Algebra: Algebraic Manipulation
Basic Algebraic Manipulation
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Understand the properties of real numbers, including: commutative, associative, distributive, and identity.
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Familiarise yourself with the operations of addition, subtraction, multiplication, division and exponentiation of algebraic expressions.
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Learn and apply the order of operations (BIDMAS: Brackets, Indices, Division and Multiplication, Addition and Subtraction).
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Be confident in factorising quadratics, cubics and higher order polynomials using common factorisation, the difference of two squares and The Factor Theorem.
Equations and Inequalities
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Develop skills in solving linear, quadratic, cubic and higher order equations, as well as simultaneous equations using analytical and graphical methods.
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Understand and apply the concepts of absolute value equations and inequalities, and know how to solve them.
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Familiarise yourself with the concepts of rational equations and inequalities.
Algebraic Fractions
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Know how to simplify complex algebraic fractions, including those with polynomials in the numerator or denominator.
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Be able to add, subtract, divide and multiply algebraic fractions, and to simplify to lowest terms.
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Learn how to solve equations involving algebraic fractions.
Powers and Roots
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Recall the laws of indices and apply them to manipulate expressions involving powers and roots.
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Be vigilant on checking the conditions under which the rules of algebra holds.
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Understand how to simplify and rationalise surds.
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Be able to express complex numbers in a+bi form.
Further Techniques and Applications
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Gain confidence in working with complex numbers particularly, the arithmetic of complex numbers, the modulus-argument form and the use of De Moivre's Theorem.
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Have a good understanding of the binomial theorem for rational indices, and their use in series expansion and approximations.
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Learn to solve equations with variable powers using the logarithm properties.
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Use algebraic manipulation to simplify, rearrange and solve real-world problems.