MT - GEOMETRY - SEMI PRELIM - I : PAPER - 4
|
|
- Noel Atkins
- 5 years ago
- Views:
Transcription
1 07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 y intercept of the line (c) 0 By slope intercept form, The equation of the line is y m + c y (4) + (0) y 4 MT - GEOMETRY - SEMI PRELIM - I : Time : Hours Model Answer Paper Ma. Marks : 40 The equation of the given line is y 4 (ii) If the terminal arm lies on the positive Y-ais, then angle made is 90º or 70º. (iii) Equation of a line parallel to Y-ais and passing through point (, 0) is. (iv) tan 5 + tan sec + 5 sec + 5 sec sec 6 sec 4 [Taking square roots] (v) y 5 ( + ) Comparing with the equation of a line in slope point form, y y m ( ) m 5 Slope of the line y 5 ( + ) is 5 (vi) + 90º [Given] tan 4 [Given]
2 / MT cot tan [ cot tan (90 )] cot 4 A.. Solve ANY FOUR of the following : (i) (Analytical figure) P.4 cm R P.4 cm R mark for circle mark for tangent (ii) The terminal arm passes through P (5, ) 5 and y r y (5)( ) r units
3 / MT Let the angle be sin y r cos r 5 tan y 5 cosec sec cot r y r y 5 5 (iii) P (, 4), Q (, 6), R (8, ), S (0, k) Line PQ is parallel to line RS Slope of line PQ Slope of line RS 6 4 k 0 8 k 4 k k 4 + k 5 (iv) Value of k is 5. L (Analytical figure) L.6 cm M O N.6 cm A N M A mark for drawing circle mark for drawing tangent
4 4 / MT (v) sin + sin² [Given] sin sin² sin cos sin + cos sin cos sin cos 4 [Squaring both sides] cos cos 4 cos² + cos 4 sin + cos cos sin (vi) Let,A (0, 5) (, y ) B (5, 6) (, y ) The line passes through points A and B The equation of the line by two point form is y y y y y y 5 5 (y 5) 5y 5 5y + 5 y [Dividing throughout by 5] y + 5 is the equation of the line passing through (0, 5) 5 and (5, 6) A.. Solve ANY THREE of the following : (i) (Analytical figure) L K 60º 55º 7 cm M
5 5 / MT L O K 60º 55º 7 cm M mark for triangle mark for perpendicular bisectors mark for circumcircle (ii) sec cos sec cos sin + cos sin + sin + 4 sin 4
6 6 / MT sin 4 4 sin 4 sin cosec sin cosec is in IV quadrant cosec cos ec ( ) cos ec ( ) cos ec cos ec cos ec cos ec [Taking square roots] (iii) Let, A, 5 (, y ) B, k (, y ) C 4, 0 5 (, y ) Points A, B and C are collinear Slope of line AB Slope of line BC y y y y k 0 k 5 k k 0
7 7 / MT k 0 0 k k k k + k 4k k 4 The value of k is 4 (iv) a cos + b sin m (a cos + b sin ) m...(i) [Squaring both sides] (a sin b cos ) n (a sin b cos ) n...(ii) [Squaring both sides] Adding (i) and (ii), (a cos + b sin ) + (a sin b cos ) m + n a cos + ab cos. sin + b sin + a sin ab sin. cos + b cos m + n a cos + b cos + a sin + b sin m + n cos (a + b ) + sin (a + b ) m + n (a + b ) (cos + sin ) m + n a + b m + n [ sin + cos ] (v) Let, A (, ), B ( 9, 6), C (, 4), D (6, 9) Slope of a line Slope of side AB Slope of line AB Slope of line CD Slope of line CD y y 6 9 ( ) ( )
8 8 / MT Slope of line AB and slope of line CD are equal. line AB line CD The line joining (, ) and ( 9, 6) is parallel to the line joining (, 4) and (6, 9). A.4. Solve ANY TWO of the following : (i) L.H.S. cos ec cos ec cos ec cos ec cos ec cos ec cos ec cos ec cos ec cot cos ec cot cos ec cot cot cot cos ec cot cos ec sin cos sin tan tan cos sec tan (sec tan )(sec tan ) (sec tan ) sec tan sec tan tan sec sec tan sec tan R.H.S. cosec cosec + sec + tan
9 9 / MT (ii) (Analytical figure) S S 4.9 cm 95º R 5.9 cm N 4.9 cm I 95º R 5.9 cm N mark for triangle mark for angle bisectors mark for perpendicular mark for incircle (iii) L.H.S. tan cot cot tan sin cos cos sin cos sin sin cos sin cos cos sin sin cos cos sin sin cos sin cos cos(sin cos) sin(cos sin) sin cos cos(sin cos) sin(sin cos) sin cos sin cos cos sin
10 0 / MT sin cos sin cos cos sin sin cos sin sin cos cos sin cos cos sin sin sin. cos cos cos. sin sin. cos cos. sin [ sin + cos ] sin. cos cos. sin cos. sin cos sin sec. cosec + R.H.S. tan cot + cot tan sec, cos ec cos sin + sec. cosec. A.5. Solve ANY TWO of the following : (i) (Analytical figure) U R 5.8 cm 5. cm S 4.5 cm H V S S S S4 S 5
11 / MT U R 5.8 cm 5. cm S 4.5 cm H V S S S S 4 mark for drawing Analytical figure mark for SHR mark for constructing 5 congruent parts mark for constructing VS 5 S HS S mark for constructing UVS RHS S 5 (ii) A 0º 60º E Seg AB represents a tower. 60º 0º B C D Let A be a position of an observer. D and C are the initial and final position of the car. EAD and EAC are angles of depression
12 / MT m EAD m ADB 0º [Converse of alternate angles m EAC m ACB 60º test] The car took 6 sec. to travel from D to C Let the speed of car be units/seconds Distance speed time CD 6 CD 6 units...(i) In right angled ABC tan 60 AB BC [By definition] AB BC AB BC...(ii) In right angled ABD, tan 0 AB BD AB BD AB BD...(iii) BC BD [From (ii) and (iii)] BC BD BC BC + CD [ B - C - D] BC BC CD BC CD BC 6 [From (i)] BC 6 BC Time Dis tance Speed BC seconds The time taken by the car to reach the foot of the tower is seconds.
13 / MT (iii) seg AD is the median of seg BC D is midpoint of seg BC D + y + y, + +( 8), 8, 0, (, 5) By two point form, The equation of median AD y y y y 5 5 ( ) y 4 4 ( 5) y y ( 5) 6 (y 4) y 4 9 6y y 0 y 7 0 [Dividing throughout by ] The equation of median AD is y 7 0 Slope of line AC y y
14 4 / MT Slope of parallel lines are equal Slope of the line parallel to line AC is The line passes through B (, ) The equation of the line parallel to line AC passing through point B by the slope point form is y y m ( ) y ( ) [ ( )] y + ( + ) y y y The equation of the line parallel to AC passing through point B is y + 7 0
MT - GEOMETRY - SEMI PRELIM - I : PAPER - 1
07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 5 intercept of the line (c) B slope intercept form, The equation of the line is m + c 5 () + ( ) 5 MT - GEOMETRY - SEMI PRELIM
More informationMT - GEOMETRY - SEMI PRELIM - I : PAPER - 2
07 00 MT MT - GEOMETRY - SEMI PRELIM - I : PAPER - Time : Hours Model Answer Paper Ma. Marks : 40 A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 intercept of the line (c) 3 B slope
More informationTime : 2 Hours (Pages 3) Max. Marks : 40. Q.1. Solve the following : (Any 5) 5 In PQR, m Q = 90º, m P = 30º, m R = 60º. If PR = 8 cm, find QR.
Q.P. SET CODE Q.1. Solve the following : (ny 5) 5 (i) (ii) In PQR, m Q 90º, m P 0º, m R 60º. If PR 8 cm, find QR. O is the centre of the circle. If m C 80º, the find m (arc C) and m (arc C). Seat No. 01
More informationMT - w A.P. SET CODE MT - w - MATHEMATICS (71) GEOMETRY- SET - A (E) Time : 2 Hours Preliminary Model Answer Paper Max.
.P. SET CODE.. Solve NY FIVE of the following : (i) ( BE) ( BD) ( BE) ( BD) BE D 6 9 MT - w 07 00 - MT - w - MTHEMTICS (7) GEOMETRY- (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40 [Triangles
More informationMT - MATHEMATICS (71) GEOMETRY - PRELIM II - PAPER - 6 (E)
04 00 Seat No. MT - MTHEMTIS (7) GEOMETRY - PRELIM II - (E) Time : Hours (Pages 3) Max. Marks : 40 Note : ll questions are compulsory. Use of calculator is not allowed. Q.. Solve NY FIVE of the following
More informationBOARD QUESTION PAPER : MARCH 2016 GEOMETRY
BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential
More informationBOARD ANSWER PAPER :OCTOBER 2014
BRD NSWER PPER :CTBER 04 GEETRY. Solve any five sub-questions: BE i. BE ( BD) D BE 6 ( BD) 9 ΔBE (ΔBD) ----[Ratio of areas of two triangles having equal base is equal to the ratio of their corresponding
More informationTime : 2 Hours Preliminary Model Answer Paper Max. Marks : 40. [Given] [Taking square roots]
.P. SET CODE MT - w 05 00 - MT - w - MTHEMTICS (7) GEOMETRY - (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40.. ttempt NY FIVE of the following : (i) BC ~ PQ [Given] ( BC) ( PQ) BC PQ [reas
More informationMaharashtra 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
More informationSolved Paper SSC Maharashtra Exam March 207 Class - X Geometry Time : 2 Hours Max. Marks : 40 Note : (i) Solve all questions. Draw diagrams wherever necessary. (ii) Use of calculator is not allowed. (iii)
More informationMaharashtra State Board Class X Mathematics - Geometry Board Paper 2016 Solution
Maharashtra State Board Class X Mathematics - Geometry Board Paper 016 Solution 1. i. ΔDEF ΔMNK (given) A( DEF) DE A( MNK) MN A( DEF) 5 5 A( MNK) 6 6...(Areas of similar triangles) ii. ΔABC is 0-60 -90
More information2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW
FEB EXAM 06 SEC 4 ADDITIONAL MATHEMATICS CW & HW Find the values of k for which the line y 6 is a tangent to the curve k 7 y. Find also the coordinates of the point at which this tangent touches the curve.
More informationLesson-3 TRIGONOMETRIC RATIOS AND IDENTITIES
Lesson- TRIGONOMETRIC RATIOS AND IDENTITIES Angle in trigonometry In trigonometry, the measure of an angle is the amount of rotation from B the direction of one ray of the angle to the other ray. Angle
More information1 / 23
CBSE-XII-07 EXAMINATION CBSE-X-00 EXAMINATION MATHEMATICS Series: LRH/ Paper & Solution Code: 30// Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question
More informationMathematics Class X Board Paper 2011
Mathematics Class X Board Paper Solution Section - A (4 Marks) Soln.. (a). Here, p(x) = x + x kx + For (x-) to be the factor of p(x) = x + x kx + P () = Thus, () + () k() + = 8 + 8 - k + = k = Thus p(x)
More informationMaharashtra 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.
More informationMarking Scheme. Mathematics Class X ( ) Section A
Marking Scheme Mathematics Class X (017-18) Section A S.No. Answer Marks 1. Non terminating repeating decimal expansion.. k ±4 3. a 11 5 4. (0, 5) 5. 9 : 49 6. 5 Section B 7. LCM (p, q) a 3 b 3 HCF (p,
More informationClass X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. Section-A
Class X Mathematics Sample Question Paper 08-9 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections
More informationModel Answer Paper 24(24 1) 2 12
ICSE X SUBJECT : MATHEMATICS Marks : 80 Exam No. : MT/ICSE/Semi Prelim II- Set-B-00 Model Answer Paper Time : ½ hrs. SECTION I (40 Marks) A. (a) Maturity value ` 0,000 No. of months (n) 4 months Rate of
More informationSAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80
SAMPLE QUESTION PAPER Class-X (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided
More informationObjective Mathematics
. In BC, if angles, B, C are in geometric seq- uence with common ratio, then is : b c a (a) (c) 0 (d) 6. If the angles of a triangle are in the ratio 4 : :, then the ratio of the longest side to the perimeter
More informationMT - MATHEMATICS (71) GEOMETRY - PRELIM II - PAPER - 1 (E)
04 00 eat No. MT - MTHEMTI (7) GEOMETY - PELIM II - PPE - (E) Time : Hours (Pages 3) Max. Marks : 40 Note : (i) ll questions are compulsory. Use of calculator is not allowed. Q.. olve NY FIVE of the following
More informationSpecial Mathematics Notes
Special Mathematics Notes Tetbook: Classroom Mathematics Stds 9 & 10 CHAPTER 6 Trigonometr Trigonometr is a stud of measurements of sides of triangles as related to the angles, and the application of this
More informationSAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80
SAMPLE QUESTION PAPER Class-X (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided
More informationPreview from Notesale.co.uk Page 2 of 42
. CONCEPTS & FORMULAS. INTRODUCTION Radian The angle subtended at centre of a circle by an arc of length equal to the radius of the circle is radian r o = o radian r r o radian = o = 6 Positive & Negative
More informationMAHESH TUTORIALS. Time : 1 hr. 15 min. Q.1. Solve the following : 3
S.S.. MHESH TUTRILS Test - II atch : S Marks : 30 Date : GEMETRY hapter : 1,, 3 Time : 1 hr. 15 min..1. Solve the following : 3 The areas of two similar triangles are 18 cm and 3 cm respectively. What
More information( Bifurcated Syllabus ) ( According to Syllabus of Class X only) PART - I
Karunamoyee, Salt Lake, Kolkata : 70009 Mathematics (COMPULSORY) (Compulsory) Full marks : NEW 90 - For SYLLABUS Regular Candidates { Time 00 ---3 Hours - For 5 Eternal Minutes Candidates ( First 5 minutes
More information(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
More informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More informationCBSE 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
More informationCBSE QUESTION PAPER CLASS-X MATHS
CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1: In figure, AB = 5 3 cm, DC = 4cm, BD = 3cm, then tan θ is (a) (b) (c) (d) 1 3 2 3 4 3 5 3 Question 2: In figure, what values of x will make DE
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 QUESTION PAPER CODE 30/1/1 SECTION - A
MATHEMATICS Time allowed : 3 hours Maximum Marks : 100 GENERAL INSTRUCTIONS : 1. All questions are compulsory 2. The question paper consists of 30 questions divided into four sections - A, B, C and D.
More informationMathematics Class X Past Year Paper Time: 2½ hour Total Marks: 80
Pas Year Paper Mathematics Class X Past Year Paper - 013 Time: ½ hour Total Marks: 80 Solution SECTION A (40 marks) Sol. 1 (a) A + X B + C 6 3 4 0 X 0 4 0 0 6 6 4 4 0 X 0 8 0 0 6 4 X 0 8 4 6 X 8 0 4 10
More informationDESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80
DESIGN OF THE QUESTION PAPER Mathematics Class X Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage to Content/ Subject Units : S.No. Content
More informationClass 10 Application of Trigonometry [Height and Distance] Solved Problems
Class 10 Application of Trigonometry [Height and Distance] Solved Problems Question 01: The angle of elevation of an areoplane from a point on the ground is 45 o. After a flight of 15 seconds, the elevation
More informationPART B MATHEMATICS (2) (4) = +
JEE (MAIN)--CMP - PAR B MAHEMAICS. he circle passing through (, ) and touching the axis of x at (, ) also passes through the point () (, ) () (, ) () (, ) (4) (, ) Sol. () (x ) + y + λy = he circle passes
More informationTrigonometry and modelling 7E
Trigonometry and modelling 7E sinq +cosq º sinq cosa + cosq sina Comparing sin : cos Comparing cos : sin Divide the equations: sin tan cos Square and add the equations: cos sin (cos sin ) since cos sin
More information4-3 Trigonometric Functions on the Unit Circle
Find the exact value of each trigonometric function, if defined. If not defined, write undefined. 9. sin The terminal side of in standard position lies on the positive y-axis. Choose a point P(0, 1) on
More information1 / 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
More informationCore Mathematics 2 Trigonometry (GCSE Revision)
Core Mathematics 2 Trigonometry (GCSE Revision) Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Trigonometry 1 1 Trigonometry The sine and cosine rules, and the area of a triangle
More information( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x 2 = - 8y.
PROBLEMS 04 - PARABOLA Page 1 ( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x - 8. [ Ans: ( 0, - ), 8, ] ( ) If the line 3x 4 k 0 is
More informationEdexcel New GCE A Level Maths workbook Trigonometry 1
Edecel New GCE A Level Maths workbook Trigonometry 1 Edited by: K V Kumaran kumarmaths.weebly.com 1 Trigonometry The sine and cosine rules, and the area of a triangle in the form 21 ab sin C. kumarmaths.weebly.com
More informationQuestion 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
More informationKENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32. SECTION A Questions 1 to 6 carry 1 mark each.
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER TEST 09 (2018-19) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions
More informationare its positions as it is moving in anti-clockwise direction through angles 1, 2, 3 &
T: Introduction: The word trigonometry is derived from Greek words trigon meaning a triangle and metron meaning measurement. In this branch of mathematics, we study relationship of sides and angles of
More informationAptitude Height and Distance Practice QA - Difficult
Aptitude Height and Distance Practice QA - Difficult 1. A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the
More informationMATHEMATICS CLASS : XI. 1. Trigonometric ratio identities & Equations Exercise Fundamentals of Mathematics - II Exercise 28-38
CONTENT Preface MATHEMATICS CLASS : XI Page No.. Trigonometric ratio identities & Equations Eercise 0-7. Fundamentals of Mathematics - II Eercise 8-8. Straight Line Eercise 9-70 4. Circle Eercise 70-9
More informationJEE MAIN 2013 Mathematics
JEE MAIN 01 Mathematics 1. The circle passing through (1, ) and touching the axis of x at (, 0) also passes through the point (1) (, 5) () (5, ) () (, 5) (4) ( 5, ) The equation of the circle due to point
More information1/19 Warm Up Fast answers!
1/19 Warm Up Fast answers! The altitudes are concurrent at the? Orthocenter The medians are concurrent at the? Centroid The perpendicular bisectors are concurrent at the? Circumcenter The angle bisectors
More informationKENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 03 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit
More informationAlg. (( 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 =..
More informationPaper: 02 Class-X-Math: Summative Assessment - I
1 P a g e Paper: 02 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] The relation connecting the measures of central tendencies is [Marks:1]
More informationHigher Order Thinking Skill questions
Higher Order Thinking Skill questions TOPIC- Constructions (Class- X) 1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60. Then construct a triangle whose sides are times the corresponding
More informationCircles, Mixed Exercise 6
Circles, Mixed Exercise 6 a QR is the diameter of the circle so the centre, C, is the midpoint of QR ( 5) 0 Midpoint = +, + = (, 6) C(, 6) b Radius = of diameter = of QR = of ( x x ) + ( y y ) = of ( 5
More information[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,
More informationFIRST SEMESTER DIPLOMA EXAMINATION IN ENGINEERING/ TECHNOLIGY- OCTOBER, TECHNICAL MATHEMATICS- I (Common Except DCP and CABM)
TED (10)-1002 (REVISION-2010) Reg. No.. Signature. FIRST SEMESTER DIPLOMA EXAMINATION IN ENGINEERING/ TECHNOLIGY- OCTOBER, 2010 TECHNICAL MATHEMATICS- I (Common Except DCP and CABM) (Maximum marks: 100)
More information1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.
Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient
More informationCBSE QUESTION PAPER CLASS-X MATHS
CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1:If sin α = 1 2, then the value of 4 cos3 α 3 cos α is (a)0 (b)1 (c) 1 (d)2 Question 2: If cos 2θ = sin(θ 12 ), where2θ and (θ 12 ) are both acute
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 03 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit
More informationKENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 02 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit
More informationDESIGN OF THE QUESTION PAPER Mathematics Class X
SET-I DESIGN OF THE QUESTION PAPER Mathematics Class X Time : 3 Hours Maximum Marks : 80 Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage
More informationy mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent
Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()
More informationNATIONAL SENIOR CERTIFICATE MEMORANDUM MATHEMATICS MEMORANDUM P2 SEPTEMBER 2016 GRADE 12
NATIONAL SENIOR CERTIFICATE MEMORANDUM MATHEMATICS MEMORANDUM P SEPTEMBER 06 GRADE This memo consists of 5 pages Income Maths Memo / P September 06 QUESTION.. 700 answer ().. 700 answer ().. 45 minutes
More informationTrigonometric Functions 6C
Trigonometric Functions 6C a b c d e sin 3 q æ ö ø 4 tan 6 q 4 æ ö tanq ø cos q æ ö ø 3 cosec 3 q - sin q sin q cos q sin q (using sin q + cos q ) So - sin q sin q æ ö ø 6 4cot 6 q sec q cot q secq cos
More informationSOLUTIONS 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
More informationKARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE S. S. L. C. EXAMINATION, MARCH/APRIL, » D} V fl MODEL ANSWERS
CCE RF CCE RR O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALE 560 00 G È.G È.G È.. Æ fioê,» ^È% / HØ È 08 S. S. L. C. EXAMINATION,
More informationVKR Classes TIME BOUND TESTS 1-7 Target JEE ADVANCED For Class XI VKR Classes, C , Indra Vihar, Kota. Mob. No
VKR Classes TIME BOUND TESTS -7 Target JEE ADVANCED For Class XI VKR Classes, C-9-0, Indra Vihar, Kota. Mob. No. 9890605 Single Choice Question : PRACTICE TEST-. The smallest integer greater than log +
More informationEXTRA HOTS SUMS CHAPTER : 1 - SIMILARITY. = (5 marks) Proof : In ABQ, A ray BP bisects ABQ [Given] AP PQ = AB. By property of an angle...
MT EDURE LTD. EXTR HOTS SUMS HTER : 1 - SIMILRITY GEOMETRY 1. isectors of and in meet each other at. Line cuts the side at Q. Then prove that : + Q roof : In Q, ray bisects Q [Given] Q y property of an
More informationCollege Prep Geometry MID-TERM STUDY GUIDE. Mrs. Miller. Name: Due: Thursday, January 9, 2014
College Prep Geometry MID-TERM STUDY GUIDE Mrs. Miller Name: Due: Thursday, January 9, 04 To receive full credit you must have Tried EVERY PROBLEM Work shown for EVERY PROBLEM All work done in this packet
More informationTotal number of printed pages : MATHEMATICS
Total number of printed pages : 6 Total marks : 80 016 MATHEMATICS NB-T/M Time : 3 hours General Instructions: i) Approximately 15 minutes is allotted to read the question paper and revise the answers.
More informationCollege Prep Geometry MID-TERM STUDY GUIDE. Mrs. Miller. Name: Due: Thursday, January 9, 2014
College Prep Geometry MID-TERM STUDY GUIDE Mrs. Miller Name: Due: Thursday, January 9, 04 To receive full credit you must have Tried EVERY PROBLEM Work shown for EVERY PROBLEM All work done in this packet
More informationName: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination 3 Secondary 4
Name: Inde Number: Class: CATHOLIC HIGH SCHOOL Preliminary Eamination 3 Secondary 4 ADDITIONAL MATHEMATICS 4047/1 READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work
More informationNEW YORK CITY INTERSCHOLASTIC MATHEMATICS LEAGUE Senior A Division CONTEST NUMBER 1
Senior A Division CONTEST NUMBER 1 PART I FALL 2011 CONTEST 1 TIME: 10 MINUTES F11A1 Larry selects a 13-digit number while David selects a 10-digit number. Let be the number of digits in the product of
More informationPaper: 03 Class-X-Math: Summative Assessment - I
1 P a g e Paper: 03 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] Triangle ABC is similar to triangle DEF and their areas are 64 cm
More informationAMB121F Trigonometry Notes
AMB11F Trigonometry Notes Trigonometry is a study of measurements of sides of triangles linked to the angles, and the application of this theory. Let ABC be right-angled so that angles A and B are acute
More informationMATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )
Total No. of Printed Pages 6 X/5/M 0 5 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00
More informationGeometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES
Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Warm-Up 1.) What is the distance between the points (2, 3) and (5, 7). 2.) If < 1 and < 2 are complements, and m < 1 = 49, then what is
More informationUNIT 7: TRIGONOMETRY.
UNIT 7: TRIGONOMETRY. Trigonometry: Trigonometry (from Greek trigonom triangle and metron measure ) is a branch of mathematics that studies triangles and the relationships between their sides and their
More informationInternational Mathematical Olympiad. Preliminary Selection Contest 2017 Hong Kong. Outline of Solutions 5. 3*
International Mathematical Olympiad Preliminary Selection Contest Hong Kong Outline of Solutions Answers: 06 0000 * 6 97 7 6 8 7007 9 6 0 6 8 77 66 7 7 0 6 7 7 6 8 9 8 0 0 8 *See the remar after the solution
More information1. B (27 9 ) = [3 3 ] = (3 ) = 3 2. D. = c d dy d = cy + c dy cy = d + c. y( d c) 3. D 4. C
HKDSE03 Mathematics (Compulsory Part) Paper Full Solution. B (7 9 ) [3 3 ] (3 ) 3 n + 3 3 ( n + ) 3 n + 5 3 6 n + 5. D y y + c d dy d cy + c dy cy d + c y( d c) c + d c + d y d c 3. D hl kl + hm km hn
More informationCBSE X Mathematics 2012 Solution (SET 1) Section D
Section D Q 9. A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. Let the number of books
More informationVAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ
More informationSSC EXAMINATION GEOMETRY (SET-A)
GRND TEST SS EXMINTION GEOMETRY (SET-) SOLUTION Q. Solve any five sub-questions: [5M] ns. ns. 60 & D have equal height ( ) ( D) D D ( ) ( D) Slope of the line ns. 60 cos D [/M] [/M] tan tan 60 cos cos
More information10 th MATHS SPECIAL TEST I. Geometry, Graph and One Mark (Unit: 2,3,5,6,7) , then the 13th term of the A.P is A) = 3 2 C) 0 D) 1
Time: Hour ] 0 th MATHS SPECIAL TEST I Geometry, Graph and One Mark (Unit:,3,5,6,7) [ Marks: 50 I. Answer all the questions: ( 30 x = 30). If a, b, c, l, m are in A.P. then the value of a b + 6c l + m
More informationInternational General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS PAPER 2 MAY/JUNE SESSION 2002
International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS ADDITIONAL MATHEMATICS 0606/2 PAPER 2 MAY/JUNE SESSION 2002 2 hours Additional materials: Answer paper Electronic
More information(e) (i) Prove that C(x) = C( x) for all x. (2)
Revision - chapters and 3 part two. (a) Sketch the graph of f (x) = sin 3x + sin 6x, 0 x. Write down the exact period of the function f. (Total 3 marks). (a) Sketch the graph of the function C ( x) cos
More information10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152]
foot of the altitude of ABM from M and let A M 1 B. Prove that then MA > MB if and only if M 1 A > M 1 B. 8. If M is the midpoint of BC then AM is called a median of ABC. Consider ABC such that AB < AC.
More informationAdd Math (4047) Paper 2
1. Solve the simultaneous equations 5 and 1. [5]. (i) Sketch the graph of, showing the coordinates of the points where our graph meets the coordinate aes. [] Solve the equation 10, giving our answer correct
More informationTrigonometric Identities Exam Questions
Trigonometric Identities Exam Questions Name: ANSWERS January 01 January 017 Multiple Choice 1. Simplify the following expression: cos x 1 cot x a. sin x b. cos x c. cot x d. sec x. Identify a non-permissible
More informationy hsn.uk.net Straight Line Paper 1 Section A Each correct answer in this section is worth two marks.
Straight Line Paper 1 Section Each correct answer in this section is worth two marks. 1. The line with equation = a + 4 is perpendicular to the line with equation 3 + + 1 = 0. What is the value of a?.
More information1. SETS AND FUNCTIONS
. SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,
More informationICSE QUESTION PAPER Class X Maths (2016) Solution
ICSE QUESTION PAPER Class X Maths (016) Solution SECTION A 1. (a) Let f(x) x x kx 5 Using remainder theorem, f() 7 () () k() 5 7 (8) (4) k() 5 7 16 1 k 5 7 k 16 1 5 7 k 6 k 1 (b) A = 9A + MI A 9A mi...
More informationKENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 3 SAMPLE PAPER 06 (018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I ( marks) SA II (3 marks) LA (4 marks) Total Unit
More informationTriangle 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
More informationA2T Trig Packet Unit 1
A2T Trig Packet Unit 1 Name: Teacher: Pd: Table of Contents Day 1: Right Triangle Trigonometry SWBAT: Solve for missing sides and angles of right triangles Pages 1-7 HW: Pages 8 and 9 in Packet Day 2:
More informationSURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS
SURA's Guides for rd to 1th Std for all Subjects in TM & EM Available 10 th STD. MARCH - 017 Public Exam Question Paper with Answers MATHEMATICS [Time Allowed : ½ Hrs.] [Maximum Marks : 100] SECTION -
More informationright angle an angle whose measure is exactly 90ᴼ
right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two
More informationChapter 20 Exercise 20.1
Chapter Eercise. Q.. (i B = (, A = (, (ii C (, + = (, (iii AC ( + ( ( + ( 9 + CB ( + + ( ( + ( 9 + AC = CB (iv Slope of AB = = = = ( = ( = + + = (v AB cuts the -ais at =. + = = = AB cuts the -ais at (,.
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationCBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80
CBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided
More information