3?k.Vs vf/kdre

### Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal (Not to be printed with the question paper) ) This question paper is strictly meant for use in school based SA-I, September-0 only. This question paper is

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 3 SAMPLE PAPER 01 FOR PERIODIC TEST II EXAM (018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR PERIODIC TEST II EXAM: CLASS IX Chapter VSA (1 mark) SA I (

### 3. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:

Solved Paper 2 Class 9 th, Mathematics, SA 2 Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3.

### CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)

### 0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle

### Revision Question Bank

Revision Question Bank Triangles 1. In the given figure, find the values of x and y. Since, AB = AC C = B [angles opposite to the equal sides are equal] x = 50 Also, the sum of all angles of a triangle

### Class IX - NCERT Maths Exercise (10.1)

Class IX - NCERT Maths Exercise (10.1) Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater

### Nozha Directorate of Education Form : 2 nd Prep

Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep Nozha Language Schools Geometry Revision Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. In the parallelogram, each

### [Class-X] MATHEMATICS SESSION:

[Class-X] MTHEMTICS SESSION:017-18 Time allowed: 3 hrs. Maximum Marks : 80 General Instructions : (i) ll questions are compulsory. (ii) This question paper consists of 30 questions divided into four sections,

### CBSE Sample Paper-03 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90

CBSE Sample Paper-3 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX Time allowed: 3 hours Maximum Marks: 9 General Instructions: a) All questions are compulsory. b) The question paper consists

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 F SESSING ENDING EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 FOR HALF YEARLY EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX Chapter VSA (1 mark) SA I (2 marks) SA

### Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40

Maharashtra Board Class X Mathematics - Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note: - () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas

### ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)

ANSWERS CLASS: VIII TERM - 1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) -21/24 (ii) -4/7 < -4/11 (iii)16/19 (iv)11/13 and -11/13 (v) 0 2. Answer True or False:

### CBSE Class IX Mathematics Term 1. Time: 3 hours Total Marks: 90. Section A

CBSE sample papers, Question papers, Notes for Class 6 to 1 CBSE Class IX Mathematics Term 1 Time: 3 hours Total Marks: 90 General Instructions: 1. All questions are compulsory.. The question paper consists

### Label carefully each of the following:

Label carefully each of the following: Circle Geometry labelling activity radius arc diameter centre chord sector major segment tangent circumference minor segment Board of Studies 1 These are the terms

### KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 02 FOR PERIODIC TEST II EXAM (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR PERIODIC TEST II EXAM: CLASS IX Chapter VSA (1 mark) SA I

### Mathematics. Mock Paper. With. Blue Print of Original Paper. on Latest Pattern. Solution Visits:

10 th CBSE{SA I} Mathematics Mock Paper With Blue Print of Original Paper on Latest Pattern Solution Visits: www.pioneermathematics.com/latest_updates www.pioneermathematics.com S.C.O. - 36, Sector 40

### Properties of Isosceles and Equilateral Triangles

Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg

### Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior)

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies

### CBSE MATHEMATICS (SET-2)_2019

CBSE 09 MATHEMATICS (SET-) (Solutions). OC AB (AB is tangent to the smaller circle) In OBC a b CB CB a b CB a b AB CB (Perpendicular from the centre bisects the chord) AB a b. In PQS PQ 4 (By Pythagoras

### STUDY MATERIAL SUBJECT: MATHEMATICS CLASS - IX

STUDY MATERIAL SUBJECT: MATHEMATICS CLASS - IX 2 INDEX PART - I SA - 1 1. Number System 2. Polynomials 3. Coordinate Geometry 4. Introduction to Euclid Geometry 5. Lines and Angles 6. Triangles 7. Heron's

### Maharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40

Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note:- () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.

### Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

### PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation

### Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.

### CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A.

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX Time allowed: hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper consists of

### Question Bank Tangent Properties of a Circle

Question Bank Tangent Properties of a Circle 1. In quadrilateral ABCD, D = 90, BC = 38 cm and DC = 5 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 7 cm. Find

### Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal (Not to be printed with the question paper) ) This question paper is strictly meant for use in school based SA-I, September-202 only. This question paper

### Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal (Not to be printed with the question paper) ) This question paper is strictly meant for use in school based SA-I, September-0 only. This question paper is

### QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

### (D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

### SUMMATIVE ASSESSMENT I (2011) Lakdfyr ijh{kk &I. MATHEMATICS / xf.kr Class IX / & IX

SUMMATIVE ASSESSMENT I (011) Lakdfyr ijh{kk &I MATHEMATICS / xf.kr Class IX / & IX 46003 Time allowed: 3 hours Maximum Marks: 90 fu/kkzfjr le; % 3?k.Vs vf/kdre vad % 90 General Instructions: (i) All questions

### RMT 2013 Geometry Test Solutions February 2, = 51.

RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,

### Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,

### 0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

### 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?

1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined

### RD Sharma Solutions for Class 10 th

RD Sharma Solutions for Class 10 th Contents (Click on the Chapter Name to download the solutions for the desired Chapter) Chapter 1 : Real Numbers Chapter 2 : Polynomials Chapter 3 : Pair of Linear Equations

### Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31

Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1

### 0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.

0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD

### UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'

### Math 9 Chapter 8 Practice Test

Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the

### Year 9 Term 3 Homework

Yimin Math Centre Year 9 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 5 Year 9 Term 3 Week 5 Homework 1 5.1 Geometry (Review)................................... 1 5.1.1 Angle sum

### A plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line)

Geometry - Semester 1 Final Review Quadrilaterals (Including some corrections of typos in the original packet) 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that

### Alg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3

Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch [1] Complete : 1) 3 216 =.. Alg. (( Sheet 1 )) 1 8 2) 3 ( ) 2 =..

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 03 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)

### Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.

Triangles Two geometric figures having the same shape and size are said to be congruent figures. Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.

### DESIGN OF THE QUESTION PAPER

SET-II DESIGN OF THE QUESTION PAPER MATHEMATICS CLASS IX Time : 3 Hours Maximum Marks : 80 The weightage or the distribution of marks over different dimensions of the question paper shall be as follows:

### THEOREMS WE KNOW PROJECT

1 This is a list of all of the theorems that you know and that will be helpful when working on proofs for the rest of the unit. In the Notes section I would like you to write anything that will help you

### CHAPTER 10 CIRCLES Introduction

168 MATHEMATICS CIRCLES CHAPTER 10 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of

### 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)

### LLT Education Services

8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the

### 0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.

Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would

### 0811ge. Geometry Regents Exam

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

### Chapter 8 Similar Triangles

Chapter 8 Similar Triangles Key Concepts:.A polygon in which all sides and angles are equal is called a regular polygon.. Properties of similar Triangles: a) Corresponding sides are in the same ratio b)

### Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =

Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain