GRE GEOMETRY AND ARITHMETIC PROBLEMS
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This document contains multiple geometry problems and their solutions: 1) Calculating the area of a shaded portion using Pythagoras theorem. 2) Determining that the relationship between the area of a quadrilateral and a given quantity cannot be determined without more information. 3) Finding that quantity B is greater based on the relationships between variables x and y. 4) Calculating the areas of two rectangles where one length and breadth vary by 10% and 20% respectively from a third rectangle, and determining that the area of rectangle A is greater.
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The document discusses calculating the area of composite figures, which are shapes made up of two or more simple figures. It provides examples of calculating the area of individual shapes like squares, triangles, circles, and trapezoids. It then prompts working through examples of composite figures made up of multiple shapes, explaining that the total area is found by adding the individual areas of each shape together.
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Maths (quadrilateral)
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- There are different types of quadrilaterals defined by their properties, including squares, rectangles, parallelograms, trapezoids, rhombuses, kites, and irregular quadrilaterals.
- The area of each type of quadrilateral is calculated using a specific formula related to its defining properties, such as side lengths, angles, or diagonals. For example, the area of a rectangle is length x width, and the area of a parallelogram is base x height.
- An irregular quadrilateral requires calculating the areas of the two triangles formed by its diagonal and adding them together.
Đề Thi HK2 Toán 8 - THCS EMASI Nam Long
This document is a math exam for grade 8 in Ho Chi Minh City, Vietnam. It contains 39 multiple choice questions testing concepts in algebra, geometry, and measurement. The exam covers solving linear and quadratic equations, properties of similar triangles, calculating lengths and areas of geometric shapes, and word problems involving ratios.
Circumference of a circle
The document discusses the circumference of circles. It defines circumference as the distance around a circle and diameter as the distance across a circle. It presents the formula for circumference which is C=πd, where C is circumference, d is diameter, and π is approximately 3.14. Several examples are given of using the formula to calculate the circumference given the diameter. The document also discusses using the alternative radius-based formula, C=2πr, to find circumference when given the radius instead of the diameter.
Linear equations
The document discusses equations and their properties. It begins by defining an equation as a statement that shows the relationship between two or more quantities. Equations can contain known or unknown quantities. Letters like x, y, z are usually used to denote unknown quantities or variables. The four basic arithmetic operations can be applied to variables as well. Simultaneous equations can be solved using elimination or substitution methods. The nature of solutions to simultaneous equations can be unique, infinite, or none. The document provides examples and explanations of simple equations, solving single-variable equations, and solving simultaneous equations.
Scalars and vectors
Vectors have both magnitude and direction and are represented by arrows. Scalars have only magnitude. There are two main types of operations on vectors: addition and multiplication. Vector addition uses the parallelogram or triangle rule to find the resultant vector. Multiplication of a vector by a scalar changes its magnitude but not direction. The dot product of vectors is a scalar that depends on their relative orientation. The cross product of vectors is another vector perpendicular to both original vectors. Examples demonstrate calculating vector components, additions, subtractions and products.
Qwizdom - Module 5 foundation qwizdom
The document contains a series of math problems covering topics such as area, perimeter, circles, angles, Pythagoras' theorem, simplifying expressions, expanding brackets, solving equations, and graphs. Multiple choice questions are asked relating to calculating values, identifying formulas, finding missing sides of shapes, determining which expression is equivalent, expanding algebraic expressions, solving linear equations, identifying equations of lines from graphs, and interpreting a real-life graph showing speed over time.
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Shares and dividend -Part 2-Class 10 math
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Formulas for system of equations matrix form
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There are formulae for finding the echelon form of a matrix and converting a matrix to its normal form.
Gauss Elimination method and Gauss Jordan method
Gauss Seidel iterative method
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Basic Concepts of Probability
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Permutations of distinct objects
Welcome to my course on Permutations and Combinations.I have a teaching experience of over 2 decades both at the high school level and undergraduate level.
The topic " Permutations and Combinations " have intrigued many students. This is because each problem is different. There is no one magic formula which applies to all problems. Permutations and Combinations is an important topic used extensively in Probability, also useful for the GRE QUANT and GMAT QUANT section. This course is divided into
I. introduction to Permutations
2. Permutations when all objects are not different
3.Circular Permutations
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5. Mixed problems on Combinations.
As a foreword, students taking this course are requested to practice the problems along with me. As an additional practice, you can practice the project. Feel free to contact me for any further help.
For the complete course on skillshare, use the link
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Newton's law of cooling and LR circuits/Engineering Maths
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Introducing videos on demand! Custom made videos on any math topic of your choice from classes 11 to the graduate level. Just drop a mail for your individual requirements.
Trigonometric functions of sums and differences/ class 11 maths
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Engineering maths/Exact Differential equations
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Consider subscribing to this channel for more videos.
http://lnnk.in/@mathmadeeasy22
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http://lnnk.in/@engineering-maths-1
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GRE QUANT: PROBLEMS ON MIXTURES ,HELPFUL TRICKS
This is designed for students preparing for the GRE QUANT section. It explains problems on mixtures and solutions . A helpful technique is illustrated wherein we divide the problems into 2 types. In one type, 2 solutions are mixed and the other type deals with only one solution. Problems are illustrated in a step by step method.
For more videos, consider subscribing to my channel .
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APPROXIMATIONS IN DERIVATIVES
This is a useful topic for class 12 maths students and NATA maths students.
What are approximations?
Here, we use the concept of differential to find the approximate value of a function. We can find the values easily with a calculator as well! If y = f(x), we learn the differential of y, and learn the formulae used to calculate the approximate values of y. This video is application oriented. It focuses on solving problems based on the formula. We also learn about absolute error, approximate error and %error. As a teacher, I have found students getting confused about approximate error and actual value of the function.i have explained the difference in the video. So, watch this video to understand approximations.
This video is useful for Class 12 Maths students , ISC MATHS, CBSE MATHS and other boards.It is also useful for the NATA (maths) aptitude test for architecture
Consider subscribing to my channel for more videos.
Visit my page https://www.mathmadeeasy.co/about
Subscribe to my playlist
https://www.youtube.com/playlist?list=PL26R7TjUyi8zDE3-OcadJuTKlXApnFJG6
For further help, you can enrol for my masterclass on Applications of Derivatives which involves derivative as a rate measure, approximations, tangent and normal, increasing and decreasing functions, maxima and minima problems. Students tend to find this topic difficult.
TYPES OF PARABOLA
This presentation explains the 4 basic types of parabolas. It also shows how the focus, vertex, equation of the axis and directrix can be determined in each case. It also explains how the values change when the origin is shifted.
This is useful for grade eleven maths students.
This channel has videos for grades 11, 12, engineering mathematics and the NATA eligibility test for architecture. Consider subscribing to my channel for more videos.
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Syllabus
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Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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GRE GEOMETRY AND ARITHMETIC PROBLEMS
- 2. 4cm 3 cm 2cm x Calculate area of the shaded portion By Pythagoras theorem x = 5 cm A(rectangle)= 5(2)=10 cm mathews.suman@gmail.com
- 3. A B C D Diameter of the circle is 10 cm Quantity A Quantity B A(quadrilateral ABCD) 40 a) Quantity A is greater b) Quantity B is greater c) The 2 quantities are equal d) The relationship cannot be determined from the information given. Answer is d Even if AC were the diameter of the circle, to determine the area , we need more than 1 side of the figure mathews.suman@gmail.com
- 4. 𝑥2 𝑦 > 0, 𝑥𝑦2 < 0 Quantity A x Quantity B y if 𝑥2 𝑦 > 0, 𝑦 > 0 If x𝑦2 < 0, 𝑥 < 0 Hence y is greater. Answer = B mathews.suman@gmail.com
- 5. Given 3 rectangles A, B, C, The length of rectangle A IS 10 % more than the length of C and the breadth of A is 10 % lesser than the breadth of C. The length of rectangle B is 20 % more than the length of rectangle C The breadth of rectangle B is 20 % lesser than the breadth of rectangle C. Quantity A A(rectangle A) Quantity B A(rectangle B) C x y A 1.1x 0.9y B 1.2x 0.8y mathews.suman@gmail.com
- 6. A(rectangle A ) = 1.1x(0.9y)=0.99xy A(rectangle B)= 1.2x (0.8y) = .96xy A (rectangle A ) is greater Ans : = Quantity A mathews.suman@gmail.com