Individual Events 1 I2 x 0 I3 a. Group Events. G8 V 1 G9 A 9 G10 a 4 4 B

Size: px
Start display at page:

Download "Individual Events 1 I2 x 0 I3 a. Group Events. G8 V 1 G9 A 9 G10 a 4 4 B"

Transcription

1 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 I a Individual Events I x 0 I3 a I r 3 I5 a b 3 y 3 b 8 s b c 3 z c t 5 c d w d 0 u d G6 a 5 G7 a Group Events G8 V G9 A 9 G0 a b b V 0 B 6 b 3 c c 700 r 3 C 8 c 6 d 995 Individual Event I. Find a, if a log d 333 V 35 D d. a log log I. In the figure, AB AD DC, BD a. Find b, the length of BC. Let ADB, CDB 80 (adj. s on st. line) In ABD, cos a 8 A B a D Apply cosine formula on BCD. b (a) + (a)cos(80 ) b + 6 ( cos ) b 3 I.3 It is given that f (x) px 3 + qx + 5 and f ( 7) b +. Find c, if c f (7). Reference: 006 FG. p( 7) 3 + q( 7) [p(7) 3 + q(7)] c f (7) p(7) 3 + q(7) I. Find the least positive integer d, such that d c is divisible by 0 + c. d is divisible by d 0 C Page

2 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Individual Event x I. If x x x x 3 Reference: 998 HI3 x, find x. x 0 or (x )(x ) (x )(x 3) x 0 or x 5x + x 5x + 6 x 0 or 6 x 0 I. If f (t) 35 t and y f (x), find y. y f (0) I.3 A can finish a job in y days, B can finish a job in (y + 3) days. If they worked together, they can finish the job in z days, find z. z z 3 6 I. The probability of throwing z dice to score 7 is w, find w. 6 P( sum of dice 7) P((,6), (,5), (3,), (,3), (5,), (6, )) 36 6 w 6 Page

3 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Individual Event 3 I3. If a sin 30 + sin sin 3000, find a. 3 3 a + sin( ) 3 I3. It is given that x + y k () z + x 3k () x y z x 3 y + z k (3) () + () + (3): (x + y + z) 9k (36)( ) 9k y z and x + y + z 36a. Find the value of b, if b x y. k b x + y k () 8 I3.3 It is given that the equation x k k(x + b) has positive integral solution. Find c, the least value of k. x k k(x + 8) (k )x 6 If k, the equation has no solution 6 If k, x k The positive integral solution, 6 must be divisible by k. The least positive factor of 6 is, c I3. A car has already travelled 0% of its journey at an average speed of 0c km/h. In order to make the average speed of the whole journey become 00 km/h, the speed of the car is adjusted to d km/h to complete the rest of the journey. Find d. Let the total distance be s. s 0.s 0.6s 0 d d 0 00d d Page 3

4 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Individual Event I. In triangle ABC, B 90, BC 7 and AB. If r is the radius of the inscribed circle, find r. Let O be the centre of the inscribed circle, which touches BC, CA, AB at P, Q, R respectively. OP BC, OQ AC, OR AB (tangent radius) ORBP is a rectangle (it has 3 right angles) BR r, BP r (opp. sides of rectangle) CP 7 r, AR r AC AB + BC (Pythagoras Theorem) AC 5 CQ 7 r, AQ r (tangent from ext. point) CQ + AQ AC 7 r + r 5 r 3 I. If x + x 0 and s x 3 + x + r, find s. By division, s x 3 + x + 3 (x + )(x + x ) + C B C 7 - r Q 7 - r r r - r P O r r B r R - r I.3 It is given that F F and F n F n + F n, where n 3. If F t s +, find t. F t + 5 F 3 +, F + 3, F t 5 A A I. If u t t t 3 t, find u. Reference: 993 HG6, 996 FG0., 000 FG3., 00 FG3., 0 FI.3 u u Page

5 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Individual Event 5 I5. It is given that log 7 (log 3 (log x)) 0. Find a, if a 3 x. log 3 (log x) log x 3 x 3 8 a 3 x I5. In the figure, PQ is a diagonal of the cube and PQ a. Find b, if b is the total surface area of the cube. Reference: 99 HI, 003 HI7 Let the length of the cube be x. PQ x + x + x (Pythagoras Theorem) 3x The total surface area b 6x I5.3 In the figure, L and L are tangents to the three circles. If the radius of the largest circle is 8 and the radius of the smallest circle is b, find c, where c is the radius of the circle W. Let the centres of the 3 circles be A, B, C as shown in the figure. L touches the circles at D, E, F as shown. AD L, WE L, BF L (tangent radius) Let AB intersects the circle W at P and Q. AD AP b 8, EW WQ PW c QB BF 8 (radii of the circle) D Draw AG // DE, WH // EF as shown 8 EW // FB (int. supp.) A AWG WBH (corr. s EW // FB) AG GW, WH HB (by construction) AGW ~ WHB (equiangular) GW c 8, BH c + 8 (opp. sides of rectangle) c 8 8 c (ratio of sides, ~ ) c 8 c 8 (c 8)(c + 8) (c + 8)(8 c) c + 0c c + 0c + c () c I5. Refer to the figure, ABCD is a rectangle. AE BD and BE EO 6 c. Find d, the area of the rectangle ABCD. E G c - 8 W Q 8 c c 8 A P W P F H B Q 8 - c L D L BO OD AO OC (diagonal of rectangle) AE OA OE (Pythagoras Theorem) AE 3 ABD CDB (R.H.S.) d area of ABD B E O C Page 5

6 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Group Event 6 G6. a 9 b is a four digit number and its thousands digit is, its hundreds digit is a, its tens digit is 9 and its units digit is b, find a, b. a 9 b a b If a 0, 9 b b , No solution for a a > 0 and 0 b 3, a b is divisible by b 0 or If b 0, a a 0 0, 08, 096 and 0 a 9 No solution for a b, a + 9 is divisible by 9 + a m, where m is a positive integer a 5, b Check: (5) G6. Find c, if c Reference: 006 FI. Let x, y, then c x(y ) y(x ) x + y 3 3 G6.3 Find d, if d x, y d x(y ) y(x ) x + y Page 6

7 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Group Event 7 G7. Let p, q, r be the three sides of triangle PQR. If p + q + r r (p + q ), find a, where a cos R and R denotes the angle opposite r. p cos R a cos R q r pq p q r p q p q r p q p r p q r p q p q p r p q q r q r p q p q G7. Refer to the diagram, P is any point inside the square OABC and b is the minimum value of PO + PA + PB + PC, find b. PO + PA + PB + PC OB + AC (triangle inequality) OB A O P C B (, ) b G7.3 Identical matches of length l are used to arrange the following pattern, if c denotes the total length of matches used, find c. st row st row + nd row st + nd + 3 rd c st th row [ + (5 )] na n d G7. Find d, where d. Reference: 000 FI. (00 ) d 333 } 5. rows Page 7

8 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Group Event 8 Rectangles of length and breadth b where, b are positive integers, are drawn on square grid paper. For each of these rectangles, a diagonal is drawn and the number of vertices V intersected (excluding the two end points) is counted (see figure). G8. Find V, when 6, b. Intersection point (3, ) V G.8. Find V, when 5, b 3 As 3 and 5 are relatively prime, there is no intersection V 0 b 3 V G8.3 When and < b <, find r, the number of different values of b that makes V 0? b 5, 7, are relatively prime to. The number of different values of b 3 G8. Find V, when 08, b 7. H.C.F. (08, 7) 36, , 7 36 Intersection points (3, ), (6, ), (9, 6),, (05, 70) V 35 Page 8

9 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Group Event 9 A, B, C, D are different integers ranging from 0 to 9 and A A B C Find A, B, C and D. B A C B If A 0, then B, (AABC) (BACB) < 0 rejected D A C D A > 0, consider the hundreds digit: If there is no borrow digit in the hundreds digit, then A A A A 0 rejected There is a borrow digit in the hundreds digit. Also, there is a borrow digit in the thousands digit 0 + A A A A 9 Consider the thousands digit: A B D B + D 8 () Consider the units digit: If C < B, then 0 + C B D 0 + C B + D 0 + C 8 by () C (rejected) C > B and there is no borrow digit in the tens digit Consider the tens digit: 0 + B C C 0 + B C () Consider the units digit, C > B C B D C B + D C 8 by () Sub. C 8 into () 0 + B 6 B 6 Sub. B 6 into (), 6 + D 8 D A 9, B 6, C 8, D Page 9

10 Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Group Event 0 Lattice points are points on a rectangular coordinate plane having both x- and y-coordinates being integers. A moving point P is initially located at (0, 0). It moves unit along the coordinate lines (in either directions) in a single step. G0. If P moves step then P can reach a different lattice points, find a. (, 0), (, 0), (0, ), (0, ) a G0. If P moves not more than steps then P can reach b different lattice points, find b. (, 0), (, 0), (0, ), (0, ), (, ), (, (, ), (, ), (, ) (, 0), (, 0), (0, ), (0, ), (0, 0) b 3 G0.3 If P moves 3 steps then P can reach c different lattice points, find c. (, 0), (, 0), (0, ), (0, ), (3, 0), (, ), (, ), (0, 3), (, ), (, ), ( 3, 0), (, ), (, ), (0, 3), (, ), (, ); c + 6 G0. If d is the probability that P lies on the straight line x + y 9 when P advances 9 steps, find d. Total number of outcomes Favourable outcomes {(0,9), (,8), (,7),, (9,0)}, number 0 Probability 0 y x Page 0

1983 FG8.1, 1991 HG9, 1996 HG9

1983 FG8.1, 1991 HG9, 1996 HG9 nswers: (1- HKMO Heat Events) reated by: Mr. Francis Hung Last updated: 6 February 017 - Individual 1 11 70 6 1160 7 11 8 80 1 10 1 km 6 11-1 Group 6 7 7 6 8 70 10 Individual Events I1 X is a point on

More information

2 13b + 37 = 54, 13b 37 = 16, no solution

2 13b + 37 = 54, 13b 37 = 16, no solution Answers: (999-00 HKMO Final Events) Created by: Mr. Francis Hung Last updated: 6 February 07 Individual Events SI P 6 I P 5 I P 6 I P I P I5 P Q 7 Q 8 Q 8 Q Q Q R R 7 R R 996 R R S 990 S 6 S S 666 S S

More information

CBSE X Mathematics 2012 Solution (SET 1) Section B

CBSE X Mathematics 2012 Solution (SET 1) Section B CBSE X Mathematics 01 Solution (SET 1) Section B Q11. Find the value(s) of k so that the quadratic equation x kx + k = 0 has equal roots. Given equation is x kx k 0 For the given equation to have equal

More information

2, find the value of a.

2, find the value of a. Answers: (99-9 HKMO Final Events) reated by: Mr. Francis Hung Last updated: 7 December 05 Individual Events I a I a 6 I a 4 I4 a 8 I5 a 0 b b 60 b 4 b 9 b c c 00 c 50 c 4 c 57 d d 50 d 500 d 54 d 7 Group

More information

Answers: ( HKMO Final Events) Created by: Mr. Francis Hung Last updated: 2 September 2018

Answers: ( HKMO Final Events) Created by: Mr. Francis Hung Last updated: 2 September 2018 Answers: (008-09 HKMO Final Events) Created b: Mr. Francis Hung Last updated: September 08 Individual Events SI A I R 0 I a 6 I m I m B S 0 b 9 n 9 n C T c 6 p p 9 D 8 U 7 d q q 8 Group Events SG z 0 G

More information

CBSE CLASS X MATH -SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1.

CBSE CLASS X MATH -SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1. CBSE CLASS X MATH -SOLUTION 011 Q1 The probability of an event is always greater than or equal to zero and less than or equal to one. Here, 3 5 = 0.6 5% = 5 100 = 0.5 Therefore, 0.6, 0.5 and 0.3 are greater

More information

CBSE CLASS-10 MARCH 2018

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

More information

11 is the same as their sum, find the value of S.

11 is the same as their sum, find the value of S. Answers: (998-99 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 Individual Events I P 4 I a 8 I a 6 I4 a I5 a IS a Q 8 b 0 b 7 b b spare b 770 R c c c c 0 c 57 S 0 d 000 d 990 d

More information

CBSE MATHEMATICS (SET-2)_2019

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

More information

1 / 23

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

More information

1 / 23

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

More information

1 / 24

1 / 24 CBSE-XII-017 EXAMINATION CBSE-X-01 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instuctions : 1. All questions are compulsory.. The question paper consists of 34 questions

More information

S Group Events G1 a 47 G2 a *2

S Group Events G1 a 47 G2 a *2 Answers: (003-0 HKMO Final Events) Created by: Mr. Francis Hung Last updated: 9 September 07 Individual Events I a 6 I P I3 a I a IS P 8 b + Q 6 b 9 b Q 8 c 7 R 6 c d S 3 d c 6 R 7 8 d *33 3 see the remark

More information

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Write your name here Surname Other names Edexcel International GCSE Centre Number Mathematics A Paper 4H Monday 16 January 2012 Morning Time: 2 hours Candidate Number Higher Tier Paper Reference 4MA0/4H

More information

TOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X

TOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X TOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X M.M: 80 TIME : 3-3 2 Hrs. GENERAL INSTRUCTIONS :. All questions are compulsory. 2. The question paper consists of 34 questions divided

More information

It is known that the length of the tangents drawn from an external point to a circle is equal.

It is known that the length of the tangents drawn from an external point to a circle is equal. CBSE -MATHS-SET 1-2014 Q1. The first three terms of an AP are 3y-1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)

More information

Page 1 of 15. Website: Mobile:

Page 1 of 15. Website:    Mobile: Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5

More information

[Class-X] MATHEMATICS SESSION:

[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 information

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

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

More information

2012 GCSE Maths Tutor All Rights Reserved

2012 GCSE Maths Tutor All Rights Reserved 2012 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com This book is under copyright to GCSE Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents angles

More information

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

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

More information

Mathematics CLASS : X. Time: 3hrs Max. Marks: 90. 2) If a, 2 are three consecutive terms of an A.P., then the value of a.

Mathematics CLASS : X. Time: 3hrs Max. Marks: 90. 2) If a, 2 are three consecutive terms of an A.P., then the value of a. 1 SAMPLE PAPER 4 (SAII) MR AMIT. KV NANGALBHUR Mathematics CLASS : X Time: 3hrs Max. Marks: 90 General Instruction:- 1. All questions are Compulsory. The question paper consists of 34 questions divided

More information

CBSE CLASS-10 MARCH 2018

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

More information

Question Bank Tangent Properties of a Circle

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

More information

2 and v! = 3 i! + 5 j! are given.

2 and v! = 3 i! + 5 j! are given. 1. ABCD is a rectangle and O is the midpoint of [AB]. D C 2. The vectors i!, j! are unit vectors along the x-axis and y-axis respectively. The vectors u! = i! + j! 2 and v! = 3 i! + 5 j! are given. (a)

More information

Udaan School Of Mathematics Class X Chapter 10 Circles Maths

Udaan School Of Mathematics Class X Chapter 10 Circles Maths Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in

More information

Class X Delhi Math Set-3 Section A

Class X Delhi Math Set-3 Section A Class X Delhi Math Set-3 Section A 1. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30. The distance of the car from the base of the tower (in m.) is:

More information

Individual Events 5 I3 a 6 I4 a 8 I5 A Group Events

Individual Events 5 I3 a 6 I4 a 8 I5 A Group Events Answers: (993-94 HKMO Final Events) Created by: Mr. Francis Hung Last updated: 8 August 08 SI a I a 6 I A Individual Events I3 a 6 I4 a 8 I A 6 b 4 b B 60 b *9 see the remarks b 0 B 36 c c 0 C c 6 c 3

More information

9 th CBSE Mega Test - II

9 th CBSE Mega Test - II 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

More information

SAMPLE PAPER 3 (SA II) Mathematics CLASS : X. Time: 3hrs Max. Marks: 90

SAMPLE PAPER 3 (SA II) Mathematics CLASS : X. Time: 3hrs Max. Marks: 90 1 SAMPLE PAPER 3 (SA II) MRS.KIRAN WANGNOO Mathematics CLASS : X Time: 3hrs Max. Marks: 90 General Instruction:- 1. All questions are Compulsory. 1. The question paper consists of 34 questions divided

More information

81-E 2. Ans. : 2. Universal set U = { 2, 3, 5, 6, 10 }, subset A = { 5, 6 }. The diagram which represents A / is. Ans. : ( SPACE FOR ROUGH WORK )

81-E 2. Ans. : 2. Universal set U = { 2, 3, 5, 6, 10 }, subset A = { 5, 6 }. The diagram which represents A / is. Ans. : ( SPACE FOR ROUGH WORK ) 81-E 2 General Instructions : i) The question-cum-answer booklet contains two Parts, Part A & Part B. ii) iii) iv) Part A consists of 60 questions and Part B consists of 16 questions. Space has been provided

More information

KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018

KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018 CCE RR REVISED & UN-REVISED O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 G È.G È.G È.. Æ fioê, d È 08 S. S. L.

More information

MODEL QUESTION PAPERS WITH ANSWERS SET 1

MODEL QUESTION PAPERS WITH ANSWERS SET 1 MTHEMTICS MODEL QUESTION PPERS WITH NSWERS SET 1 Finish Line & Beyond CLSS X Time llowed: 3 Hrs Max. Marks : 80 General Instructions: (1) ll questions are compulsory. (2) The question paper consists of

More information

SAMPLE QUESTION PAPER 11 Class-X ( ) Mathematics

SAMPLE QUESTION PAPER 11 Class-X ( ) Mathematics SAMPLE QUESTION PAPER 11 Class-X (2017 18) Mathematics GENERAL INSTRUCTIONS (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided into four sections A, B,C and D. (iii)

More information

UNIT-8 SIMILAR TRIANGLES Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. 1. ABC is a right-angled triangle, right-angled

More information

CBSE CLASS X MATH

CBSE CLASS X MATH CBSE CLASS X MATH - 2011 Q.1) Which of the following cannot be the probability of an event? A. 1.5 B. 3 5 C. 25% D. 0.3 Q.2 The mid-point of segment AB is the point P (0, 4). If the Coordinates of B are

More information

COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use

COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE I. Length of a Line Segment: The distance between two points A ( x1, 1 ) B ( x, ) is given b A B = ( x x1) ( 1) To find the length of a line segment joining

More information

97-98 Individual Group

97-98 Individual Group nswers: (997-98 HKO Heat vents) reated by: r. Francis Hung Last updated: June 08 97-98 Individual 0 6 66 7 9 8 9 0 7 7 6 97-98 Group 6 7 8 9 0 0 9 Individual vents I Given that + + 8 is divisible by (

More information

chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

chapter 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 information

SAMPLE QUESTION PAPER 09 Class-X ( ) Mathematics

SAMPLE QUESTION PAPER 09 Class-X ( ) Mathematics SAMPLE QUESTION PAPER 09 Class-X (2017 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 information

( )( ) PR PQ = QR. Mathematics Class X TOPPER SAMPLE PAPER-1 SOLUTIONS. HCF x LCM = Product of the 2 numbers 126 x LCM = 252 x 378

( )( ) PR PQ = QR. Mathematics Class X TOPPER SAMPLE PAPER-1 SOLUTIONS. HCF x LCM = Product of the 2 numbers 126 x LCM = 252 x 378 Mathematics Class X TOPPER SAMPLE PAPER- SOLUTIONS Ans HCF x LCM Product of the numbers 6 x LCM 5 x 378 LCM 756 ( Mark) Ans The zeroes are, 4 p( x) x + x 4 x 3x 4 ( Mark) Ans3 For intersecting lines: a

More information

BOARD QUESTION PAPER : MARCH 2016 GEOMETRY

BOARD 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 information

KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018

KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018 CCE PR REVISED & UN-REVISED O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 G È.G È.G È.. Æ fioê, d È 08 S. S. L.

More information

= ( +1) BP AC = AP + (1+ )BP Proved UNIT-9 CIRCLES 1. Prove that the parallelogram circumscribing a circle is rhombus. Ans Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is

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

(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 information

CO-ORDINATE GEOMETRY. 1. Find the points on the y axis whose distances from the points (6, 7) and (4,-3) are in the. ratio 1:2.

CO-ORDINATE GEOMETRY. 1. Find the points on the y axis whose distances from the points (6, 7) and (4,-3) are in the. ratio 1:2. UNIT- CO-ORDINATE GEOMETRY Mathematics is the tool specially suited for dealing with abstract concepts of any ind and there is no limit to its power in this field.. Find the points on the y axis whose

More information

MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 QUESTION PAPER CODE 30/1/1 SECTION - A

MATHEMATICS. 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 information

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

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

More information

Geometry Facts Circles & Cyclic Quadrilaterals

Geometry Facts Circles & Cyclic Quadrilaterals Geometry Facts Circles & Cyclic Quadrilaterals Circles, chords, secants and tangents combine to give us many relationships that are useful in solving problems. Power of a Point Theorem: The simplest of

More information

nx + 1 = (n + 1)x 13(n + 1) and nx = (n + 1)x + 27(n + 1).

nx + 1 = (n + 1)x 13(n + 1) and nx = (n + 1)x + 27(n + 1). 1. (Answer: 630) 001 AIME SOLUTIONS Let a represent the tens digit and b the units digit of an integer with the required property. Then 10a + b must be divisible by both a and b. It follows that b must

More information

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

VAISHALI 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 information

2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term.

2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term. CBSE Board Class X Set 3 Mathematics Board Question Paper 2018 Time: 3 hrs. Marks: 80 Note: Please check that this question paper contains 11 printed pages. Code number given on the right hand side of

More information

Intermediate Math Circles February 22, 2012 Contest Preparation II

Intermediate Math Circles February 22, 2012 Contest Preparation II Intermediate Math Circles February, 0 Contest Preparation II Answers: Problem Set 6:. C. A 3. B 4. [-6,6] 5. T 3, U and T 8, U 6 6. 69375 7. C 8. A 9. C 0. E Australian Mathematics Competition - Intermediate

More information

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

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

More information

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

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.

More information

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 4HR Centre Number Monday 12 January 2015 Afternoon Time: 2 hours Candidate Number Higher Tier Paper Reference

More information

81-E If set A = { 2, 3, 4, 5 } and set B = { 4, 5 }, then which of the following is a null set? (A) A B (B) B A (C) A U B (D) A I B.

81-E If set A = { 2, 3, 4, 5 } and set B = { 4, 5 }, then which of the following is a null set? (A) A B (B) B A (C) A U B (D) A I B. 81-E 2 General Instructions : i) The question-cum-answer booklet contains two Parts, Part A & Part B. ii) iii) iv) Part A consists of 60 questions and Part B consists of 16 questions. Space has been provided

More information

Created by T. Madas 2D VECTORS. Created by T. Madas

Created by T. Madas 2D VECTORS. Created by T. Madas 2D VECTORS Question 1 (**) Relative to a fixed origin O, the point A has coordinates ( 2, 3). The point B is such so that AB = 3i 7j, where i and j are mutually perpendicular unit vectors lying on the

More information

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

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

More information

1 / 22

1 / 22 CBSE-XII-017 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions divided into

More information

Paper Reference. Mathematics A Paper 5 (Non Calculator) Higher Tier Tuesday 8 June 2004 Afternoon Time: 2 hours

Paper Reference. Mathematics A Paper 5 (Non Calculator) Higher Tier Tuesday 8 June 2004 Afternoon Time: 2 hours Centre No. Paper Reference Surname Initial(s) Candidate No. 5505 05 Signature Paper Reference(s) 5505/05 Edexcel GCSE Mathematics A 1387 Paper 5 (Non Calculator) Higher Tier Tuesday 8 June 2004 Afternoon

More information

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =

More information

Euclidian Geometry Grade 10 to 12 (CAPS)

Euclidian Geometry Grade 10 to 12 (CAPS) Euclidian Geometry Grade 10 to 12 (CAPS) Compiled by Marlene Malan marlene.mcubed@gmail.com Prepared by Marlene Malan CAPS DOCUMENT (Paper 2) Grade 10 Grade 11 Grade 12 (a) Revise basic results established

More information

CAREER POINT. PRMO EXAM-2017 (Paper & Solution) Sum of number should be 21

CAREER POINT. PRMO EXAM-2017 (Paper & Solution) Sum of number should be 21 PRMO EXAM-07 (Paper & Solution) Q. How many positive integers less than 000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3? Sum

More information

Grade 9 Circles. Answer the questions. For more such worksheets visit

Grade 9 Circles. Answer the questions. For more such worksheets visit ID : ae-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer the questions (1) Two circles with centres O and O intersect at two points A and B. A line PQ is drawn parallel

More information

HMMT November 2012 Saturday 10 November 2012

HMMT November 2012 Saturday 10 November 2012 HMMT November 01 Saturday 10 November 01 1. [5] 10 total. The prime numbers under 0 are:,, 5, 7, 11, 1, 17, 19,, 9. There are 10 in. [5] 180 Albert s choice of burgers, sides, and drinks are independent

More information

Math 9 Chapter 8 Practice Test

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

More information

1. Suppose that a, b, c and d are four different integers. Explain why. (a b)(a c)(a d)(b c)(b d)(c d) a 2 + ab b = 2018.

1. Suppose that a, b, c and d are four different integers. Explain why. (a b)(a c)(a d)(b c)(b d)(c d) a 2 + ab b = 2018. New Zealand Mathematical Olympiad Committee Camp Selection Problems 2018 Solutions Due: 28th September 2018 1. Suppose that a, b, c and d are four different integers. Explain why must be a multiple of

More information

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3HR Centre Number Wednesday 14 May 2014 Morning Time: 2 hours Candidate Number Higher Tier Paper Reference

More information

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3HR Friday 10 January 2014 Morning Time: 2 hours Centre Number Candidate Number Higher Tier Paper Reference

More information

2016 Canadian Team Mathematics Contest

2016 Canadian Team Mathematics Contest The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 016 Canadian Team Mathematics Contest April 016 Solutions 016 University of Waterloo 016 CTMC Solutions Page Individual Problems

More information

Class IX Chapter 8 Quadrilaterals Maths

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

More information

Class IX Chapter 8 Quadrilaterals Maths

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

More information

number. However, unlike , three of the digits of N are 3, 4 and 5, and N is a multiple of 6.

number. However, unlike , three of the digits of N are 3, 4 and 5, and N is a multiple of 6. C1. The positive integer N has six digits in increasing order. For example, 124 689 is such a number. However, unlike 124 689, three of the digits of N are 3, 4 and 5, and N is a multiple of 6. How many

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

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 =,

More information

Pre-Regional Mathematical Olympiad Solution 2017

Pre-Regional Mathematical Olympiad Solution 2017 Pre-Regional Mathematical Olympiad Solution 07 Time:.5 hours. Maximum Marks: 50 [Each Question carries 5 marks]. How many positive integers less than 000 have the property that the sum of the digits of

More information

PRMO Solution

PRMO Solution PRMO Solution 0.08.07. How many positive integers less than 000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3?. Suppose a, b

More information

2003 AIME Given that ((3!)!)! = k n!, where k and n are positive integers and n is as large as possible, find k + n.

2003 AIME Given that ((3!)!)! = k n!, where k and n are positive integers and n is as large as possible, find k + n. 003 AIME 1 Given that ((3!)!)! = k n!, where k and n are positive integers and n is as large 3! as possible, find k + n One hundred concentric circles with radii 1,, 3,, 100 are drawn in a plane The interior

More information

p and q are two different primes greater than 25. Pass on the least possible value of p + q.

p and q are two different primes greater than 25. Pass on the least possible value of p + q. A1 p and q are two different primes greater than 25. Pass on the least possible value of p + q. A3 A circle has an area of Tπ. Pass on the area of the largest square which can be drawn inside the circle.

More information

2018 Canadian Team Mathematics Contest

2018 Canadian Team Mathematics Contest The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 08 Canadian Team Mathematics Contest April 08 Solutions 08 University of Waterloo 08 CTMC Solutions Page Individual Problems. Since

More information

SAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80

SAMPLE 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 information

BRITISH COLUMBIA SECONDARY SCHOOL MATHEMATICS CONTEST,

BRITISH COLUMBIA SECONDARY SCHOOL MATHEMATICS CONTEST, BRITISH COLUMBIA SECONDARY SCHOOL MATHEMATICS CONTEST, 014 Solutions Junior Preliminary 1. Rearrange the sum as (014 + 01 + 010 + + ) (013 + 011 + 009 + + 1) = (014 013) + (01 011) + + ( 1) = 1 + 1 + +

More information

CBSE Class X Mathematics Sample Paper 04

CBSE Class X Mathematics Sample Paper 04 CBSE Class X Mathematics Sample Paper 04 Time Allowed: 3 Hours Max Marks: 80 General Instructions: i All questions are compulsory ii The question paper consists of 30 questions divided into four sections

More information

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. 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

More information

RMT 2013 Geometry Test Solutions February 2, = 51.

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,

More information

UNCC 2001 Comprehensive, Solutions

UNCC 2001 Comprehensive, Solutions UNCC 2001 Comprehensive, Solutions March 5, 2001 1 Compute the sum of the roots of x 2 5x + 6 = 0 (A) (B) 7/2 (C) 4 (D) 9/2 (E) 5 (E) The sum of the roots of the quadratic ax 2 + bx + c = 0 is b/a which,

More information

Second Degree Equations

Second Degree Equations Second Degree Equations 1) Find the missing terms 2x 2-9 = 3x 2x 2-3x = -------- x 2-3 2 x = ---------- x 2-3 x+ --------- = --------- + --------- 2 (--------) 2 = (------) 2 --------- = ----------- x

More information

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Write your name here Surname Other names Edexcel Certificate Edexcel International GCSE Mathematics A Paper 3H Friday 10 May 2013 Afternoon Time: 2 hours Centre Number Candidate Number Higher Tier Paper

More information

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 (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 information

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is

More information

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Write your name here Surname Other names Edexcel International GCSE Centre Number Candidate Number Mathematics A Paper 3HR Friday 10 May 2013 Afternoon Time: 2 hours Higher Tier Paper Reference 4MA0/3HR

More information

Solutions to RSPL/1. Mathematics 10

Solutions to RSPL/1. Mathematics 10 Solutions to RSPL/. It is given that 3 is a zero of f(x) x 3x + p. \ (x 3) is a factor of f(x). So, (3) 3(3) + p 0 8 9 + p 0 p 9 Thus, the polynomial is x 3x 9. Now, x 3x 9 x 6x + 3x 9 x(x 3) + 3(x 3)

More information

MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 31/1

MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 31/1 CBSE - X MT EDUCARE LTD. SUMMATIVE ASSESSMENT - 03-4 Roll No. Code No. 3/ Series RLH Please check that this question paper contains 6 printed pages. Code number given on the right hand side of the question

More information

LLT Education Services

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

More information

Paper Reference. Paper Reference(s) 7361/01 London Examinations GCE. Mathematics Syllabus B Ordinary Level Paper 1

Paper Reference. Paper Reference(s) 7361/01 London Examinations GCE. Mathematics Syllabus B Ordinary Level Paper 1 Centre No. Candidate No. Paper Reference 7 3 6 1 0 1 Surname Signature Paper Reference(s) 7361/01 London Examinations GCE Mathematics Syllabus B Ordinary Level Paper 1 Friday 11 January 2008 Afternoon

More information

H. London Examinations IGCSE

H. London Examinations IGCSE Centre No. Candidate No. Paper Reference 4 4 0 0 3 H Surname Signature Initial(s) Paper Reference(s) 4400/3H London Examinations IGCSE Mathematics Paper 3H Higher Tier Monday 10 May 2004 Morning Time:

More information

Mathematics Class X Board Paper 2011

Mathematics 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 information

Regent College. Maths Department. Core Mathematics 4. Vectors

Regent College. Maths Department. Core Mathematics 4. Vectors Regent College Maths Department Core Mathematics 4 Vectors Page 1 Vectors By the end of this unit you should be able to find: a unit vector in the direction of a. the distance between two points (x 1,

More information

Methods in Mathematics

Methods in Mathematics Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 1: Methods 1 For Approved Pilot Centres ONLY Higher Tier Monday 17 June 2013 Morning Time:

More information

ADDITIONAL MATHEMATICS

ADDITIONAL MATHEMATICS 005-CE A MATH HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 005 ADDITIONAL MATHEMATICS :00 pm 5:0 pm (½ hours) This paper must be answered in English 1. Answer ALL questions in Section A and any FOUR

More information