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Algebraic operations are critical to many fields of study. In science, they are used to calculate forces to accelerate a car or determine the rate of a chemical reaction. In engineering, they can be used to design safe and efficient systems. They also underpin algorithms and data structures, which are...
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Find out how to replace pronumerals with numbers in a formula to get a numerical value for some quantity. In many courses you will be required to use formulae to calculate something of interest. The process of substituting numbers for pro-numerals in an expression or formula is called substitution. Pro-numerals...
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What do I do with the brackets? Brackets are useful to group numbers, pronumerals and operations together as a whole. Whatever is around the brackets affects all the things inside the brackets. Brackets are commonly used to express mathematical formulae. In order to manipulate expressions containing brackets it is necessary...
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How do I deal with fractions involving pronumerals? Adding and subtracting fractions always requires a common denominator (which is the lower half of the fraction). These need to be the same before you can add or subtract. This means converting some of the fractions to forms that are consistent in...
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What is an algebraic fraction? The numerator (top) or denominator (bottom) of a fraction can be in algebraic form involving numbers and variables (represented by pronumerals or letters). We cover the multiplication and division of fractions containing algebraic terms. Simplifying fractions You have probably seen numerical fractions like \(\frac{18}{24}\) before....
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Let's take a look at algebraic fractions where the denominator is a quadratic expression. Such fractions are common in mathematics and engineering. More complicated algebraic fractions can involve polynomials of any order. However in your studies, it is unlikely that you will have to deal with polynomials higher than quadratics....
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Find out how to express an algebraic fraction as a sum of simpler algebraic fractions (partial fractions). The method of partial fractions involves breaking up an algebraic fraction into simpler parts that are added together. This is useful in integration and in finding inverse Laplace and Fourier transforms. Adding fractions...
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Rearranging formulas, also called transposition of formulas, is a necessary skill for most courses. Let's work on some essential skills in manipulating formulas. Introduction Some of the most important equations that we might be required to transpose occur frequently in science, engineering and economics. They are called formulae and give...
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Learn how to manipulate or rearrange formulas that involve fractions and brackets. Formulas are used in many branches of economics, science and engineering. For example, the formula for simple interest is:1 Note that when we write \(nr\) we mean \(n\times r\). Most of the time we ignore the multiplication sign...
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Are you still trying to get that variable on its own from the formula, but it is in a tricky place – or maybe it appears more than once? Here we demonstrate manipulating or rearranging complex formulas, with overviews and practice questions. Let's look at some more complicated formulas where...
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A common factor is a number or pronumeral that is common to terms in an algebraic expression. Removing the common factors allows us to factorise algebraic expressions and write them in a simpler form. Factorisation using common factors is a basic skill in mathematics so we'll discuss that too. Expansion...
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The idea of a perfect square permeates mathematics and especially algebra. Properties of perfect squares will help you in factorising and expanding algebraic expressions. An understanding of perfect squares is essential for success in mathematics. A perfect square is something like \(5^{2}, x^{2}\) or \(\left(x+1\right)^{2}\). In this module we deal...
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What is the Difference of two squares (DOTS) rule? If you have a squared expression subtracted from another squared expression, you can factorise this quickly according to the DOTS rule. The difference of two squares formula is commonly used in mathematics. It allows us to factorise terms such as \[\begin{align*}...
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Quadratic expressions have the general form \[ax^2+bx+c\] where \(a\), \(b\) and \(c\) are real numbers and \(a\neq 0\). Quadratics frequently arise in mathematics, science and engineering. This module explains how to factorise a quadratic into two linear factors. For example \[x^2+5x+6 = \left(x+2\right)\left(x+3\right).\] The general form of a quadratic expression...
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Quadratic expressions have the general form \[ax^2+bx+c\] where \(a\), \(b\) and \(c\) are real numbers and \(a\neq 0\). Quadratics frequently arise in mathematics, science and engineering. Let's factorise a quadratic into two linear factors using the "completing the square" method. This is a general method that allows any quadratic to...
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1 An integer is a positive or negative whole number and may include \(0.\) For example in the case that the result was an integer we could have This means that \(6750\div15=450\) or \(6750=15\times450.\) In case the numbers do not exactly divide we could have This means that \[\begin{align*} 6751\div15...
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What is algebra? Why are there letters in the equation? This page links to resources that will help you answer these questions. Algebraic expressions involve pronumerals (letters) to represent values. Pronumerals can take many different values. We often need to plug our own values into a given formula for calculating...
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This short video is the second of three videos in Nursing calculations: Finding the volume required. It explains how to calculate medication dosage from labels using the method of mental calculation and proportionality to get the right dosage for drugs in solution....
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How do you convert between units? Nurses use units that begin with milli and micro a lot. If you express your dosage in a smaller unit, the number must get bigger, and vice versa. Find out how to convert dosages between larger and smaller units....
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How do you convert IV flow rates? In the previous video, we looked at converting between millilitres (ml) and drops. This time we are converting not only the volumes, (drops and mls) but the units for time as well....
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Drops are just another unit for measuring the amount of fluid flowing into a patient’s system. Discover what ‘drop factor’ means, and how to convert between millilitres and drops....
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What is volume required formula? This formula tells us how much liquid-form medication we need to give a patient, considering the strength they need and the source that it comes from. Defining the formula This short video is the first of three videos in Nursing calculations: Finding the volume required....
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What do you do if the flow rate calculation involves fractions such as ¼ of an hour or 0.5 litres? Find out how this is managed mathematically....
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How do you deal with a unit like mg/kg? Milligrams per kilogram means that you must give a certain amount (mgs) of a drug for each kilogram of the patient’s body mass. Bigger patients need a bigger dose! Learn what this unit means and when and how to use it....
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This short video is the third of three videos in Nursing calculations: Finding the volume required. It explains the formula for calculating the quantity of a drug in solution for correct dosage by determining the stock strength and volume (have), then calculating a fraction of that stock volume for prescribed...
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Pythagoras’ theorem shows the relationship between the sides of a right-angled triangle. Knowing the length of two sides of a right-angled triangle, the length of the third side can be calculated. This mathematical formula is fundamental for finding lengths and distances that are difficult to physically measure. Right angled triangles...
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Sine, cos and tan can be defined using side lengths of a right-angled triangle. These side lengths are identified as either the hypotenuse or the opposite or adjacent sides to the angle. This module shows how to apply trigonometric ratios to find a missing side length, or angle, in a...
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How can we apply trigonometry to triangles that do not possess a right-angle? The sine rule shows that the ratio of the length of a side, to the sine of its opposite angle, will be the same for all three sides. The Sine rule can be used to find angles...
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The cosine rule is a generalisation of Pythagoras’ theorem. If you have any two sides of a triangle, as long as you know the angle between them, you can calculate the length of the third side. The cosine rule can be used to solve non-right triangles. The cosine rule Consider...
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Angles are frequently measured in degrees. However, it is sometimes useful to define angles in terms of the length around the unit circle (a circle of radius = 1). This module introduces radians as a measure of angle. Definition of the radian Though angles have commonly been measured in degrees...
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The trigonometric ratios that have been defined in right-angled triangles can be extended to angles greater than 90 degrees Trigonometric functions such as sin, cos and tan are usually defined as the ratios of sides in a right angled triangle. This module defines the trigonometric functions using angles in a...
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If you know the value of a trigonometric function, how do I find all the possible angles that satisfy this expression? The calculator may only give you one answer to an inverse trig question between 0 and 90 degrees (say InvCos = 40°). The unit circle can help you visualise...
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Both the functions y = sin x and y = cos x have a domain of R and a range of [-1,1]. The graphs of both functions have an amplitude of 1 and a period of 2π radians. The functions \(y=\sin x\) and \(y=\cos x\) have a domain of \(\mathbb{R}\)...
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Trigonometric identities are equations involving trigonometric functions that are true for all values of the involved variables. They are essential tools for simplifying expressions and solving equations in mathematics. On this page, you'll learn about fundamental identities, double angle formulas, sums and difference, and other trigonometric functions. An algebraic expression...
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What does "flow rate = volume/time" mean? Flow rate is determined by the volume of liquid that passes by (into a patient) within a certain time period. This is the fundamental formula for all IV problems. This short video uses practical examples to explain the formula for calculating the flow...
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Trigonometry is a branch of mathematics involving the study of triangles. Ancient builders and mariners used it for finding lengths that are not physically measurable (because they were so large) but they could be defined by angles. Trigonometry has applications in fields such as engineering, surveying, navigation, optics, electronics, aviation,...
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If you need double the dose of medication, you need to give double the volume of the liquid that it is dissolved in and so on. This is the simple principle behind the volume required formula. Learn how you could solve these problems before applying the formula....
