A Level FSMQ Additional Maths OCR

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 modulus-argument 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 real-world problems.