Borehole Problems. Horizontal Level Ground. Boreholes Sunk on Horizontal Ground. Depth Diagram (Not to Scale)
|
|
- Virgil Curtis
- 6 years ago
- Views:
Transcription
1 Borehole roblems 43 4 Borehole roblems Horizontal Level Ground In order to determine the subsurface geology of an area, boreholes are sunk at convenient places in areas such as cultivated lands, forests deserts, alluvium, etc. The surface is completely covered and the outcrops are very few. Such boreholes reveal the presence of economic deposits of coal, petroleum, etc. The subsurface geological formations, rock types and their dip and strike can be determined from such borehole data, which render very valuable information for plans to exploit the hidden treasures. Boreholes Sunk on Horizontal Ground Example: 1. Three boreholes are sunk at three points of an equilateral triangle whose sides are 480 m each. Is West of Q and R is North of midpoint Q? Boreholes and R-reach the upper surface of a rich coal seam at,, and 260 m depths respectively. (a) Determine the attitude (Dip and strike) of the coal seam. (b) Another borehole is sunk at S, midpoint of QR. Determine at what depth the borehole S reaches the coal seam. Depth Diagram (Not to Scale) rocedure: Construct an equilateral triangle with a suitable scale. Show the positions of the boreholes. The coal seam is reached at point and Q at and. So the coal seam dips from to Q. To determine the inclination (gradient) along Q construct through sketch depth diagram and determine the gradient it is 120 m in 480 m. So it is 1 in 4. Similarly construct the depth diagram along R it is 160 m in 480 m i.e. 1 in 3. Take convenient scale and mark 4 units along Q and 3 units along R from. They are A and B. Join AB and extend. It is the true strike direction (TSD). Draw a perpendicular to AB from. It cuts AB at C. Measure C it is 2.85 i.e. the gradient is 1 in It is true dip. Gradient of Q 120/480 = 1 in 4 Gradient of R 160/480 = 1 in 3
2 44 Applied Engineering Geology racticals Q R 260 m 120 m 1 in 4 1 in m Fig. 4.1 To determine the direction of true dip, measure the angles CQ = 45. So direction of true dip is the complementary angle from North direction so (90 45 ) 45. So it is N45 E or NE. True dip 1 in 2.85 along NE. Strike = SE and NW. To determine the depth at which the borehole S reaches the coal seam, join S it intersects AB line (true strike direction) at T. Measure T with units selected it is 3 cm. So the gradient along T is 1 in 3. Measure S it is 4.2 cm = 420 m. Depth = Horizontal distance S Gradient + Depth of borehole at = 420 1/ = = 240 m To check whether this calculation is correct or not, let us find out the gradient of coal seam along QR. Draw depth diagram. The Gradient is 1 in 12 from Q, QS is 240 m. Q 480 m R 480 m 1 in 12 Fig. 4.2
3 Borehole roblems 45 Depth = (Horizontal distance Gradient) + Depth of Borehole Q = 240 1/ = = 240 m Scale 1 cm = Gradient 1 cm = 1 unit. R B S N C T 1 in 2.85 TSD A Q Fig Three boreholes are sunk at SW, SE, and NW corners of square level ground. The side of the square is 150 m long. The boreholes are X, Y, Z respectively. The boreholes meet the coal seam at 15 m, in X, 45 m in Y, and 60 m in Z. (a) Determine the attitude of the coal seam. (b) Fourth borehole is proposed at, the NE corner of the square land. Calculate at what depth, the borehole encounters the coal seam. Depth Diagram (Not to Scale) Y X Z 15 M 150 m 150 m 15 m 45 m 1 in 5 1 in 3 65 m 30 M 50 m Gradient of XY = 30/150 =1 in 5 Gradient of XZ = 50/150 = 1 in 3 Fig. 4.4
4 46 Applied Engineering Geology racticals Scale 1 cm = 30 m Gradient Scale 1cm = 1 unit Z A N 1 in in 2.7 T 710 M TST X 150 metres Fig. 4.5 Y B True depth = 1 in 2.55 along North 30 E Strike = N60 W and S60 E Depth of unknown point = Horizontal distance Gradient + Depth of borehole at minimum depth = 216 1/ = = 95 m EXERCISE 1. Four boreholes are proposed at A, B, C, D at corners of a featureless square land. The sides of the square land are 360 m long. A is West of B and D is South of B. A coal seam is encountered in at 160 m, in B at 60 m and in D at 240 m. (a) Determine the attitude of the coal seam. (b) Another borehole is proposed at C. Calculate at what depth it reaches the coal seam. [Ans. (a) True dip 1 in 1.65 along S35 W, Strike S55 E and N 55 W; (b) Depth at borehole C = 360 m] 2. Three boreholes are sunk at the corners of an isosceles triangle. The base AB is East West 400 m. A is West of B, C borehole is 500 m from A and B and North of midpoint AB. The boreholes touch the oil-bearing stratum in A at 30 m, in B 80 m and in C 130 m. (a) Determine the attitude of the oil-bearing stratum. (b) Another borehole is proposed at midpoint of BC. Calculate at what depth the same oil bearing stratum is met. [Ans. (a) True dip 1 in 4.8 along N23 E, Strike N67 W and S67 E; (b) Depth at midpoint BC = 105 m] (Contd.)
5 Borehole roblems Boreholes are sunk at the corners of a scalene triangle on a featureless ground. AB is 500 m, BC is 600 m and AC is 400 m. B is West of C and A is on the Northern side of BC. The boreholes A, B and C meet a coal seam at 150 m, 350 m and 250 m respectively. (a) Determine the true dip and strike of the coal seam. (b) A borehole is proposed on BC line due south of A. Calculate at what depth the same coal seam is met in the proposed borehole. [Ans. (a) True dip 1 in 2.25 along S23 W, Strike S67 E and N67 W; (b) Depth in proposed borehole 285 m] 4. Three boreholes are sunk at three points ABC of an equilateral triangle whose sides are 600 m each. B is West of C and A is North of midpoint of BC. Boreholes ABC reach the coal seam at 20 m, 50 m and 60 m depth respectively. Determine (a) The attitude of the coal seam. (b) Another borehole is at D at a distance of 1000 m from A. Determine at what depth the borehole D reaches the coal seam. [Ans. Depth in proposed borehole is 89 m]
EAS 233 Geologic Structures and Maps Winter Miscellaneous practice map exercises. 1. Fault and separation:
Miscellaneous practice map exercises 1. Fault and separation: With respect to Map 1, what are (a) the orientation of the fault, and (b) the orientation of bedding in the units cut by the fault. (c) Mark
More informationCircles, Mixed Exercise 6
Circles, Mixed Exercise 6 a QR is the diameter of the circle so the centre, C, is the midpoint of QR ( 5) 0 Midpoint = +, + = (, 6) C(, 6) b Radius = of diameter = of QR = of ( x x ) + ( y y ) = of ( 5
More informationReview 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
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationMEP Pupil Text 13-19, Additional Material. Gradients of Perpendicular Lines
Graphs MEP Pupil Text -9, Additional Material.B Gradients of Perpendicular Lines In this section we explore the relationship between the gradients of perpendicular lines and line segments. Worked Example
More informationLAB 1: ORIENTATION OF LINES AND PLANES
LAB 1: ORIENTATION OF LINES AND PLANES Read the introductory section, chapter 1, pages 1-3, of the manual by Rowland et al (2007) and make sure you understand the concepts of bearing, strike, dip, trend,
More informationName. GEOL.5220 Structural Geology Faults, Folds, Outcrop Patterns and Geologic Maps. I. Properties of Earth Materials
I. Properties of Earth Materials GEOL.5220 Structural Geology Faults, Folds, Outcrop Patterns and Geologic Maps Name When rocks are subjected to differential stress the resulting build-up in strain can
More informationMAPS AND CROSS SECTIONS (I)
GG303 Lab 3 8/27/09 1 MAPS AND CROSS SECTIONS (I) I Main Topics A Three point problems B Rule of vees C Map interpretation and cross sections II Three point problems (see handout) A Three points define
More informationMath 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
More information(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
More information3D GEOMETRY. 3D-Geometry. If α, β, γ are angle made by a line with positive directions of x, y and z. axes respectively show that = 2.
D GEOMETRY ) If α β γ are angle made by a line with positive directions of x y and z axes respectively show that i) sin α + sin β + sin γ ii) cos α + cos β + cos γ + 0 Solution:- i) are angle made by a
More informationAnswers: Internal Processes and Structures (Isostasy)
Answers: Internal Processes and Structures (Isostasy) 1. Analyse the adjustment of the crust to changes in loads associated with volcanism, mountain building, erosion, and glaciation by using the concept
More informationTriangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?
Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel
More informationStructural Geology Lab. The Objectives are to gain experience
Geology 2 Structural Geology Lab The Objectives are to gain experience 1. Drawing cross sections from information given on geologic maps. 2. Recognizing folds and naming their parts on stereoscopic air
More informationStructural Geology Lab. The Objectives are to gain experience
Geology 2 Structural Geology Lab The Objectives are to gain experience 1. Drawing cross sections from information given on geologic maps. 2. Recognizing folds and naming their parts on stereoscopic air
More informationGeometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES
Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Warm-Up 1.) What is the distance between the points (2, 3) and (5, 7). 2.) If < 1 and < 2 are complements, and m < 1 = 49, then what is
More information2010 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
More informationA.M. TUESDAY, 12 May hours
Candidate Name Centre Number 2 Candidate Number GCE AS/A level 1212/01 New AS GEOLOGY - GL2a Investigative Geology A.M. TUESDAY, 12 May 2009 1 1 2 hours For Examiner s Use Only ADDITIONAL MATERIALS In
More informationUnit 8. ANALYTIC GEOMETRY.
Unit 8. ANALYTIC GEOMETRY. 1. VECTORS IN THE PLANE A vector is a line segment running from point A (tail) to point B (head). 1.1 DIRECTION OF A VECTOR The direction of a vector is the direction of the
More informationCO-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 informationIn this lab, we will study and analyze geologic maps from a few regions, including the Grand Canyon, western Wyoming, and coastal California.
Name: Lab Section: work in groups, but each person turns in his/her own GEOSCIENCE 001 LAB UNDERSTANDING GEOLOGIC MAPS Geologic maps are colorful and even beautiful, but they also contain an amazing amount
More informationUNDERSTANDING GEOLOGIC M APS
Name: Lab Section: work in groups, but each person turns in his/her own GEOSCIENCE 001 L AB UNDERSTANDING GEOLOGIC M APS Geologic maps are colorful and even beautiful, but they also contain an amazing
More informationThe 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
More informationMTH 250 Graded Assignment 4
MTH 250 Graded Assignment 4 Measurement Material from Kay, sections 2.4, 3.2, 2.5, 2.6 Q1: Suppose that in a certain metric geometry* satisfying axioms D1 through D3 [Kay, p78], points A, B, C and D are
More information6. 地質圖 6.1 岩層於地形圖上的分布 6.2 地質剖面圖 6.3 地質圖判識 地調所五萬分之一地質圖台中圖幅
6. 地質圖 6.1 岩層於地形圖上的分布 6.2 地質剖面圖 6.3 地質圖判識 A geological shows how geological features (rock units, faults, etc.) are distributed across a region. It is a twodimensional representation of part of the Earth
More informationAdditional Mathematics Lines and circles
Additional Mathematics Lines and circles Topic assessment 1 The points A and B have coordinates ( ) and (4 respectively. Calculate (i) The gradient of the line AB [1] The length of the line AB [] (iii)
More informationCHAPTER 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
More informationA. Refer to Appendix F in back of lab manual for list of commonly used geologic map symbols
Structural Geology Lab 2: Outcrop Patterns and Structure Contours I. Geologic Map Symbols A. Refer to Appendix F in back of lab manual for list of commonly used geologic map symbols 1. Emphasis: a. strike
More informationQ1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians
Class: VII Subject: Math s Topic: Properties of triangle No. of Questions: 20 Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. Greater
More informationb g 6. P 2 4 π b g b g of the way from A to B. LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON ASSIGNMENT DUE
A Trig/Math Anal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON HW NO. SECTIONS (Brown Book) ASSIGNMENT DUE V 1 1 1/1 Practice Set A V 1 3 Practice Set B #1 1 V B 1
More informationName Date. Parent comment: Triangles Levels 4-6 (15-20 mins)
Name Date Farsley Farfield Primary School Parent comment: Triangles Levels 4-6 (15-20 mins) Q1. Here are six triangles. One of them is an equilateral triangle. Put a tick ( ) in the equilateral triangle.
More informationYear 11 Math Homework
Yimin Math Centre Year 11 Math Homework Student Name: Grade: Date: Score: Table of contents 8 Year 11 Topic 8 Trigonometry Part 5 1 8.1 The Sine Rule and the Area Formula........................... 1 8.1.1
More informationDownloaded from
Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar
More informationMidterm Review Packet. Geometry: Midterm Multiple Choice Practice
: Midterm Multiple Choice Practice 1. In the diagram below, a square is graphed in the coordinate plane. A reflection over which line does not carry the square onto itself? (1) (2) (3) (4) 2. A sequence
More informationGeo 303 Lab 6 9/8/09 1 LAB 6 - ROTATIONS
Geo 303 Lab 6 9/8/09 1 LAB 6 - ROTATIONS Exercise 1: Apparent dip problem (28 points total) 1a) An apparent dip of 52 to the southwest is measured for a bedding plane in a vertical cross section that strikes
More informationStraight Line. SPTA Mathematics Higher Notes
H Straight Line SPTA Mathematics Higher Notes Gradient From National 5: Gradient is a measure of a lines slope the greater the gradient the more steep its slope and vice versa. We use the letter m to represent
More informationGEOLOGY - GL4 INTERPRETING THE GEOLOGICAL RECORD
Candidate Name Centre Number 2 Candidate Number GCE A level 1214/01 GEOLOGY - GL4 INTERPRETING THE GEOLOGICAL RECORD A.M. MONDAY, 21 June 2010 2 hours Section A 1. 2. 3. 15 15 15 1214 01 01 4. 15 Section
More informationGM1.1 Answers. Reasons given for answers are examples only. In most cases there are valid alternatives. 1 a x = 45 ; alternate angles are equal.
Cambridge Essentials Mathematics Extension 8 GM1.1 Answers GM1.1 Answers Reasons given for answers are examples only. In most cases there are valid alternatives. 1 a x = 45 ; alternate angles are equal.
More informationDisproving Conjectures with Counterexamples
Disproving Conjectures with Counterexamples Consider the simple conjecture given below. If two lines are both intersected by a transversal, then they are parallel. This conjecture is false: two lines do
More informationStructural Geology, GEOL 330 Fold mapping lab: Even folds get parasites Spring, 2012
Structural Geology, GEOL 330 Name: Fold mapping lab: Even folds get parasites Spring, 2012 This exercise is meant to mimic a field experience in which you, the student, will measure beddingcleavage relationships
More informationMathematics. Knox Grammar School 2012 Year 11 Yearly Examination. Student Number. Teacher s Name. General Instructions.
Teacher s Name Student Number Kno Grammar School 0 Year Yearly Eamination Mathematics General Instructions Reading Time 5 minutes Working Time 3 hours Write using black or blue pen Board approved calculators
More informationcos/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.
More information9.7 Extension: Writing and Graphing the Equations
www.ck12.org Chapter 9. Circles 9.7 Extension: Writing and Graphing the Equations of Circles Learning Objectives Graph a circle. Find the equation of a circle in the coordinate plane. Find the radius and
More informationSample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours
Sample Question Paper Mathematics First Term (SA - I) Class IX Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided
More informationlecture 8 Methods of Structural Geology This lecture Mas Rabassers de Dalt (Spain) Mas Rabassers de Dalt (Spain)
This lecture Methods of Structural Geology lecture 8 Discuss the plotting exercise on Mas Rabassers de Dalt Look at folding related to shear zones Show an example of the application of new theory: Cap
More informationAlgebra 1. Predicting Patterns & Examining Experiments. Unit 5: Changing on a Plane Section 4: Try Without Angles
Section 4 Examines triangles in the coordinate plane, we will mention slope, but not angles (we will visit angles in Unit 6). Students will need to know the definition of collinear, isosceles, and congruent...
More information1. The unit vector perpendicular to both the lines. Ans:, (2)
1. The unit vector perpendicular to both the lines x 1 y 2 z 1 x 2 y 2 z 3 and 3 1 2 1 2 3 i 7j 7k i 7j 5k 99 5 3 1) 2) i 7j 5k 7i 7j k 3) 4) 5 3 99 i 7j 5k Ans:, (2) 5 3 is Solution: Consider i j k a
More informationEdexcel New GCE A Level Maths workbook Circle.
Edexcel New GCE A Level Maths workbook Circle. Edited by: K V Kumaran kumarmaths.weebly.com 1 Finding the Midpoint of a Line To work out the midpoint of line we need to find the halfway point Midpoint
More informationGeometry First Semester Exam Review
Geometry First Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name three points that are collinear. a. points T, Q, and R c. points
More informationCHAPTER 12 HERON S FORMULA Introduction
CHAPTER 1 HERON S FORMULA 1.1 Introduction You have studied in earlier classes about figures of different shapes such as squares, rectangles, triangles and quadrilaterals. You have also calculated perimeters
More informationActivity Submitted by Tim Schroeder, Bennington College,
Structural Analysis of a Hot Dry Rock Geothermal Energy System Activity Submitted by Tim Schroeder, Bennington College, tschroeder@bennington.edu Description: This project applies basic geologic skills
More information11.1 Three-Dimensional Coordinate System
11.1 Three-Dimensional Coordinate System In three dimensions, a point has three coordinates: (x,y,z). The normal orientation of the x, y, and z-axes is shown below. The three axes divide the region into
More informationThe gradient of the radius from the centre of the circle ( 1, 6) to (2, 3) is: ( 6)
Circles 6E a (x + ) + (y + 6) = r, (, ) Substitute x = and y = into the equation (x + ) + (y + 6) = r + + + 6 = r ( ) ( ) 9 + 8 = r r = 90 = 0 b The line has equation x + y = 0 y = x + y = x + The gradient
More informationAnswers. Investigation 4. ACE Assignment Choices. Applications. The number under the square root sign increases by 1 for every new triangle.
Answers Investigation 4 ACE Assignment Choices Problem 4. Core, Other Connections 6 Problem 4. Core, 4, Other Applications 6 ; Connections 7, 6, 7; Extensions 8 46; unassigned choices from earlier problems
More informationSeismic tests at Southern Ute Nation coal fire site
Seismic tests at Southern Ute Nation coal fire site Sjoerd de Ridder and Seth S. Haines ABSTRACT We conducted a near surface seismic test at the Southern Ute Nation coal fire site near Durango, CO. The
More informationBasic Trigonometry. Trigonometry deals with the relations between the sides and angles of triangles.
Basic Trigonometry Trigonometry deals with the relations between the sides and angles of triangles. A triangle has three sides and three angles. Depending on the size of the angles, triangles can be: -
More informationThe Theorem of Pythagoras
CONDENSED LESSON 9.1 The Theorem of Pythagoras In this lesson you will Learn about the Pythagorean Theorem, which states the relationship between the lengths of the legs and the length of the hypotenuse
More informationNCERT Solutions for Class 7 Maths Chapter 14
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Class 7 Chapter 14 Symmetry Exercise 14.1, 14.2, 14.3 Solutions Exercise 14.1 : Solutions of Questions on Page Number : 268 Q1 : Copy the figures with
More information7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.
1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition
More informationGrade 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
More informationTest Corrections for Unit 1 Test
MUST READ DIRECTIONS: Read the directions located on www.koltymath.weebly.com to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are
More informationAREAS OF PARALLELOGRAMS AND TRIANGLES
AREAS OF PARALLELOGRAMS AND TRIANGLES Main Concepts and Results: The area of a closed plane figure is the measure of the region inside the figure: Fig.1 The shaded parts (Fig.1) represent the regions whose
More informationKing Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question
More information(b) the equation of the perpendicular bisector of AB. [3]
HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Coordinate Geometr 1 Set 1 1 In the figure, ABCD is a rhombus with coordinates A(2, 9) and C(8, 1). The diagonals AC and BD cut at
More information10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152]
foot of the altitude of ABM from M and let A M 1 B. Prove that then MA > MB if and only if M 1 A > M 1 B. 8. If M is the midpoint of BC then AM is called a median of ABC. Consider ABC such that AB < AC.
More informationUNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 9: Proving Theorems About Triangles Instruction
Prerequisite Skills This lesson requires the use of the following skills: identifying and using vertical angles, supplementary angles, and complementary angles to find unknown angle measures recognizing
More informationCoordinate Geometry and Pythagorean Theorem Practice [197 marks]
Coordinate Geometry and Pythagorean Theorem Practice [197 marks] The diagram shows a right triangular prism, ABCDEF, in which the face ABCD is a square. AF = 8 cm, BF = 9.5 cm, and angle BAF is 90. Calculate
More informationGeometry Essentials ( ) Midterm Review. Chapter 1 For numbers 1 4, use the diagram below. 1. Classify as acute, obtuse, right or straight.
Geometry Essentials (2015-2016) Midterm Review Name: Chapter 1 For numbers 1 4, use the diagram below. 1. Classify as acute, obtuse, right or straight. 2. is a linear pair with what other angle? 3. Name
More informationGeometry. Class Examples (July 1) Paul Yiu. Department of Mathematics Florida Atlantic University. Summer 2014
Geometry lass Examples (July 1) Paul Yiu Department of Mathematics Florida tlantic University c b a Summer 2014 21 Example 11: Three congruent circles in a circle. The three small circles are congruent.
More informationGeology 12 FINAL EXAM PREP. Possible Written Response Exam Questions
Geology 12 FINAL EXAM PREP Possible Written Response Exam Questions Use this study guide to prepare for the written response portion of the final exam. Name FINAL EXAM - POSSIBLE WRITTEN RESPONSE QUESTIONS
More informationGG303 Lecture 17 10/25/09 1 MOHR CIRCLE FOR TRACTIONS
GG303 Lecture 17 10/5/09 1 MOHR CIRCLE FOR TRACTIONS I Main Topics A Stresses vs. tractions B Mohr circle for tractions II Stresses vs. tractions A Similarities between stresses and tractions 1 Same dimensions
More information5-1 Practice Form K. Midsegments of Triangles. Identify three pairs of parallel segments in the diagram.
5-1 Practice Form K Midsegments of Triangles Identify three pairs of parallel segments in the diagram. 1. 2. 3. Name the segment that is parallel to the given segment. 4. MN 5. ON 6. AB 7. CB 8. OM 9.
More informationSUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX. Time allowed : 3 hours Maximum Marks :90
SUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX Time allowed : 3 hours Maximum Marks :90 General Instructions: i. All questions are compulsory. ii. The question paper consists of 34 questions divided
More informationStructural Style and Tectonic Evolution of the Nakhon Basin, Gulf of Thailand
Structural Style and Tectonic Evolution of the Nakhon Basin, Gulf of Thailand Piyaphong Chenrai Petroleum Geoscience Program, Department of Geology, Faculty of Science, Chulalongkorn University, Bangkok
More informationName: Period: Date: Given: is the bisector of Draw JD and DL such that it makes triangle DJL. Then answer the question. a. 17 b. 73 c. 118 d.
Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement is not necessarily true? Name: Given: is the bisector of Draw JD and DL such that it makes
More informationGRAAD 12 NATIONAL SENIOR CERTIFICATE GRADE 10
GRAAD 12 NATIONAL SENIOR CERTIFICATE GRADE 10 TECHNICAL MATHEMATICS EXEMPLAR 2016 MARKS: 100 TIME: 2 hours This question paper consists of 9 pages and 1 diagram sheet. Technical Mathematics/P2 2 DBE/2016
More informationIntermediate Math Circles for Wednesday 13 October 2010
University of Waterloo Faculty of Mathematics entre for ducation in Mathematics and omputing Intermediate Math ircles for Wednesday 13 October 2010 2. Intermediate Week 1 roblem Set 1: Solving More roblems
More informationMathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.
() Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other
More informationNozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite
More informationPage 1 of 8 Name: 1. Write in symbolic form the inverse of ~p q. 1. ~q p 2. q ~ p 3. p q 4. p ~ q 2. In symbolic form, write the contrapositive of p ~q. 1. q ~ p 2. ~p ~q 3. ~p q 4. ~q p 3. Figure 1 In
More informationA shape which can be divided by a straight line, so that each part is the mirror image of the other has reflective symmetry.
SYMMETRY There are two kinds of symmetry: a) reflective symmetry b) rotational symmetry a) Reflective Symmetry A shape which can be divided by a straight line, so that each part is the image of the other
More information1. Town A is 48 km from town B and 32 km from town C as shown in the diagram. A 48km
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
More information, correct to 4 significant figures?
Section I 10 marks Attempt Questions 1-10 Allow about 15 minutes for this section Use the multiple-choice answer sheet for Questions 1-10. 1 What is the basic numeral for (A) 0.00045378 (B) 0.0004538 (C)
More informationGEOL 3700 STRUCTURE AND TECTONICS LABORATORY EXERCISE 3
GEOL 3700 STRUCTURE AND TECTONICS LABORATORY EXERCISE 3 Goals: 1. Improve your map-reading and map-making skills. 2. Learn to generate and interpret structure contour maps. 3. Learn to generate and interpret
More informationPreliminary Mathematics
NORTH SYDNEY GIRLS HIGH SCHOOL 2011 YEARLY EXAMINATION Preliminary Mathematics General Instructions Reading Time 5 minutes Working Time 2 hours Write using black or blue pen Board-approved calculators
More informationProperties of Isosceles and Equilateral Triangles
Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg
More informationMHR Principles of Mathematics 10 Solutions 1
Course Review Note: Length and angle measures may vary slightly due to rounding. Course Review Question Page 8 a) Let l represent the length and w represent the width, then l + w 0. n+ q b) If n represents
More informationHorizontal gradient and band-pass filter of aeromagnetic data image the subsurface structure; Example from Esh El Mellaha Area, Gulf of Suez, Egypt.
Horizontal gradient and band-pass filter of aeromagnetic data image the subsurface structure; Example from Esh El Mellaha Area, Gulf of Suez, Egypt. Essam Aboud 1, Serguei Goussev 2, Hassan Hassan 2, Suparno
More informationCourse End Review Grade 10: Academic Mathematics
Course End Review Grade 10: Academic Mathematics Linear Systems: 1. For each of the following linear equations place in y = mx + b format. (a) 3 x + 6y = 1 (b) 4 x 3y = 15. Given 1 x 4y = 36, state: (a)
More informationBC VECTOR PROBLEMS. 13. Find the area of the parallelogram having AB and AC as adjacent sides: A(2,1,3), B(1,4,2), C( 3,2,7) 14.
For problems 9 use: u (,3) v (3, 4) s (, 7). w =. 3u v = 3. t = 4. 7u = u w (,3,5) 5. wt = t (,, 4) 6. Find the measure of the angle between w and t to the nearest degree. 7. Find the unit vector having
More informationTu D Understanding the Interplay of Fractures, Stresses & Facies in Unconventional Reservoirs - Case Study from Chad Granites
Tu D201 04 Understanding the Interplay of Fractures, Stresses & Facies in Unconventional Reservoirs - Case Study from Chad Granites D. Lirong (Chinese National Petroleum Company Ltd. (Chad)), C. Shrivastava*
More informationLog1 Contest Round 2 Theta Geometry
008 009 Log Contest Round Theta Geometry Name: Leave answers in terms of π. Non-integer rational numbers should be given as a reduced fraction. Units are not needed. 4 points each What is the perimeter
More informationTwitter: @Owen134866 www.mathsfreeresourcelibrary.com Prior Knowledge Check 1) Find the point of intersection for each pair of lines: a) y = 4x + 7 and 5y = 2x 1 b) y = 5x 1 and 3x + 7y = 11 c) 2x 5y =
More informationPROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS - APPLICATIONS OF DERIVATIVES Page ( ) Water seeps out of a conical filter at the constant rate of 5 cc / sec. When the height of water level in the cone is 5 cm, find the rate at which the height
More informationEdexcel New GCE A Level Maths workbook
Edexcel New GCE A Level Maths workbook Straight line graphs Parallel and Perpendicular lines. Edited by: K V Kumaran kumarmaths.weebly.com Straight line graphs A LEVEL LINKS Scheme of work: a. Straight-line
More informationNAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39
NAME: Date: HOMEWORK: C1 Question Obtained 1 2 3 4 5 6 7 8 9 10 Total/100 A 80 B 70 C 60 D 50 E 40 U 39 1. Figure 2 y A(1, 7) B(20, 7) D(8, 2) O x C(p, q) The points A(1, 7), B(20, 7) and C(p, q) form
More information2005 Pascal Contest (Grade 9)
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 005 Pascal Contest (Grade 9) Wednesday, February 3, 005
More informationMPM 2DI EXAM REVIEW. Monday, June 19, :30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED *
NAME: MPM DI EXAM REVIEW Monday, June 19, 017 11:30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED * Please Note: Your final mark in this course will be calculated as the better of:
More informationb UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100
Circles 6F a U(, 8), V(7, 7) and W(, ) UV = ( x x ) ( y y ) = (7 ) (7 8) = 8 VW = ( 7) ( 7) = 64 UW = ( ) ( 8) = 8 Use Pythagoras' theorem to show UV UW = VW 8 8 = 64 = VW Therefore, UVW is a right-angled
More informationWriting: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line?
Writing: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary
More information