Algebraic Processes
Overview
Algebra is the language that lets you describe a pattern once and use it for every number, rather than repeating a calculation again and again. Rearranging a formula, factorising an expression or simplifying a fraction of algebraic terms are the everyday moves that turn a messy expression into a usable one.
This topic builds your fluency with the basic processes of algebra, formulae and change of subject, factorising, the factor theorem applied to cubics, dividing a cubic by a linear factor, and manipulating algebraic fractions, the tools you will lean on throughout equations, graphs and further algebra.
Objectives
- Use the basic processes of algebra including collecting like terms, using the four operations, and the rules of indices with integers and fractional powers
- Construct, interpret and use formulae, including change of subject and substitution
- Factorise simple algebraic expressions
- Use the factor theorem, including application to cubics and factors of the form (ax + b) or (ax - b)
- Perform algebraic division of a cubic by a linear factor
- Manipulate simple algebraic fractions with numerical, linear or quadratic denominators, including sum, difference, product and quotient
Mind map
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Algebraic Processes. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Simplify 5x squared minus 3x plus 2x squared plus x. A) 7x^2 - 2x B) 7x^2 + 4x C) 7x^2 - 4x D) 3x^2 + 2x Answer: A
- Which is the correct factorisation of 9x^2 - 16? A) (9x - 4)(x + 4) B) (3x + 4)(3x - 4) C) (3x - 4)^2 D) (9x + 16)(x - 1) Answer: B
- If f(x) = x^3 - x^2 - 4x + 4, which value of x gives f(x) = 0? A) x = -1 B) x = 0 C) x = 1 D) x = 3 Answer: C
- Make x the subject of y = 3x + 2. A) x = (y - 2)/3 B) x = (y + 2)/3 C) x = 3y - 2 D) x = 3(y - 2) Answer: A
- Simplify (2x)/(x+1) multiplied by (x+1)/(4x^2). A) 1/(2x) B) 2x C) 1/2 D) 2/x Answer: A
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Work through these questions in the app
Recommended Books
Practice Mock Questions
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