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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 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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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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Complex numbers are a group of numbers that help us to get mathematical solutions where real numbers (which includes positive and negative, counting numbers, fractions and decimals) just can’t work. They can be useful in engineering and physical sciences. They have two parts: one part is an imaginary number. (For...
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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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Solving algebraic equations involves finding the values of variables that satisfy mathematical statements. Build on your foundational understanding of algebra by tackling how to solve various types of equations, from linear to quadratic and beyond. Getting started Solving linear equations Use this resource to learn how to solve linear equations....
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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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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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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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The quadratic formula provides a straightforward way to find the solutions of any quadratic equation, especially when factoring is difficult or impossible. By becoming familiar with this formula, you'll gain a reliable tool for solving quadratic equations and deepen your understanding of algebraic relationships. Solving quadratic equations The solutions to...
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Learn how to solve cubic equations, where the highest power of the variable is three. These types of equations can model various real-world scenarios, from physics to engineering. The factor theorem The long division of polynomials is an important tool for solving cubic equations. However, the factor theorem is equally...
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Exponential equations are common in fields such as science, finance, and population dynamics, where exponential growth or decay is observed. By learning how to isolate variables and find solutions to exponential equations, you will be able to handle a variety of real-world problems involving exponential relationships. Exponential equations Indicial (or...
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Earlier, we looked at how to transpose formulas. Now, let's combine those skills with arithmetic to solve linear equations. By mastering the techniques for solving these equations, you'll be equipped to tackle a wide range of problems and build a strong basis for more advanced mathematical concepts. Video tutorial –...
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Just as linear equations can be solved to find the value of an unknown variable, we can do the same with quadratic equations. Here, we will learn how to solve quadratic equations using the null factor law. By applying this principle, you can factorise quadratic equations and determine their solutions...
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Delve into solving simultaneous equations, where a solution works for multiple equations. This skill is essential for analysing systems with multiple variables and is widely used in fields such as engineering, economics, and science. Simultaneous equations Simultaneous equations are equations that share variables and must be solved at the same...
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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...