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8 Basic Function Graphs
This outline will assist with a basic understanding of graphing. (Helpful for many areas of math, especially Algebra classes an Pre-Calculus)
£1.25 Preview RemoveElimination By Multiplication
These notes are for Algebra 1 students. Yes, they were made by me, but I no longer need them. With these notes, you will be able to understand elimination by multiplication, in a simple and fast way.
£3.11 Preview RemovePre-Calculus
Pre-calculus math written in a very simple way for better understanding. Lots of examples included to practice
£1.50 Preview RemoveMedian
Here, I easily explained the terms of median in the subject of mathematics. I explain the median with definition and examples as well.
£2.50 Preview RemoveAlgebra _ Simultaneous Equations
Algebra _ Simultaneous Equations The simultaneous equation is an equation that involves two or more quantities that are related using two or more equations. It includes a set of few independent equations. The simultaneous equations are also known as the system of equations, in which it consists of a finite set of equations for which the common solution is sought. To solve the equations, we need to find the values of the variables included in these equations. The system of equations or simultaneous equations can be classified as: Simultaneous linear equations (Or) System of linear equations Simultaneous non-linear equations System of bilinear equations Simultaneous polynomial equations System of differential equations.
£2.50 Preview RemoveSecond Lecture of Calculus II for Physical Sciences
Summary of the contents, with examples, of the second lecture of Calculus II for Physical Sciences at the University of Toronto Scarborough.
£6.25 Preview RemoveLibrary of Functions Piecewise-Defined Functions
This is a study guide all about piecewise functions.
£1.50 Preview RemoveIntroduction for Algorithm and Flowchart
Algorithm is a finite set of instructions that specify the sequence of operations to be carried out in order to solve a specific problem or class of problems. A flowchart is a graphical representation of decisions and their results mapped out in individual shapes.
£562.50 Preview Remove9709 Mathematics Test with Answers
Mathematics Test with Answers that you can try solving to see how well you understand your studies and you can crosscheck with the answer sheet on the back after you finish!!
£1.50 Preview RemoveData structures class notes.
Data structures class notes. this is very helpfull you can easily learn these notes.
£68.75 Preview RemoveExcel for Portfolio Optimization
These notes describe how to use Microsoft Excel to perform a portfolio optimization. These are college level notes but they can also be used for high school classes and AP courses.
£3.75 Preview RemoveFor the given data below mean etc...,
notes of For the given data below mean etc...,
£14.38 Preview RemoveAll formulas you will ever need in Maths!
A must have for students studying maths!
£0.50 Preview RemoveBasic Concepts Of Percentages Aptitude special
Solve the problems in percentages Easy way Aptitude special Editions for competative exams
£6.25 Preview RemoveMétodos de Vogel
Una compañía hidroeléctrica de El Salvador dispone de cuatro plantas de generación para satisfacer la demanda diaria eléctrica de 4 departamentos, San Miguel, San Vicente, San Salvador y La Libertad. Las plantas 1,2,3 y 4 pueden satisfacer 80, 30, 60 y 45 millones de KW al día respectivamente. Las necesidades de los departamentos de San Miguel, San Vicente, San Salvador y La Libertad son de 70, 40, 70 y 35 millones de KW al día respectivamente.
£2.50 Preview RemoveThe 83rd William Lowell Putnam Mathematical Competition, 2022
The William Lowell Putnam Mathematics Competition Is a North American math contest for college students, organized by the Mathematical Association of America (MAA). Each year on the first Saturday in December, several thousands US and Canadian students spend 6 hours (in two sittings) trying to solve 12 problems. This past papers content problems and solutions.
£1.50 Preview RemoveIntegration and differentiation rules
These are math A2 integration and differentiation rules they will help you to solve any questions related to these topics
£2.50 Preview Removegeometry
In order to solve geometric word problems, you will need to have memorized some geometric formulas for at least the basic shapes (circles, squares, right triangles, etc). You will usually need to figure out from the word problem which formula to use, and many times you will need more than one formula for one exercise. So make sure you have memorized any formulas that are used in the homework, because you may be expected to know them on the test. Some problems are just straightforward applications of basic geometric formulae. The radius of a circle is 3 centimeters. What is the circle's circumference? The formula for the circumference C of a circle with radius r is: C = 2(pi)r ...where "pi" (above) is of course the number approximately equal to 22 / 7 or 3.14159. They gave me the value of r and asked me for the value of C, so I'll just "plug-n-chug": C = 2(pi)(3) = 6pi Then, after re-checking the original exercise for the required units (so my answer will be complete): the circumference is 6pi cm. Note: Unless you are told to use one of the approximations for pi, or are told to round to some number of decimal places (from having used the "pi" button on your calculator), you are generally supposed to keep your answer in "exact" form, as shown above. If you're not sure if you should use the "pi" form or the decimal form, use both: "6pi cm, or about 18.85 cm". A square has an area of sixteen square centimeters. What is the length of each of its sides? The formula for the area A of a square with side- length s is: A = s2 They gave me the area, so I'll plug this value into the area formula, and see where this leads: 16 = s2 4 = s After re-reading the exercise to find the correct units, my answer is: The length of each side is 4 centimeters... Most geometry word problems are a bit more involved than the example above. For most exercises, you will be given at least two pieces of information, such as a statement about a square's perimeter and then a question about its area. To find the solution, you will need to know the equations related to the various pieces of information; you will then probably solve one of the equations for a useful bit of new information, and then plug the result into another of the equations. In other words, geometry word problems often aren't simple one-step exercises like the one shown above. But if you take all the information that you've been given, write down any applicable formulas, try to find ways to relate the various pieces, and see where this leads, then you'll almost always end up with a valid answer. A cube has a surface area of fifty-four square centimeters. What is the volume of the cube? The formula for the volume V of a cube with edge- length e is: V = e3 To find the volume, I need the edge-length. Can I use the surface-area information to get what I need? Let's see... A cube has six sides, each of which is a square; and the edges of the cube's faces are the sides of those squares. The formula for the area of a square with side-length e is A = e2. There are six faces so there are six squares, and the cube's total surface area SA must be: SA = 6e2 Plugging in the value they gave me, I get: 54 = 6e2 54 / 6 = (6e2) / 6 9 = e2 3 = e Since the volume is the cube of the edge-length, and since the units on this cube are centimeters, then: the volume is 27 cubic centimeters, or 27 cc, or 27 mL A circle has an area of 49pi square units. What is the length of the circle's diameter? The formula for the area A of a circle with radius r is: A = (pi)r2 I know that radius r is half of the length of the diameter d, so: 49pi = (pi)r2 (49pi) / pi = [(pi)r2] / pi 49 = r2 7 = r Then the radius r has a length of 7 units, and: the length of the diameter is 14 units Warning: You can not assume that you will always be given all the geometric formulae on your tests. At some point, you will need to know at least some of them "by heart". The basic formulae you should know include the formulae for the area and perimeter (or circumference) of squares, rectangles, triangles, and circles; and the surface areas and volumes of cubes, rectangular solids, spheres, and cylinders. Depending on the class, you may also need to know the formulae for cones and pyramids. If you're not sure what your instructor expects, ask now. Sometimes geometry word problems wrap the geometry in a thick layer of "real life". You will need to be able to "see" the geometry, and extract the relevant information. Suppose a water tank in the shape of a right circular cylinder is thirty feet long and eight feet in diameter. How much sheet metal was used in its construction? What they are asking for here is the surface area of the water tank. The total surface area of the tank will be the sum of the surface areas of the side (the cylindrical part) and of the ends. If the diameter is eight feet, then the radius is four feet. The surface area of each end is given by the area formula for a circle with radius r: A = (pi)r2. (There are two end pieces, so I will be multiplying this area by 2 when I find my total-surface-area formula.) The surface area of the cylinder is the circumference of the circle, multiplied by the height: A = 2(pi)rh. Side view of the cylindrical tank, showing the radius "r". An "exploded" view of the tank, showing the three separate surfaces whose areas I need to find. Then the total surface area of this tank is given by: 2 ×( (pi)r2 ) + 2(pi)rh (the two ends, plus the cylinder) = 2( (pi) (42) ) + 2(pi) (4)(30) = 2( (pi) × 16 ) + 240(pi) = 32(pi) + 240(pi) = 272(pi) Since the original dimensions were given in terms of feet, then my area must be in terms of square feet: the surface area is 272(pi) square feet. By the way, this is one of those exercises that doesn't translate well into "real life". In reality, the sheet metal has thickness, and adjustments would be required in order to account for this thickness. For example, if you needed to figure out the amount of sheet metal required to create a tank with a certain volume, you'd have to account for the fact that the volume is on the inside, while the surface area is on the outside. Since the walls of a real-world tank have thickness, the real-world answer would not match the "ideal" mathematical one. A piece of 16-gauge copper wire 42 cm long is bent into the shape of a rectangle whose width is twice its length. Find the dimensions of the rectangle. ADVERTISEMENT Ads by Google Ad covers the page Stop seeing this ad Do I care that the wire is made of copper, or that the wire is a length of sixteen-gauge? No; all I care is that the length is forty-two units, that the units are centimeters, that the rectangle is twice as long in one direction as the other, and that I'm supposed to find the values of each of these directions. I can ignore the other information. Since the wire is 42 centimeters long, then the perimeter of the rectangle is 42 centimeters. That is: 2L + 2W = 42 I also know that the width is twice the length, so: W = 2L Then: Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved 2L + 2(2L) = 42 (by substitution for W from the above equation) 2L + 4L = 42 6L = 42 L = 7 Since the width is related to the length by W = 2L, then W = 14, and the rectangle is 7 centimeters long and 14 centimeters wide. A circular swimming pool with a diameter of 28 feet has a deck of uniform width built around it. If the area of the deck is 60(pi) square feet, find its width. I have this situation: A pool is surrounded by a deck. The pool has radius 14, and the deck has width "d ". If the diameter of the pool is 28, then the radius is 14. The area of the pool is then: (pi)r2 = (pi)(14)2 = 196(pi) Then the total area of the pool plus the surrounding decking is: 196(pi) + 60(pi) = 256(pi) Working backwards from the area formula, I can find the radius of the whole pool-plus-deck area: 256(pi) = (pi)r2 256 = r2 16 = r Since I already know that the pool has a radius of 14 feet, and I now know that the whole area has a radius of 16, then clearly: the deck is two feet wide. If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square. Find the dimensions of the rectangle. I'm starting from a square with sides of some unknown length. The sides of the rectangle are defined in terms of that unknown length. So I'll pick a variable for the unknown side-length, create expressions for the rectangle's sides, and then work from there. square's side length: x one side is doubled: 2x next side is decreased by two: x – 2 square's area: x2 rectangle's area: (2x)(x – 2) = 2x2 – 4x new area is 96 more than old area: 2x2 – 4x = x2 + 96 2x2 – 4x = x2 + 96 x2 – 4x – 96 = 0 (x – 12)(x + 8) = 0 x = 12 or x = –8 I'm supposed to find the dimensions of a rectangle, so can I just erase that one "minus" sign and say that the rectangle is 12 by 8? No! I defined "x" as standing for the side length of the square, not as one of the sides of the rectangle. Looking back at my definitions, I see what "x = 12" (the only reasonable solution for the square) means that the sides of the rectangle have lengths 2(12) and (12) – 2:
£6.25 Preview RemoveFinding the Volume Under a Curve
Calculus 1/2 and Technical Calculus Show you how to find the volume under the curve of a graph
£2.50 Preview RemoveThe 67th William Lowell Putnam Mathematical Competition, 2006
The William Lowell Putnam Mathematics Competition Is a North American math contest for college students, organized by the Mathematical Association of America (MAA). Each year on the first Saturday in December, several thousands US and Canadian students spend 6 hours (in two sittings) trying to solve 12 problems. This past papers content problems and solutions.
£1.50 Preview RemoveLaboratory Activity: Naming and Classification of Chemical Compounds
This is my answer sheet in our laboratory activity in chemistry for engineers subject. This is all about the Naming and Classification of Chemical Compounds.
£2.50 Preview RemoveMathematics - Indices
A pdf which is ideal for teachers as a teaching aid in the teaching learning process. Students can master the lesson of Indices in Algebra. (Intermediate level) Consists of considerable amount of examples.
£3.74 Preview Removecontinuity on an interval
Here you will learn to recognize if a function is called continuous in the closed interval(and also the opened interval ) or not . Hope it's good .
£1.50 Preview RemoveFractions. (Grades 6-8) Part 1
Mathematics fraction notes for grades 6-8 (Part 1)
£3.13 Preview Remove