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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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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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Algebra focuses on understanding and manipulating mathematical symbols and expressions. Here, you'll explore key techniques such as simplification, factorisation, and rearranging formulas, which are essential for solving equations and understanding mathematical relationships. Getting started Algebraic operations Use this resource to learn the basics for adding, subtracting, multiplying and dividing algebraic...
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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. Before you continue with the content on this page, it is important that you are confident about identifying common factors, factorising quadratics using common factors and the difference...
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Let's combine your knowledge of fractions and algebra, and learn how to add and subtract algebraic fractions. By learning to find common denominators and simplify expressions, you'll enhance your ability to work with complex algebraic fractions, a skill crucial for solving equations and tackling advanced mathematical challenges. Video tutorial –...
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Let's build on your understanding of basic fraction operations and algebraic expressions by looking at multiplying and dividing algebraic fractions. By mastering these skills, you'll be able to simplify and manipulate complex fractions, which is essential for solving more advanced equations and applying algebra to a variety of contexts. Video...
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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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Algebraic substitution is a powerful technique for simplifying algebraic expressions and solving equations by replacing the pronumerals with known values. This skill is essential for tackling complex problems in mathematics, science, and engineering, enabling you to evaluate and manipulate expressions with ease. Algebraic expressions An algebraic term consists of a...
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Angles are commonly measured in degrees but sometimes, it is useful to define them in terms of the length around the unit circle. This resource introduces radians as a measure of angle. Being able to use radians is crucial for solving problems in engineering, such as analysing the motion of...
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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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Trigonometric functions such as sin, cos and tan are usually defined as the ratios of sides in a right-angled triangle. These ratios can be extended to angles greater than \(90^{\circ}\), using angles in a unit circle. Circular functions have applications in many STEM disciplines, such modelling oscillating motion in engineering,...
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So far, you will have come across a few situations where a quadratic cannot be further factorised into two linear factors using common factors, perfect squares, or the difference of two squares. In these cases, you can use a different method where you complete the square. Before you begin, make...
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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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Cubic polynomials are more challenging to factorise and involve polynomial long division. This method helps break down complex polynomials into simpler components. You'll gain the ability to find factors and simplify cubic equations, which will help you solve higher-degree polynomial equations. Polynomials A polynomial is an algebraic expression that consists...
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Let's learn about the difference of two squares rule. Recognising and applying this pattern allows you to factorise expressions quickly and solve equations more efficiently. Video tutorial – factorisation: difference of two squares Watch this video to learn about the difference of two squares rule. Difference of two squares (DOTS)...
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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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Brackets often appear in algebraic expressions and equations, but what do you do with them? Whatever is around the brackets affects everything inside the brackets, and being able to remove them helps set the stage for solving equations. The process of doing this is called expansion. Brackets in algebra Brackets...
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While expansion is the process of removing brackets from algebraic expressions and equations, factorisation is the opposite. Both are important to make solving algebraic problems easier. Use this resource to learn the basics of factorisation. Video tutorial – factorisation: common factors Watch this video to learn about factorisation using common...
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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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Use this resource to explore perfect squares. Understanding perfect squares will help you with recognise patterns in algebraic expressions, making factorising and expanding algebraic expressions much easier. A perfect square is an algebraic term that is the square of an integer. In other words, it is a term multiplied by...
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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. Understanding Pythagoras' theorem helps you solve problems in fields such as architecture, engineering, and computer graphs, where precise calculations...
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Quadratic expressions are fundamental in mathematics and appear frequently in various applications, from physics to finance. Use this resource to learn what quadratics are and how to factorise them. The ability to do this is crucial for solving quadratic equations and simplifying complex algebraic problems. Video tutorial – factorisation: quadratics...
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Explore the relationships between the angles and side lengths of a right-angled triangle. You will learn how to use trigonometric ratios to find unknown angles and lengths, enhancing your ability to solve geometric problems. Mastering this concept is vital for fields such as engineering, physics, and architecture, where precise calculations...
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A calculator may only give you one answer to an inverse trigonometry question between \(0\) and \(90^{\circ}\). When you use the unit circle, you can visualise the many different solutions for the angle. Understanding this concept will help you in many STEM fields, such as satellite navigation in physics and...
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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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Like the sine rule, the cosine rule comes in handy for triangles that are not right-angled. Use this resource to learn about the cosine rule, how it is applied to find unknown sides and angles, and its importance in solving complex geometric problems involving any type of triangle. The cosine...
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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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The trigonometric ratios are handy for real-life situations where right-angled triangles are involves, but what about triangles that are not right-angled? We use the sine rule. Use this resource to learn what the sine rule is and how it is applied. The sine rule shows that the ratio of the...
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The transposition of formulas involves rearranging equations to solve for a specific pronumeral or variable. You need to be able to first isolate your desired variable in order to solve problems various fields. Mastering transposition will enhance your ability to manipulate and understand mathematical relationships effectively. Video tutorial – transposition...
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Expand your transposition skills by exploring how to rearrange formulas involving brackets and fractions. By doing this, you will develop the skills needed to isolate variables in more complex expressions and prepare yourself well for advanced problem-solving in STEM. You will have learned the necessary theory when you were first...
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Trigonometry is 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. Use these resources to develop a solid understanding of trigonometry and its practical applications. Getting started Pythagoras’ theorem...
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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....