CBSE X Mathematics 2012 Solution (SET 1) Section C
|
|
- Sydney Page
- 5 years ago
- Views:
Transcription
1 CBSE X Mathematics 01 Solution (SET 1) Q19. Solve for x : 4x 4ax + (a b ) = 0 Section C The given quadratic equation is x ax a b 4x 4ax a b 0 4x 4ax a b a b x [ a a b b] x ( a b)( a b) 0 4x b a x a b x a b a b 0 4x b a x a b x a b a b 0 x[ x ( a b)] a b [ x ( a b)] 0 [ x ( a b)][ x ( a b)] 0 x ( a b) 0 or x ( a b) 0 x a b or x a b a b a b x or x Thus, the solution of the given quadratic equation is given by a b or a x x b. OR Solve for x x x :3 6 0 The given quadratic equation is3x 6 x 0. Comparing with the quadratic equation ax + bx + c = 0, we have a = 3, b 6 and c = Discriminant of the given quadratic equation, D = b 4ac
2 CBSE X Mathematics 01 Solution (SET 1) 6 0 b D x x 3 a x x Thus, the solution of the given quadratic equation is x = 6 3. Q0. Prove that the parallelogram circumscribing a circle is a rhombus. Since ABCD is a parallelogram, AB = CD (1) BC = AD () It can be observed that DR = DS (Tangents on the circle from point D) CR = CQ (Tangents on the circle from point C) BP = BQ (Tangents on the circle from point B) AP = AS (Tangents on the circle from point A) Adding all these equations, we obtain DR + CR + BP + AP = DS + CQ + BQ + AS (DR + CR) + (BP + AP) = (DS + AS) + (CQ + BQ) CD + AB = AD + BC On putting the values of equations (1) and () in this equation, we obtain AB = BC AB = BC (3) Comparing equations (1), (), and (3), we obtain AB = BC = CD = DA Hence, ABCD is a rhombus.
3 CBSE X Mathematics 01 Solution (SET 1) OR Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. Let ABCD be a quadrilateral circumscribing a circle centered at O such that it touches the circle at point P, Q, R, S. Let us join the vertices of the quadrilateral ABCD to the center of the circle. Consider OAP and OAS, AP = AS (Tangents from the same point) OP = OS (Radii of the same circle) OA = OA (Common side) OAP OAS (SSS congruence criterion) Therefore, A A, P S, O O And thus, POA = AOS 1 = 8 Similarly, = 3 4 = 5 6 = = 360º (1 + 8) + ( + 3) + (4 + 5) + (6 + 7) = 360º = 360º (1 + ) + (5 + 6) = 360º (1 + ) + (5 + 6) = 180º AOB + COD = 180º Similarly, we can prove that BOC + DOA = 180º Hence, opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
4 CBSE X Mathematics 01 Solution (SET 1) Q1. Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are 3 5 times the corresponding sides of the given triangle. Given: BC = 6 cm, C = 8 cm The triangle to be formed is to be right angled triangle. Steps of construction: 1. Draw a line segment BC = 6 cm.. Draw a ray CN making an angle of 90 at C. 3. With C as centre, taking 8 cm as the radius make an arc at CN intersecting it at A. Join AB. 4. Now, ABC is the triangle whose similar triangle is to be drawn. 5. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A. 6. Locate 5 (Greater of 3 and 5 in 3 5 ) points B 1, B, B 3, B 4 and B 5 on BX so that BB 1 = B 1 B = B B 3 = B 3 B 4 = B 4 B 5 7. Join B 5 C and draw a line through B 3 (Smaller of 3 and 5 in 3 5 ) parallel to B 5C to intersect BC at C. 8. Draw a line through Cparallel to the line CA to intersect BA at A.
5 CBSE X Mathematics 01 Solution (SET 1) 9. ABCis the required similar triangle whose sides are 3 times the corresponding sides of 5 ABC. Q. In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If POQ = 30, then find the area of the shaded region. Use 7 PQ and AB are the arcs of two concentric circles of radii 7 cm and 3.5 cm respectively. Let r 1 and r be the radii of the outer and the inner circle respectively. Suppose be the angle subtended by the arcs at the centre O. Then r 1 7 cm, r 3.5 cm and 30 Area of the shaded region = Area of sector OPQ Area of sector OAB r1 r r1 r cm 3.5 cm cm cm cm Thus, the area of the shaded region is 9.65 cm.
6 CBSE X Mathematics 01 Solution (SET 1) Q3. From a solid cylinder of height 7 cm and base diameter 1 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. Use 7 It is given that, height (h) of cylindrical part = height (h) of the conical part = 7 cm Diameter of the cylindrical part = 1 cm 1 Radius (r) of the cylindrical part cm = 6cm Radius of conical part = 6 cm Slant height (l) of conical part r h cm = 6 7 cm = cm = 85 cm = 9. cm (approx.) Total surface area of the remaining solid = CSA of cylindrical part + CSA of conical part + Base area of the circular part = rh + rl + r 6 7 cm 6 9. cm 6 6 cm cm cm cm 551cm OR A cylindrical bucket, 3 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 4 cm, then find the radius and slant height of the heap.
7 CBSE X Mathematics 01 Solution (SET 1) Height (h 1 ) of cylindrical bucket = 3 cm Radius (r 1 ) of circular end of bucket = 18 cm Height (h ) of conical heap = 4 cm Let the radius of the circular end of conical heap be r. The volume of sand in the cylindrical bucket will be equal to the volume of sand in the conical heap. Volume of sand in the cylindrical bucket = Volume of sand in conical heap 1 πr1 h1 π r h 3 1 π18 3 πr π18 3 π r r r = 18 = 36 cm Slant height = (3 ) 1 13 cm Therefore, the radius and slant height of the conical heap are 36 cm and 1 13 cm respectively. Q4. The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45 and 30. If the ships are 00 m apart, find the height of the light house. The given situation can be represented diagrammatically as,
8 CBSE X Mathematics 01 Solution (SET 1) Here, AB is the light house and the ships are at the points C and D; h is the height of the light house and BC = x. In right angled ABC: AB tan 45 AC h tan 45 x h 1 x x h In right angled ABD, AB tan 30 BD h tan 30 x 00 h tan 30 x h h 00 1 h 3 h 00
9 CBSE X Mathematics 01 Solution (SET 1) h 00 h 3 h 3 h 00 h h 00 m h h 31 h Hence, the height of the light house is m. Q5. A point P divides the line segment joining the points A (3, 5) and B ( 4, 8) such that AP K. If P lies on the line x + y = 0, then find the value of K. PB 1 The given points are A (3, 5) and B ( 4, 8). Here, x 3, y 5, x 4 and y Since AP K, the point P divides the line segment joining the points A and B in the ratio K:1. PB 1 mx nx1 my ny1 The co-ordinates of P can be found using the section formula, m n m n. Here, m = K and n = 1 K K K+3 8K 5 Co-ordinates of P,, K + 1 K + 1 K+1 K+1 It is given that, P lies on the line x + y = 0.
10 CBSE X Mathematics 01 Solution (SET 1) 4K+3 8K 5 0 K+1 K+1 4K 3 8K 5 0 K +1 4K 0 4K 1 K Thus, the required value of K is 1. Q6. If the vertices of a triangle are (1, 3), (4, p) and ( 9, 7) and its area is 15 sq. units, find the value(s) of p. Given, vertices of a triangle are (1, 3), (4, p) and ( 9, 7). x 1, y x 4, y p x 9, y Area of given triangle 1 x y y x y y x y y p p 1 p p 1 10 p 60 5 p 6 = Here, the obtained expression may be positive or negative. 5 p 6 15 or 5 p 6 15 p 6 3 or p 6 3 p 3 or p 9
11 CBSE X Mathematics 01 Solution (SET 1) Q7. A box contains 100 red cards, 00 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card. Number of red cards = 100 Number of yellow cards = 00 Number of blue cards = 50 Total number of cards = = 350 Number of blue cards i P a blue card Total number of cards Number of cards other than yellow ii P not a yellow card Total number of cards Number of red cards + Number of blue cards Total number of cards Number of cards which are neither yellow nor blue iii P Neither yellow nor a blue card Total number of cards Number of red cards Total number of cards Q8. The 17 th term of an AP is 5 more than twice its 8 th term. If the 11 th term of the AP is 43, then find its n th term.
12 CBSE X Mathematics 01 Solution (SET 1) Let a be the first term and d be the common difference of the given A.P. According to the given question, 17 th term = 8 th term + 5 i.e., a a a 17 1 d a 8 1 d 5 (as an a n 1 d) a 16d a 7d 5 a 16d a 14d 5 a d Also, 11 th term, a 11 = 43 a 111 d 43 a10d 43 d 5 10d 43 Using 1 1d 48 d 4 a d 5 (4) Thus, n th term of the AP, 1 a a n d On putting the respective values of a and d, we get a 3 n n 4 4n 1 n Hence, n th term of the given AP is 4n 1. n
Time: 3 hour Total Marks: 90
Time: 3 hour Total Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into four sections A, B, C, and D. 3. Section A contains of 8
More informationCBSE SAMPLE PAPERS SUMMATIVE ASSESSMENT-II (MATHS) CLASS 10
CBSE SAMPLE PAPERS SUMMATIVE ASSESSMENT-II (MATHS) CLASS 10 Time: 3 Hrs Max Marks: 90 General Instructions: A) All questions are compulsory. B) The question paper consists of 34 questions divided into
More informationnot to be republished NCERT CONSTRUCTIONS CHAPTER 10 (A) Main Concepts and Results (B) Multiple Choice Questions
CONSTRUCTIONS CHAPTER 10 (A) Main Concepts and Results Division of a line segment internally in a given ratio. Construction of a triangle similar to a given triangle as per given scale factor which may
More informationCBSE CLASS X MATHS , 1 2p
CBSE CLASS X MATHS -2013 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A,B,C and D. (iii) Sections A contains 8 questions
More informationGrade IX. Mathematics Geometry Notes. #GrowWithGreen
Grade IX Mathematics Geometry Notes #GrowWithGreen The distance of a point from the y - axis is called its x -coordinate, or abscissa, and the distance of the point from the x -axis is called its y-coordinate,
More information9.2 SECANT AND TANGENT
TOPICS PAGES. Circles -5. Constructions 6-. Trigonometry -0 4. Heights and Distances -6 5. Mensuration 6-9 6. Statistics 40-54 7. Probability 55-58 CIRCLES 9. CIRCLE A circle is the locus of a points which
More informationCIRCLE. Circle is a collection of all points in a plane which are equidistant from a fixed point.
CIRCLE Circle is a collection of all points in a plane which are equidistant from a fixed point. The fixed point is called as the centre and the constant distance is called as the radius. Parts of a Circle
More informationQ-1 The first three terms of an AP respectively are 3y 1, 3y +5 and 5y +1. Then y equals
CBSE CLASS X Math Paper-2014 Q-1 The first three terms of an AP respectively are 3y 1, 3y +5 and 5y +1. Then y equals (A) -3 (B) 4 (C) 5 (D) 2 Q-2 In Fig. 1, QR is a common tangent to the given circles,
More informationMathematics Class 10 Board Sample paper-1
1 Mathematics Class 10 Board Sample paper-1 Time allowed: 3 hours Maximum Marks: 80 General Instructions: a) All questions are compulsory. b) The question paper consists of 30 questions divided into four
More informationCONSTRUCTIONS Introduction Division of a Line Segment
216 MATHEMATICS CONSTRUCTIONS 11 111 Introduction In Class IX, you have done certain constructions using a straight edge (ruler) and a compass, eg, bisecting an angle, drawing the perpendicular bisector
More informationCBSE Board Paper 2011 (Set-3) Class X
L.K.Gupta (Mathematic Classes) Ph: 981551, 1-4611 CBSE Board Paper 11 (Set-3) Class X General Instructions 1. All questions are compulsory.. The question paper consists of 34 questions divided into four
More informationSolved Paper 1 Class 9 th, Mathematics, SA 2
Solved Paper 1 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.
More informationGeometry. Geometry is one of the most important topics of Quantitative Aptitude section.
Geometry Geometry is one of the most important topics of Quantitative Aptitude section. Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles are always equal. If any
More informationKENDRIYA VIDYALAYA GACHIBOWLI, HYDERABAD 32
KENDRIYA VIDYALAYA GACHIBOWLI, HYDERABAD 32 SAMPLE PAPER 04 FOR SA II (2015-16) SUBJECT: MATHEMATICS BLUE PRINT : SA-II CLASS X Unit/Topic Algebra Quadratic Equations & Arithmetic Progression Geometry
More informationFdaytalk.com. Acute angle The angle which is less than Right angle The angle which is equal to 90 0
Acute angle The angle which is less than 90 0 Right angle The angle which is equal to 90 0 Obtuse angle The angle which is greater than 90 0 Straight angle The angle which is 180 0 Reflexive angle The
More informationMathematics Class 10 Board Sample paper-2
1 Mathematics Class 10 Board Sample paper-2 Time allowed: 3 hours Maximum Marks: 80 General Instructions: a) All questions are compulsory. b) The question paper consists of 30 questions divided into four
More informationSAMPLE PAPER 2 (SA II) Mathematics CLASS : X. Time: 3hrs Max. Marks: 90
SAMPLE PAPER 2 (SA II) Mathematics MR SANDESH KUMAR BHAT KV 1 JAMMU CLASS : X Time: 3hrs Max. Marks: 90 General Instruction:- 1. All questions are Compulsory. 1. The question paper consists of 34 questions
More informationShortcuts, Formulas & Tips
& present Shortcuts, Formulas & Tips For MBA, Banking, Civil Services & Other Entrance Examinations Vol. 3: Geometry Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles
More informationMathematics. Time Allowed: 3 hours Maximum : The question paper consists of 31 questions divided into four sections A, B, C and D.
Sample Paper (CBSE) Series SC/SP Code No. SP-16 Mathematics Time Allowed: 3 hours Maximum : 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided
More informationcbsemath.com: Bathinda based website since Feb 2006.
Attempt option 1 for challenging questions and 2 for easy-moderate questions Section A 1 Mark Each 1. If a + b + c = 0, a 0 and a, b, c are real numbers then roots of equation ax 2 +bx + c = 0 are (A)
More informationChapter 7 Coordinate Geometry
Chapter 7 Coordinate Geometry 1 Mark Questions 1. Where do these following points lie (0, 3), (0, 8), (0, 6), (0, 4) A. Given points (0, 3), (0, 8), (0, 6), (0, 4) The x coordinates of each point is zero.
More informationPerimeter. Area. Surface Area. Volume. Circle (circumference) C = 2πr. Square. Rectangle. Triangle. Rectangle/Parallelogram A = bh
Perimeter Circle (circumference) C = 2πr Square P = 4s Rectangle P = 2b + 2h Area Circle A = πr Triangle A = bh Rectangle/Parallelogram A = bh Rhombus/Kite A = d d Trapezoid A = b + b h A area a apothem
More information4. The following diagram shows the triangle AOP, where OP = 2 cm, AP = 4 cm and AO = 3 cm.
Circular Functions and Trig - Practice Problems (to 07) 1. In the triangle PQR, PR = 5 cm, QR = 4 cm and PQ = 6 cm. Calculate (a) the size of ; (b) the area of triangle PQR. 2. The following diagram shows
More informationMaharashtra Board Class IX Mathematics (Geometry) Sample Paper 1 Solution
Maharashtra Board Class IX Mathematics (Geometry) Sample Paper 1 Solution Time: hours Total Marks: 40 Note: (1) All questions are compulsory. () Use of a calculator is not allowed. 1. i. In the two triangles
More information1. Each interior angle of a polygon is 135. How many sides does it have? askiitians
Class: VIII Subject: Mathematics Topic: Practical Geometry No. of Questions: 19 1. Each interior angle of a polygon is 135. How many sides does it have? (A) 10 (B) 8 (C) 6 (D) 5 (B) Interior angle =. 135
More informationMathematics
Mathematics Total Score 80 Time 2 ½ hours Instructions Read the instructions against each question before answering them Logical explanations should be given wherever necessary If two questions have OR
More informationDrill Exercise - 1. Drill Exercise - 2. Drill Exercise - 3
Drill Exercise -. Find the distance between the pair of points, (a sin, b cos ) and ( a cos, b sin ).. Prove that the points (a, 4a) (a, 6a) and (a + 3 a, 5a) are the vertices of an equilateral triangle.
More informationKENDRIYA VIDYALAYA, AFS,Bagdogra ( )
KENDRIYA VIDYALAYA, AFS,Bagdogra (2017-18) SUBJECT: MATHEMATICS(041) Class - X 1. Show that 12 n cannot end with the digit 0 or 5 for any natural number n. 2. Find the value of k for which the quadratic
More informationBOARD PAPER - MARCH 2014
BOARD PAPER - MARCH 2014 Time : 2 Hours Marks : 40 Notes : (i) Solve all questions. Draw diagrams wherever necessary. Use of calculator is not allowed. Figures to the right indicate full marks. Marks of
More informationDELHI PUBLIC SCHOOL BOKARO STEEL CITY
DELHI PUBLIC SCHOOL BOKARO STEEL CITY ASSIGNMENT FOR THE SESSION 2015-2016 Class: X Subject : Mathematics Assignment No. 3 QUADRATIC EQUATIONS 1. Solve by completing the square 2x 2 + x 4 = 0. 2. Solve
More informationFURTHER MATHS. WELCOME TO A Level FURTHER MATHEMATICS AT CARDINAL NEWMAN CATHOLIC SCHOOL
FURTHER MATHS WELCOME TO A Level FURTHER MATHEMATICS AT CARDINAL NEWMAN CATHOLIC SCHOOL This two-year Edexcel Pearson syllabus is intended for high ability candidates who have achieved, or are likely to
More informationGeometry Final Exam - Study Guide
Geometry Final Exam - Study Guide 1. Solve for x. True or False? (questions 2-5) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines are
More informationCBSE Sample Papers for Class 10 SA2 Maths Solved 2016 (Set 3)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 (Set 3) Code-LNCBSE Roll No. Please check that this question paper contains 5 printed pages. Code number given on the right hand side of the question
More informationK.S.E.E.B., Malleshwaram, Bangalore SSLC Model Question Paper-2 (2015) MATHEMATICS
Max Marks: 80 No. of Questions: 40 K.S.E.E.B., Malleshwaram, Bangalore SSLC Model Question Paper- (015) MATHEMATICS 81E Time: Hours 45 minutes Code No. : 81E Four alternatives are given for the each question.
More informationPage 1 of 32. Website: Mobile:
Exercise 7.1 Question 1: Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) ( 5, 7), ( 1, 3) (iii) (a, b), ( a, b) (i) Distance between the two points is given by (ii) Distance
More informationCOORDINATE GEOMETRY. 7.1 Introduction
COORDINATE GEOMETRY 55 COORDINATE GEOMETRY 7 7. Introduction In Class IX, you have studied that to locate the position of a point on a plane, we require a pair of coordinate axes. The distance of a point
More informationArea of Circle, Sector and Segment
1 P a g e m a t h s c l a s s x 1. Find the circumference and area of a circle of radius 10.5 cm. 2. Find the area of a circle whose circumference is 52.8 cm. 3. Afield is in the form of a circle. The
More informationSOME IMPORTANT PROPERTIES/CONCEPTS OF GEOMETRY (Compiled by Ronnie Bansal)
1 SOME IMPORTANT PROPERTIES/CONCEPTS OF GEOMETRY (Compiled by Ronnie Bansal) 1. Basic Terms and Definitions: a) Line-segment: A part of a line with two end points is called a line-segment. b) Ray: A part
More informationSection A. 3. The number of solid spheres, each of diameter that could be moulded to form a solid metal cylinder of height and diameter is:
Class X Mathematics Section A 1. If the equation has real and distinct roots, then: 2. The from the end of the A.P. is: 3. The number of solid spheres, each of diameter that could be moulded to form a
More informationCBSE Sample Papers for Class 10 SA2 Maths Solved 2016 (Set 2)
CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 (Set 2) Code-LNCBSE Roll No. Please check that this question paper contains 5 printed pages. Code number given on the right hand side of the question
More informationMoore Catholic High School Math Department
Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during
More informationDepartment of Mathematics
Department of Mathematics TIME: 3 Hours Setter: DAS DATE: 07 August 2017 GRADE 12 PRELIM EXAMINATION MATHEMATICS: PAPER II Total marks: 150 Moderator: GP Name of student: PLEASE READ THE FOLLOWING INSTRUCTIONS
More informationSarvaakarshak classes
Sarvaakarshak classes Revision_Test_2 The best way to learn SECTION-A Question numbers 1 to 8 carry 2 marks each. 1. If the equation kx 2-2kx + 6 = 0 has equal roots, then find the value of k. 2. Which
More informationDownloaded from
Lines and Angles 1.If two supplementary angles are in the ratio 2:7, then the angles are (A) 40, 140 (B) 85, 95 (C) 40, 50 (D) 60, 120. 2.Supplementary angle of 103.5 is (A) 70.5 (B) 76.5 (C) 70 (D)
More information1 www.gradestack.com/ssc Dear readers, ADVANCE MATHS - GEOMETRY DIGEST Geometry is a very important topic in numerical ability section of SSC Exams. You can expect 14-15 questions from Geometry in SSC
More informationS.S.L.C MATHS IMPORTANT FIVE MARKS COMPULSORY QUESTIONS
S.S.L.C MATHS IMPORTANT FIVE MARKS COMPULSORY QUESTIONS 1. The 10 th and 18 th terms of an A.P. are 41 and 73 respectively. Find the 27 th term. 2. The sum of three consecutive terms in an A.P. is 6 and
More informationAngles. An angle is: the union of two rays having a common vertex.
Angles An angle is: the union of two rays having a common vertex. Angles can be measured in both degrees and radians. A circle of 360 in radian measure is equal to 2π radians. If you draw a circle with
More informationVAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY PROF. RAHUL MISHRA VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CONSTRUCTIONS Class :- X Subject :- Maths Total Time :- SET A Total Marks :- 240 QNo. General Instructions Questions 1 Divide
More informationGrade VIII. Mathematics Geometry Notes. #GrowWithGreen
Grade VIII Mathematics Geometry Notes #GrowWithGreen Polygons can be classified according to their number of sides (or vertices). The sum of all the interior angles of an n -sided polygon is given by,
More informationSUMMATIVE ASSESSMENT II, II, MATHEMATICS / Class X /
Page 1 of 10 SUMMATIVE ASSESSMENT II, II, MATHEMATICS / Class X / X Time allowed : 3 hours Maximum Marks : 80 3 80 General Instructions : (i) All questions are compulsory. (ii) The question paper consists
More informationMathematics For Class IX Lines and Angles
Mathematics For Class IX Lines and Angles (Q.1) In Fig, lines PQ and RS intersect each other at point O. If, find angle POR and angle ROQ (1 Marks) (Q.2) An exterior angle of a triangle is 110 and one
More informationINTERNATIONAL INDIAN SCHOOL, RIYADH SUBJECT: MATHEMATICS PT III
\ CLASS: X INTERNATIONAL INDIAN SCHOOL, RIYADH SUBJECT: MATHEMATICS PT III ❶ SOME APPLICATIONS OF TRIGONOMETRY 1. A 1.6 m tall girl stands at a distance of 3.2m from a lamp post and casts a shadow of 4.8
More informationLINES AND ANGLES CHAPTER 6. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 6 LINES AND ANGLES (A) Main Concepts and Results Complementary angles, Supplementary angles, Adjacent angles, Linear pair, Vertically opposite angles. If a ray stands on a line, then the adjacent
More informationSECTION A / 1. Any point where graph of linear equation in two variables cuts x-axis is of the form. (a) (x, y) (b) (0, y) (c) (x, 0) (d) (y, x)
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. 1 8 1 1. Any
More informationADVANCED EXERCISE 09B: EQUATION OF STRAIGHT LINE
ADVANCED EXERCISE 09B: EQUATION OF STRAIGHT LINE It is given that the straight line L passes through A(5, 5) and is perpendicular to the straight line L : x+ y 5= 0 (a) Find the equation of L (b) Find
More informationDrill Exercise - 1. Drill Exercise - 2. Drill Exercise - 3
Drill Exercise - 1 1. Find the distance between the pair of points, (a sin, b cos ) and ( a cos, b sin ). 2. Prove that the points (2a, 4a) (2a, 6a) and (2a + 3 a, 5a) are the vertices of an equilateral
More informationIf three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: a b 1.
ASSIGNMENT ON STRAIGHT LINES LEVEL 1 (CBSE/NCERT/STATE BOARDS) 1 Find the angle between the lines joining the points (0, 0), (2, 3) and the points (2, 2), (3, 5). 2 What is the value of y so that the line
More informationMoore Catholic High School Math Department
Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during
More informationTrig Practice 09 & Nov The diagram below shows a curve with equation y = 1 + k sin x, defined for 0 x 3π.
IB Math High Level Year : Trig: Practice 09 & 0N Trig Practice 09 & Nov 0. The diagram below shows a curve with equation y = + k sin x, defined for 0 x. The point A, lies on the curve and B(a, b) is the
More informationCBSE - Class X Math. General Instructions:
CBSE - Class X Math General Instructions: (I) (II) (III) (IV) All questions are compulsory. The question paper consists of 31 questions divided into four sections A,B, C and D Section A contains 4 questions
More informationEducation Resources. This section is designed to provide examples which develop routine skills necessary for completion of this section.
Education Resources Straight Line Higher Mathematics Supplementary Resources Section A This section is designed to provide examples which develop routine skills necessary for completion of this section.
More informationCARIBBEAN CORRESPONDENCE SCHOOL
Final Examination CARIBBEAN CORRESPONDENCE SCHOOL Module Name: Groups: Duration: MATHEMATICS Online 3 Hours INSTRUCTIONS TO CANDIDATES 1. This Paper consists of THREE sections. 2. There is one question
More informationCoordinate Geometry. Topic 1. DISTANCE BETWEEN TWO POINTS. Point 2. The distance of the point P(.x, y)from the origin O(0,0) is given by
Topic 1. DISTANCE BETWEEN TWO POINTS Point 1.The distance between two points A(x,, y,) and B(x 2, y 2) is given by the formula Point 2. The distance of the point P(.x, y)from the origin O(0,0) is given
More informationA. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: REVIEW FOR FINAL EXAM - GEOMETRY 2 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C.
More informationProperties of a Circle Diagram Source:
Properties of a Circle Diagram Source: http://www.ricksmath.com/circles.html Definitions: Circumference (c): The perimeter of a circle is called its circumference Diameter (d): Any straight line drawn
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationm 6 + m 3 = 180⁰ m 1 m 4 m 2 m 5 = 180⁰ m 6 m 2 1. In the figure below, p q. Which of the statements is NOT true?
1. In the figure below, p q. Which of the statements is NOT true? m 1 m 4 m 6 m 2 m 6 + m 3 = 180⁰ m 2 m 5 = 180⁰ 2. Look at parallelogram ABCD below. How could you prove that ABCD is a rhombus? Show that
More informationME 111: Engineering Drawing. Geometric Constructions
ME 111: Engineering Drawing Lecture 2 01-08-2011 Geometric Constructions Indian Institute of Technology Guwahati Guwahati 781039 Geometric Construction Construction of primitive geometric forms (points,
More informationAPEX PON VIDYASHRAM, VELACHERY ( ) HALF-YEARLY WORKSHEET 1 LINES AND ANGLES SECTION A
APEX PON VIDYASHRAM, VELACHERY (2017 18) HALF-YEARLY WORKSHEET 1 CLASS: VII LINES AND ANGLES SECTION A MATHEMATICS 1. The supplement of 0 is. 2. The common end point where two rays meet to form an angle
More informationEXERCISE NO:13.1. If cubes are joined end to end, the dimensions of the resulting cuboid will be 4 cm, 4cm, 8 cm. 2 lb bh lh.
Class X - NCERT Maths EXERCISE NO:1.1 Question 1: cubes each of volume 64 cm are joined end to end. Find the surface area of the resulting cuboids. Solution 1: Given that, Volume of cubes = 64 cm (Edge)
More informationGeometry CST Questions (2008)
1 Which of the following best describes deductive reasoning? A using logic to draw conclusions based on accepted statements B accepting the meaning of a term without definition C defining mathematical
More informationEQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS
EQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS Steps to Find the Median of a Triangle: -Find the midpoint of a segment using the midpoint formula. -Use the vertex and midpoint to find the
More informationNAEP Released Items Aligned to the Iowa Core: Geometry
NAEP Released Items Aligned to the Iowa Core: Geometry Congruence G-CO Experiment with transformations in the plane 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and
More informationGeneral Certificate of Secondary Education Higher Tier November Time allowed 1 hour 30 minutes
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark Mathematics General Certificate of Secondary Education Higher Tier November 2014
More informationMathematical analysis of uniform decahedron having 10 congruent faces each as a right kite by H.C. Rajpoot
From the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot Winter March 1, 2015 Mathematical analysis of uniform decahedron having 10 congruent faces each as a right kite by H.C. Rajpoot Harish Chandra
More informationPROPERTIES OF TRIANGLES AND QUADRILATERALS
Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 22 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS
More informationNCERT solution for Basic Geometrical Ideas
1 NCERT solution for Basic Geometrical Ideas Exercise 4.1 Question 1 Use the figure to name: (a) Five points (b) A line (c) Four rays (d) Five-line segments Point Line segment Line Ray A point determines
More informationUnit 6: Connecting Algebra and Geometry Through Coordinates
Unit 6: Connecting Algebra and Geometry Through Coordinates The focus of this unit is to have students analyze and prove geometric properties by applying algebraic concepts and skills on a coordinate plane.
More informationLEARNING MATERIAL CLASS - X
MINIMUM TARGET 40 LEARNING MATERIAL CLASS - X Kindly select 10 units as per choice of the student Topics Marks 1. Irrationality of numbers (5 questions) 3. Polynomials(long division) (5 questions) 4 3.
More informationKENDRIYA VIDYALAYA SANGATHAN, ERNAKULAM REGION. SECTION A (8 x 1 = 8)
This question paper contains 06 pages KENDRIYA VIDYALAYA SANGATHAN, ERNAKULAM REGION Class: X SUMMATIVE ASSESSMENT - II Max. Marks : 90 Sub: Mathematics 2013-14 Time: 3 hrs General Instructions i) All
More informationSection Congruence Through Constructions
Section 10.1 - Congruence Through Constructions Definitions: Similar ( ) objects have the same shape but not necessarily the same size. Congruent ( =) objects have the same size as well as the same shape.
More informationHigh School Mathematics Geometry Vocabulary Word Wall Cards
High School Mathematics Geometry Vocabulary Word Wall Cards Table of Contents Reasoning, Lines, and Transformations Basics of Geometry 1 Basics of Geometry 2 Geometry Notation Logic Notation Set Notation
More informationModeling with Geometry
Modeling with Geometry 6.3 Parallelograms https://mathbitsnotebook.com/geometry/quadrilaterals/qdparallelograms.html Properties of Parallelograms Sides A parallelogram is a quadrilateral with both pairs
More informationGeometry Mathematics Content Standards
85 The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical
More informationSTRAND E: Measurement. UNIT 13 Areas Student Text Contents. Section Squares, Rectangles and Triangles Area and Circumference of Circles
UNIT 13 Areas Student Text Contents STRAND E: Measurement Unit 13 Areas Student Text Contents Section 13.1 Squares, Rectangles and Triangles 13. Area and Circumference of Circles 13.3 Sector Areas and
More information1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd
Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second
More informationName Honors Geometry Final Exam Review
2014-2015 Name Honors Geometry Final Eam Review Chapter 5 Use the picture at the right to answer the following questions. 1. AC= 2. m BFD = 3. m CAE = A 29 C B 71⁰ 19 D 16 F 65⁰ E 4. Find the equation
More information2 nd Semester Final Exam Review
2 nd Semester Final xam Review I. Vocabulary hapter 7 cross products proportion scale factor dilation ratio similar extremes scale similar polygons indirect measurements scale drawing similarity ratio
More informationGEOMETRY BASIC GEOMETRICAL IDEAS. 3) A point has no dimensions (length, breadth or thickness).
CLASS 6 - GEOMETRY BASIC GEOMETRICAL IDEAS Geo means Earth and metron means Measurement. POINT 1) The most basic shape in geometry is the Point. 2) A point determines a location. 3) A point has no dimensions
More informationMathematical derivations of some important formula in 2D-Geometry by HCR
From the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot Summer March 31, 2018 Mathematical derivations of some important formula in 2D-Geometry by HCR Harish Chandra Rajpoot, HCR Available at: https://works.bepress.com/harishchandrarajpoot_hcrajpoot/61/
More informationSecond Semester Exam Review Packet
Geometry Name Second Semester Exam Review Packet CHAPTER 7 THE PYTHAGOREAN THEOREM. This theorem is used to find the lengths of the sides of a right triangle. Label the parts of the right triangle. What
More informationProving Triangles and Quadrilaterals Satisfy Transformational Definitions
Proving Triangles and Quadrilaterals Satisfy Transformational Definitions 1. Definition of Isosceles Triangle: A triangle with one line of symmetry. a. If a triangle has two equal sides, it is isosceles.
More informationMaths Module 4: Geometry. Student s Book
Maths Module 4: Geometry Student s Book Maths Module 4: Geometry and Trigonometry Contents 1. Shapes - Page 2 - Angles - Triangles - Quadrilaterals - Congruence - Similar shapes 2. Constructions - Page
More informationFSA Geometry End-of-Course Review Packet. Circles Geometric Measurement and Geometric Properties
FSA Geometry End-of-Course Review Packet Circles Geometric Measurement and Geometric Properties Table of Contents MAFS.912.G-C.1.1 EOC Practice... 3 MAFS.912.G-C.1.2 EOC Practice... 5 MAFS.912.G-C.1.3
More informationSection A. 1. If the two roots are and of a quadratic equation, then the quadratic equation is formed in:
Class X Mathematics GENERAL INSTRUCTIONS: 1. All questions are compulsory. 2. The question paper consists of thirty four questions divided into four sections A, B, C & D. Section A comprises of ten questions
More informationFrom the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot. Harish Chandra Rajpoot, HCR. Spring May 6, 2017
From the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot Spring May 6, 2017 Mathematical analysis of disphenoid (isosceles tetrahedron (Derivation of volume, surface area, vertical height, in-radius,
More informationIndiana State Math Contest Geometry
Indiana State Math Contest 018 Geometry This test was prepared by faculty at Indiana University - Purdue University Columbus Do not open this test booklet until you have been advised to do so by the test
More informationCo-ordinate Geometry
Co-ordinate Geometry 1. Find the value of P for which the points (1, -), (2, -6) and (p, -1) are collinear 2. If the point P (x, y) is equidistant from the points A (1,) and B(4, 1). Prove that 2x+y =
More informationnot to be republishe NCERT CHAPTER 8 QUADRILATERALS 8.1 Introduction
QUADRILATERALS 8.1 Introduction CHAPTER 8 You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three non-collinear points in pairs, the figure so obtained is
More informationRevision Pack. Edexcel GCSE Maths (1 9) Non-calculator Questions Shapes
Edexcel GCSE Maths (1 9) Revision Pack Non-calculator Questions Shapes Edited by: K V Kumaran kvkumaran@gmail.com 07961319548 www.kumarmaths.weebly.com kumarmaths.weebly.com 1 Q1. All the measurements
More information