1. Town A is 48 km from town B and 32 km from town C as shown in the diagram. A 48km
|
|
|
- Leslie Hicks
- 5 years ago
- Views:
Transcription
1 1. Town is 48 km from town and 32 km from town as shown in the diagram. 32km 48km Given that town is 56 km from town, find the size of angle (Total 4 marks) Â to the nearest degree. 2. The diagram shows a vertical pole Q, which is supported by two wires fixed to the horizontal ground at and. Find the height of the pole, Q; Q = 40 m ˆ Q = 36 ÂQ = 70 ˆ Q = 30 the distance between and. (Total 4 marks) Q The following diagram shows the triangle O, where O = 2 cm, = 4 cm and O = 3 cm. alculate Ô, giving your answer in radians. diagram not to scale The following diagram shows two circles which intersect at the points and. The smaller circle 1 has centre O and radius 3 cm, the larger circle 2 has centre and radius 4 cm, and O = 2 cm. The point D lies on the circumference of 1 and E on the circumference of 2.Triangle O is the same as triangle O in the diagram above. O 2 1 D E O diagram not to scale Find Ô, giving your answer in radians. I Questionbank Maths SL 1
2 Given that ˆ is 1.63 radians, calculate the area of (i) sector E; sector OD. The area of the quadrilateral O is 5.81 cm 2. (i) Find the area of OE. Hence find the area of the shaded region ED. (Total 14 marks) 4. The diagrams below show two triangles both satisfying the conditions = 20 cm, = 17 cm, ˆ = 50. Diagrams not to scale Triangle 1 Triangle 2 alculate the size of Ĉ in Triangle 2. alculate the area of Triangle 1. (Total 4 marks) 5. The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. Find the size of the smallest angle, in degrees; the area of the triangle. (Total 4 marks) The points, Q, R are three markers on level ground, joined by straight paths Q, QR, R as shown in the diagram. QR = 9 km, Qˆ R = 35, Rˆ Q = 25. Q km R Diagram not to scale Find the length R. I Questionbank Maths SL 2
3 Tom sets out to walk from Q to at a steady speed of 8 km h 1. t the same time, lan sets out to jog from R to at a steady speed of a km h 1. They reach at the same time. alculate the value of a. The point S is on [Q], such that RS = 2QS, as shown in the diagram. S Q R Find the length QS. (6) (Total 16 marks) 7. Let y = 16x x 256. Given that y has a maximum value, find (i) the value of x giving the maximum value of y; this maximum value of y. The triangle XYZ has XZ = 6, YZ = x, XY = z as shown below. The perimeter of triangle XYZ is 16. (i) Express z in terms of x. Using the cosine rule, express z 2 in terms of x and cos Z. (iii) Hence, show that cos Z = 5x 16. 3x Let the area of triangle XYZ be. Show that 2 = 9x 2 sin 2 Z. Hence, show that 2 = 16x x 256. (e) (i) Hence, write down the maximum area for triangle XYZ. What type of triangle is the triangle with maximum area? (Total 20 marks) 8. The following diagram shows two semi-circles. The larger one has centre O and radius 4 cm. The smaller one has centre, radius 3 cm, and passes through O. The line (O) meets the larger semi-circle at S. The semi-circles intersect at Q. (i) Explain why OQ is an isosceles triangle. I Questionbank Maths SL 3
4 1 Use the cosine rule to show that cos O ˆ Q =. 9 (iii) Hence show that sin O ˆ Q = (iv) Find the area of the triangle OQ. onsider the smaller semi-circle, with centre. (i) Write down the size of O ˆ Q. alculate the area of the sector OQ. onsider the larger semi-circle, with centre O. alculate the area of the sector QOS. Hence calculate the area of the shaded region. (Total 17 marks) 9. The following diagram shows a pentagon DE, with = 9.2 cm, = 3.2 cm, D = 7.1 cm, ÊD =110, Dˆ E = 52 and ˆ D = 60. Find D. Find DE. The area of triangle D is 5.68 cm 2. Find D ˆ. (e) Find. Find the area of quadrilateral D. (Total 21 marks) 10. ship leaves port on a bearing of 030. It sails a distance of 25 km to point. t, the ship changes direction to a bearing of 100. It sails a distance of 40 km to reach point. This information is shown in the diagram below. diagram not to scale I Questionbank Maths SL 4
5 second ship leaves port and sails directly to. Find the distance the second ship will travel. Find the bearing of the course taken by the second ship. (Total 7 marks) 11. farmer owns a triangular field. One side of the triangle, [], is 104 m, a second side, [], is 65 m and the angle between these two sides is 60. Use the cosine rule to calculate the length of the third side of the field. Given that sin 60 = integer. 3, find the area of the field in the form 3p 3 where p is an 2 Let D be a point on [] such that [D] bisects the 60 angle. The farmer divides the field into two parts 1 and 2 by constructing a straight fence [D] of length x metres, as shown on the diagram below. (i) Show that the area of 1 is given by 65x. 4 Find a similar expression for the area of 2. (iii) Hence, find the value of x in the form q 3, where q is an integer. (i) Explain why sindˆ sindˆ. Use the result of part (i) and the sine rule to show that D 5. D 8 (Total 18 marks) 12. The diagram below shows triangle QR. The length of [Q] is 7 cm, the length of [R] is 10 cm, and Qˆ R is 75. I Questionbank Maths SL 5
6 Find Qˆ R. Find the area of triangle QR. (Total 6 marks) 13. The diagram below shows a quadrilateral D. = 4, D = 8, D =12, Ĉ D = 25, ÂD =. Use the cosine rule to show that D = 4 5 4cos. Let = 40. (i) Find the value of sin ˆ D. Find the two possible values for the size of ˆ D. (iii) Given that ˆ D is an acute angle, find the perimeter of D. Find the area of triangle D. (12) (Total 16 marks) 14. The following diagram shows a semicircle centre O, diameter [], with radius 2. Let be a point on the circumference, with Ô = radians. Find the area of the triangle O, in terms of. Explain why the area of triangle O is the same as the area triangle O. Let S be the total area of the two segments shaded in the diagram above. I Questionbank Maths SL 6
7 Show that S = 2( 2 sin ). (e) Find the value of when S is a local minimum, justifying that it is a minimum. Find a value of for which S has its greatest value. (8) (Total 18 marks) 15. The diagram below shows a circle with centre O and radius 8 cm. The points,,, D, E and F are on the circle, and [F] is a diameter. The length of arc is 6 cm. Find the size of angle O. Hence find the area of the shaded region. (6) The area of sector ODE is 45 cm 2. Find the size of angle OE. Find EF. (Total 15 marks) 16. The diagram below shows a triangle D with = 13 cm and D = 6.5 cm. Let be a point on the line D such that = = 7 cm. Find the size of angle. Find the size of angle D. (Total 8 marks) I Questionbank Maths SL 7
Circular Functions and Trig - Practice Problems (to 07)
I Math SL: Trig Practice Problems Circular Functions and Trig - Practice Problems (to 07). In the triangle PQR, PR = 5 cm, QR = 4 cm and PQ = 6 cm. Calculate (a) the size of PQˆ R ; (b) the area of triangle
Express g(x) in the form f(x) + ln a, where a (4)
SL 2 SUMMER PACKET 2013 PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST
Express g(x) in the form f(x) + ln a, where a (4)
SL 2 SUMMER PACKET PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST DAY
CHAPTER 10 TRIGONOMETRY
CHAPTER 10 TRIGONOMETRY EXERCISE 39, Page 87 1. Find the length of side x in the diagram below. By Pythagoras, from which, 2 25 x 7 2 x 25 7 and x = 25 7 = 24 m 2. Find the length of side x in the diagram
(b) Show that sin 2 =. 9 (c) Find the exact value of cos 2. (Total 6 marks)
IB SL Trig Review. In the triangle PQR, PR = 5 cm, QR = 4 cm and PQ = 6 cm. Calculate the size of PQˆ R ; the area of triangle PQR.. The following diagram shows a triangle ABC, where AĈB is 90, AB =, AC
No Calc. 1 p (seen anywhere) 1 p. 1 p. No Calc. (b) Find an expression for cos 140. (c) Find an expression for tan (a) (i) sin 140 = p A1 N1
IBSL /4 IB REVIEW: Trig KEY (0points). Let p = sin 40 and q = cos 0. Give your answers to the following in terms of p and/or q. (a) Write down an expression for (i) sin 40; (ii) cos 70. (b) Find an expression
cos/sine rule questions studies
I Questionbank Mathematical Studies 3rd edition cos/sine rule questions studies 105 min 109 marks 1. On a map three schools, and are situated as shown in the diagram. Schools and are 625 metres apart.
Here is a link to the formula booklet:
IB MATH SL2 SUMMER ASSIGNMENT review of topics from year 1. We will be quizzing on this when you return to school. This review is optional but you will earn bonus points if you complete it. Questions?
PhysicsAndMathsTutor.com
1. The diagram above shows the sector OA of a circle with centre O, radius 9 cm and angle 0.7 radians. Find the length of the arc A. Find the area of the sector OA. The line AC shown in the diagram above
IB Math SL 1: Trig Practice Problems: MarkScheme Circular Functions and Trig - Practice Problems (to 07) MarkScheme
IB Math SL : Trig Practice Problems: MarkScheme Circular Functions and Trig - Practice Problems (to 07) MarkScheme. (a) Evidence of using the cosine rule p + r q eg cos P Qˆ R, q p + r pr cos P Qˆ R pr
Core Mathematics 2 Radian Measures
Core Mathematics 2 Radian Measures Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Radian Measures 1 Radian Measures Radian measure, including use for arc length and area of sector.
Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.
April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line
MATHEMATICS. S2 Level 3/4 Course -1- Larkhall Maths Department Academy
MTHEMTIS S2 Level 3/4 ourse -1- Larkhall Maths Department cademy 17 cm The ircle Eercise 1() Find the circumference ( 1) 2) ) of the following circles 3) 4) 1 12 cm 5 cm 28 m 5) 6) 7) 3 2 cm 8) 15 m 22
OC = $ 3cos. 1 (5.4) 2 θ = (= radians) (M1) θ = 1. Note: Award (M1) for identifying the largest angle.
4 + 5 7 cos α 4 5 5 α 0.5. Note: Award for identifying the largest angle. Find other angles first β 44.4 γ 4.0 α 0. (C4) Note: Award (C) if not given to the correct accuracy.. (a) p (C) 4. (a) OA A is
IB SL: Trig Function Practice Answers
IB SL: Trig Function Practice Answers. π From sketch of graph y = 4 sin x (M) or by observing sin. k > 4, k < 4 (A)(A)(C)(C) 4 0 0 4. METHOD cos x = sin x cos x (M) cos x sin x cos x = 0 cos x(cos x sin
Mathematics Teachers Enrichment Program MTEP 2012 Trigonometry and Bearings
Mathematics Teachers Enrichment Program MTEP 2012 Trigonometry and Bearings Trigonometry in Right Triangles A In right ABC, AC is called the hypotenuse. The vertices are labelled using capital letters.
CHAPTER 1 BASIC ARITHMETIC
CHAPTER 1 BASIC ARITHMETIC EXERCISE 1, Page 4 1. Evaluate 67 kg 8 kg + 4 kg without using a calculator 67 kg 8 kg + 4 kg = 67 kg + 4 kg 8 kg = 101 kg 8 kg = 19 kg. Evaluate 851 mm 7 mm without using a
Created by T. Madas LINE INTEGRALS. Created by T. Madas
LINE INTEGRALS LINE INTEGRALS IN 2 DIMENSIONAL CARTESIAN COORDINATES Question 1 Evaluate the integral ( x + 2y) dx, C where C is the path along the curve with equation y 2 = x + 1, from ( ) 0,1 to ( )
1. For Cosine Rule of any triangle ABC, b² is equal to A. a² - c² 4bc cos A B. a² + c² - 2ac cos B C. a² - c² + 2ab cos A D. a³ + c³ - 3ab cos A
1. For Cosine Rule of any triangle ABC, b² is equal to A. a² - c² 4bc cos A B. a² + c² - 2ac cos B C. a² - c² + 2ab cos A D. a³ + c³ - 3ab cos A 2. For Cosine Rule of any triangle ABC, c² is equal to A.
REVISION EXERCISES ON GEOMETRY END TRIGONOMETRY
REVISION EXERCISES ON GEOMETRY END TRIGONOMETRY 1 The bearing of B from A is 030. Find the bearing of A from B. 2 For triangle ABC, AB = 60 cm, BC = 80 cm and the magnitude of angle ABC is 120. Find the
IB STANDARD LEVEL MATHEMATICS FINAL REVIEW
IB STANDARD LEVEL MATHEMATICS FINAL REVIEW 01 013 SECTION 1: STATISTICS 1. At a conference of 100 mathematicians there are 7 men and 8 women. The men have a mean height of 1.79 m and the women have a mean
Western Cape Education Department. Examination Preparation Learning Resource 2016 GEOMETRY MATHEMATICS
Western ape Education Department Examination Preparation Learning Resource 06 GEOMETRY MTHEMTIS Grade Geometry Questions Grade Theorems on Razzia Ebrahim Senior urriculum Planner for Mathematics E-mail:
MATHEMATICS GRADE 12 SESSION 18 (LEARNER NOTES)
MATHEMATICS GRADE 1 SESSION 18 (LEARNER NOTES) TOPIC 1: TWO-DIMENSIONAL TRIGONOMETRY Learner Note: Before attempting to do any complex two or three dimensional problems involving trigonometry, it is essential
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.
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
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 =,
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)
Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.
Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12
Mathematics SL. Mock Exam 2014 PAPER 2. Instructions: The use of graphing calculator is allowed.
Mock Exam 2014 Mathematics SL PAPER 2 Instructions: The use of graphing calculator is allowed Show working when possible (even when using a graphing calculator) Give your answers in exact form or round
Mathematics TRIAL HSC EXAMINATION. General Instructions
,, 015 TRIAL HSC EXAMINATION Mathematics General Instructions o Reading Time - 5 minutes o Working Time - 3 hours o Write using a blue or black pen. Black pen is preferred o Board approved calculators
Mathematics. Caringbah High School. Trial HSC Examination. Total Marks 100. General Instructions
Caringbah High School 014 Trial HSC Examination Mathematics General Instructions Total Marks 100 Reading time 5 minutes Working time 3 hours Write using a blue or black pen. Black pen is preferred. Board
Chapter 18 Exercise 18.1
hapter 18 Eercise 18.1 Q. 1. (i) 180 37 = 143 ( = 143 ) (ii) 180 117 = 63 ( = 63 ) 180 90 = 90 (y = 90 ) (iii) + + 3 + 45 = 180 4.5 = 135 (iv) 180 90 = y 90 = y = 30 45 = y 66 + ( + y) + 47 = 180 + y =
Replacement for a Carpenter s Square
Lesson.1 Skills Practice Name Date Replacement for a arpenter s Square Inscribed and ircumscribed Triangles and Quadrilaterals Vocabulary nswer each question. 1. How are inscribed polygons and circumscribed
General Mathematics Paper 2,May/June
General Mathematics Paper 2,May/June. 2007 Question 1 (a). Evaluate, without using mathematical tables or calculator, (3.69 x 105) / (1.64 x 10-3), leaving your answer in the standard form. (b). A man
Solve problems involving tangents to a circle. Solve problems involving chords of a circle
8UNIT ircle Geometry What You ll Learn How to Solve problems involving tangents to a circle Solve problems involving chords of a circle Solve problems involving the measures of angles in a circle Why Is
3.3. Proving and Applying the Cosine Law. INVESTIGATE the Math
3.3 Proving and pplying the osine Law YOU WILL NEED ruler protractor calculator EXPLORE One side of a right triangle is 8 cm. One angle is 50. What could the other side lengths be? GOL Explain the steps
AREAS RELATED TO CIRCLES
HPTER 1 Points to Remember : RES RELTE T IRLES 1. circle is a collection of points which moves in a plane in such a way that its distance from a fixed point always remains the same. The fixed point is
Core Mathematics 2 Coordinate Geometry
Core Mathematics 2 Coordinate Geometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Coordinate Geometry 1 Coordinate geometry in the (x, y) plane Coordinate geometry of the circle
CIRCULAR MEASURE - SECTORS AND SEGMENTS
Mathematics Revision Guides Circular Measure Page 1 of M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier CIRCULAR MEASURE - SECTORS AND SEGMENTS Version: 3. Date: -10-014 Mathematics
Math 9 Unit 8: Circle Geometry Pre-Exam Practice
Math 9 Unit 8: Circle Geometry Pre-Exam Practice Name: 1. A Ruppell s Griffon Vulture holds the record for the bird with the highest documented flight altitude. It was spotted at a height of about 11 km
Correct substitution. cos = (A1) For substituting correctly sin 55.8 A1
Circular Functions and Trig - Practice Problems (to 07) MarkScheme 1. (a) Evidence of using the cosine rule eg cos = cos Correct substitution eg cos = = 55.8 (0.973 radians) N2 (b) Area = sin For substituting
f(x + y) + f(x y) = 10.
Math Field Day 202 Mad Hatter A A Suppose that for all real numbers x and y, Then f(y x) =? f(x + y) + f(x y) = 0. A2 Find the sum + 2 + 4 + 5 + 7 + 8 + 0 + + +49 + 50 + 52 + 53 + 55 + 56 + 58 + 59. A3
Department of Mathematical and Statistical Sciences University of Alberta
MATH 214 (R1) Winter 2008 Intermediate Calculus I Solutions to Problem Set #8 Completion Date: Friday March 14, 2008 Department of Mathematical and Statistical Sciences University of Alberta Question 1.
ANSWERS. 1. (a) l = rθ or ACB = 2 OA (M1) = 30 cm (A1) (C2) (b) AÔB (obtuse) = 2π 2 (A1) 1. Area = θ r 2 1. = (2π 2)(15) 2 (M1)(A1)
ANSWERS. (a) l = rθ or ACB = OA = 30 cm () (C) (b) AÔB (obtuse) = π () Area = θ r = (π )(5) () = 48 cm (3 sf) () (C [6] 80. AB = rθ = r θ r () =.6 5.4 () = 8 cm () OR (5.4) θ =.6 4 θ =.7 (=.48 radians)
A metal cube of side length 10 cm is melted down and recast as a sphere. Calculate the percentage change in the surface area
CARD 1 A metal cube of side length 10 cm is melted down and recast as a sphere. Calculate the percentage change in the surface area CARD 2 The two shapes have the same perimeter Calculate the difference
E Math (4048/01) Total marks : (a) Simplify 3 2x 1. Answer. [2] (b) Factorise 6x. 2. Factorise completely 4ax 12by 16ay 3bx
![E Math (4048/01) Total marks : (a) Simplify 3 2x 1. Answer. [2] (b) Factorise 6x. 2. Factorise completely 4ax 12by 16ay 3bx](/thumbs/83/88085790.jpg "E Math (4048/01) Total marks : (a) Simplify 3 2x 1. Answer. [2] (b) Factorise 6x. 2. Factorise completely 4ax 12by 16ay 3bx")
Requirement : Answer all questions Total marks : 80 Duration : 2 hour 1. (a) Simplify 3 2x 1 1. Answer. [1] (b) Factorise 6x 18xy. Answer. [1] 2. Factorise completely 4ax 12by 16ay 3bx. Prepared by Mr
IB Mathematics SL Topical Review. Algebra, Functions, and Equations
I Mathematics SL Topical Review All numbered problems are required and are to be worked ON YOUR OWN PAPER and turned in as specified on your assignment sheet. You must show your work. On questions marked
Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.
Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;
Mt. Douglas Secondary
Foundations of Math 11 Section 3.4 pplied Problems 151 3.4 pplied Problems The Law of Sines and the Law of Cosines are particularly useful for solving applied problems. Please remember when using the Law
2015 Canadian Team Mathematics Contest
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 205 Canadian Team Mathematics Contest April 205 Solutions 205 University of Waterloo 205 CTMC Solutions Page 2 Individual Problems.
QUESTION 1 50 FOR JSS 3
QUESTION 1 5 FOR JSS 3 1. The knowledge of probability is necessary for the following reasons except A. In predicting B. In deciding C. In selecting D. In drawing table E. In forecasting. Factorise 7a
Solutionbank C2 Edexcel Modular Mathematics for AS and A-Level
file://c:\users\buba\kaz\ouba\c_rev_a_.html Eercise A, Question Epand and simplify ( ) 5. ( ) 5 = + 5 ( ) + 0 ( ) + 0 ( ) + 5 ( ) + ( ) 5 = 5 + 0 0 + 5 5 Compare ( + ) n with ( ) n. Replace n by 5 and
Math 1201 Review Chapter 2
Math 1201 Review hapter 2 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan Q and tan R. P 12 Q 16 R a. tan Q = 0.428571; tan R = 0.75 c. tan
Minnesota State High School Mathematics League
03-4 Meet, Individual Event Question # is intended to be a quickie and is worth point. Each of the next three questions is worth points. Place your answer to each question on the line provided. You have
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!!! " "
ADDITIONAL MATHEMATICS
00-CE MTH HONG KONG EXMINTIONS UTHORITY HONG KONG CERTIFICTE OF EDUCTION EXMINTION 00 DDITIONL MTHEMTICS 8.0 am.00 am (½ hours) This paper must be answered in English. nswer LL questions in Section and
DEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 2 - C2 2015-2016 Name: Page C2 workbook contents Algebra Differentiation Integration Coordinate Geometry Logarithms Geometric series Series
CBSE Class X Mathematics Sample Paper 03
CBSE Class X Mathematics Sample Paper 03 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
National Quali cations Date of birth Scottish candidate number
N5FOR OFFICIAL USE X847/75/01 National Quali cations 018 Mark Mathematics Paper 1 (Non-Calculator) FRIDAY, 4 MAY 9:00 AM 10:15 AM *X8477501* Fill in these boxes and read what is printed below. Full name
Grade 7/8 Math Circles November 15 & 16, Areas of Triangles
Faculty of Mathematics Waterloo, Ontario NL 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles November 15 & 16, 016 Areas of Triangles In today s lesson, we are going to learn
Mathematical Formulae. Total amount = Curved surface area of a cone = rl. Surface area of a sphere = Volume of a cone = Volume of a sphere =
Mathematical Formulae Compound interest Total amount = r P 1 100 n Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 r Volume of a cone = 1 3 r h Volume of a sphere = 4 r 3 3
ST MARY S DSG, KLOOF GRADE: SEPTEMBER 2017 MATHEMATICS PAPER 2
ST MARY S DSG, KLOOF GRADE: 12 12 SEPTEMBER 2017 MATHEMATICS PAPER 2 TIME: 3 HOURS ASSESSOR: S Drew TOTAL: 150 MARKS MODERATORS: J van Rooyen E Robertson EXAMINATION NUMBER: TEACHER: INSTRUCTIONS: 1. This
Unit 3: Number, Algebra, Geometry 2
Unit 3: Number, Algebra, Geometry 2 Number Use standard form, expressed in standard notation and on a calculator display Calculate with standard form Convert between ordinary and standard form representations
Review exercise 2. 1 The equation of the line is: = 5 a The gradient of l1 is 3. y y x x. So the gradient of l2 is. The equation of line l2 is: y =
Review exercise The equation of the line is: y y x x y y x x y 8 x+ 6 8 + y 8 x+ 6 y x x + y 0 y ( ) ( x 9) y+ ( x 9) y+ x 9 x y 0 a, b, c Using points A and B: y y x x y y x x y x 0 k 0 y x k ky k x a
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Cayley Contest. (Grade 10) Tuesday, February 27, 2018
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 018 Cayley Contest (Grade 10) Tuesday, February 7, 018 (in North America and South America) Wednesday, February 8, 018 (outside of
2001-CE MATH MATHEMATICS PAPER 1 Marker s Examiner s Use Only Use Only Question-Answer Book Checker s Use Only
001-CE MATH PAPER 1 HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 001 Candidate Number Centre Number Seat Number MATHEMATICS PAPER 1 Marker s Use Only Examiner s Use Only
National Quali cations Date of birth Scottish candidate number
N5FOR OFFICIAL USE X847/75/01 National Quali cations 018 Mark Mathematics Paper 1 (Non-Calculator) FRIDAY, 4 MAY 9:00 AM 10:15 AM *X8477501* Fill in these boxes and read what is printed below. Full name
Mensuration Mathematics Revision Guide Page 0 of 47
Name:.. Index:. Mensuration Mathematics Revision Guide www.masdharu.info Page 0 of 47 Mensuration Mathematics Revision Guide www.masdharu.info Page 1 of 47 1. The scale on a map is 1 : 20 000. The area
AS Mathematics Assignment 9 Due Date: Friday 22 nd March 2013
AS Mathematics Assignment 9 Due Date: Friday 22 nd March 2013 NAME GROUP: MECHANICS/STATS Instructions to Students All questions must be attempted. You should present your solutions on file paper and submit
"Full Coverage": Pythagoras Theorem
"Full Coverage": Pythagoras Theorem This worksheet is designed to cover one question of each type seen in past papers, for each GCSE Higher Tier topic. This worksheet was automatically generated by the
EXTENDED MATHEMATICS CLASSIFIEDS GEOMETRY. Compiled & Edited By. Dr. Eltayeb Abdul Rhman. First Edition 2011
EXTENDED MTHEMTIS 2002 2011 LSSIFIEDS GEOMETRY ompiled & Edited y Dr. Eltayeb bdul Rhman www.drtayeb.wordpress.com First Edition 2011 4 7 O y 50 z T is a tangent at to the circle, centre O. ngle O = 50.
CIRCLES MODULE - 3 OBJECTIVES EXPECTED BACKGROUND KNOWLEDGE. Circles. Geometry. Notes
Circles MODULE - 3 15 CIRCLES You are already familiar with geometrical figures such as a line segment, an angle, a triangle, a quadrilateral and a circle. Common examples of a circle are a wheel, a bangle,
Math 5 Trigonometry Review Sheet for Chapter 5
Math 5 Trigonometry Review Sheet for Chapter 5 Key Ideas: Def: Radian measure of an angle is the ratio of arclength subtended s by that central angle to the radius of the circle: θ s= rθ r 180 = π radians.
(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
2010 Fermat Contest (Grade 11)
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 010 Fermat Contest (Grade 11) Thursday, February 5, 010
AREA RELATED TO CIRCLES
CHAPTER 11 AREA RELATED TO CIRCLES (A) Main Concepts and Results Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle
Intermediate Math Circles Wednesday October Problem Set 3
The CETRE for EDUCTI in MTHEMTICS and CMPUTIG Intermediate Math Circles Wednesday ctober 24 2012 Problem Set 3.. Unless otherwise stated, any point labelled is assumed to represent the centre of the circle.
CHAPTER 11 AREAS OF PLANE FIGURES
CHAPTER 11 AREAS OF PLANE FIGURES EXERCISE 45, Page 106 1. Find the angles p and q in diagram (a) below. p = 180-75 = 105 (interior opposite angles of a parallelogram are equal) q = 180-105 - 40 = 35.
Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)
Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) First teaching from September 2017 First certification from June 2018 2
Unit Circle: The unit circle has radius 1 unit and is centred at the origin on the Cartesian plane. POA
The Unit Circle Unit Circle: The unit circle has radius 1 unit and is centred at the origin on the Cartesian plane THE EQUATION OF THE UNIT CIRCLE Consider any point P on the unit circle with coordinates
UNIT 35 Trigonometric Problems: CSEC Revision Test
: 1. Two buildings are 45 metres apart. From a window in one of them, the angle of depression of a window in the other building is 17. 6. How far below the first window is the second window? Give your
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
Chapter-wise questions
hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm
Properties of the Circle
9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference
(Chapter 10) (Practical Geometry) (Class VII) Question 1: Exercise 10.1 Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only. Answer 1: To
Chapter 2. The laws of sines and cosines. 2.1 The law of sines. Theorem 2.1 (The law of sines). Let R denote the circumradius of a triangle ABC.
hapter 2 The laws of sines and cosines 2.1 The law of sines Theorem 2.1 (The law of sines). Let R denote the circumradius of a triangle. 2R = a sin α = b sin β = c sin γ. α O O α as Since the area of a
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
e x for x 0. Find the coordinates of the point of inflexion and justify that it is a point of inflexion. (Total 7 marks)
Chapter 0 Application of differential calculus 014 GDC required 1. Consider the curve with equation f () = e for 0. Find the coordinates of the point of infleion and justify that it is a point of infleion.
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
184/09 MATHEMATICS HIGHER TIER PAPER 1. P.M. MONDAY, 4 June (2 Hours) CALCULATORS ARE NOT TO BE USED FOR THIS PAPER
Candidate Name Centre Number Candidate Number WELSH JOINT EDUCATION COMMITTEE General Certificate of Secondary Education CYD-BWYLLGOR ADDYSG CYMRU Tystysgrif Gyffredinol Addysg Uwchradd 184/09 MATHEMATICS
0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
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 Centre Number Mathematics B Paper 1 Candidate Number Thursday 26 May 2016 Morning Time: 1 hour 30 minutes Paper Reference 4MB0/01
Fundamentals of Mathematics (MATH 1510)
Fundamentals of Mathematics () Instructor: Email: shenlili@yorku.ca Department of Mathematics and Statistics York University March 14-18, 2016 Outline 1 2 s An angle AOB consists of two rays R 1 and R
43005/1H. General Certificate of Secondary Education June 2008
Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education June 2008 MATHEMATICS (MODULAR) (SPECIFICATION B) 43005/1H Module 5
= Find the value of n.
nswers: (0- HKM Heat Events) reated by: Mr. Francis Hung Last updated: pril 0 09 099 00 - Individual 9 0 0900 - Group 0 0 9 0 0 Individual Events I How many pairs of distinct integers between and 0 inclusively
Topic 3 Part 1 [449 marks]
![Topic 3 Part 1 [449 marks]](/thumbs/90/102647102.jpg "Topic 3 Part 1 [449 marks]")
Topic 3 Part [449 marks] a. Find all values of x for 0. x such that sin( x ) = 0. b. Find n n+ x sin( x )dx, showing that it takes different integer values when n is even and when n is odd. c. Evaluate
Practice Test Student Answer Document
Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Meet #4. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Math League SCASD Meet #4 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Circles 3. Number Theory: Modular Arithmetic,
DATE: MATH ANALYSIS 2 CHAPTER 12: VECTORS & DETERMINANTS
NAME: PERIOD: DATE: MATH ANALYSIS 2 MR. MELLINA CHAPTER 12: VECTORS & DETERMINANTS Sections: v 12.1 Geometric Representation of Vectors v 12.2 Algebraic Representation of Vectors v 12.3 Vector and Parametric
Geometry Final Exam Review
Name: Date: Period: Geometry Final Exam Review 1. Fill in the flow chart below with the properties that belong to each polygon. 2. Find the measure of each numbered angle: 3. Find the value of x 4. Calculate