FSMQ Additional Maths
Algebra
Algebra: Algebraic Manipulation
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Algebra: Algebraic Manipulation
Basic Algebraic Manipulation

Understand the properties of real numbers, including: commutative, associative, distributive, and identity.

Familiarise yourself with the operations of addition, subtraction, multiplication, division and exponentiation of algebraic expressions.

Learn and apply the order of operations (BIDMAS: Brackets, Indices, Division and Multiplication, Addition and Subtraction).

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

Develop skills in solving linear, quadratic, cubic and higher order equations, as well as simultaneous equations using analytical and graphical methods.

Understand and apply the concepts of absolute value equations and inequalities, and know how to solve them.

Familiarise yourself with the concepts of rational equations and inequalities.
Algebraic Fractions

Know how to simplify complex algebraic fractions, including those with polynomials in the numerator or denominator.

Be able to add, subtract, divide and multiply algebraic fractions, and to simplify to lowest terms.

Learn how to solve equations involving algebraic fractions.
Powers and Roots

Recall the laws of indices and apply them to manipulate expressions involving powers and roots.

Be vigilant on checking the conditions under which the rules of algebra holds.

Understand how to simplify and rationalise surds.

Be able to express complex numbers in a+bi form.
Further Techniques and Applications

Gain confidence in working with complex numbers particularly, the arithmetic of complex numbers, the modulusargument form and the use of De Moivre's Theorem.

Have a good understanding of the binomial theorem for rational indices, and their use in series expansion and approximations.

Learn to solve equations with variable powers using the logarithm properties.

Use algebraic manipulation to simplify, rearrange and solve realworld problems.