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# AS 2.6 Algebra Achievement Objectives

##### Achievement Objectives

Methods include a selection from those related to:

• manipulating algebraic expressions, including rational expressions
• manipulating expressions with exponents, including fractional and negative exponents
• determining the nature of the roots of a quadratic equation
• solving exponential equations (which may include manipulating logarithms)
• forming and solving linear and quadratic equations.

## Achieve

##### Apply algebraic methods in solving problems:
• selecting and using methods
• demonstrating knowledge of algebraic concepts and terms
• communicating using appropriate representations.

Manipulate algebraic expressions
Expand brackets up to 3 factors
Factorising expressions including quadratics
Use fractional and negative indices
Change the subject of the formula
Use elementary properties of logarithms
Simplify rational expressions.

Solve equations involving.
Multi-step linear equations or inequations,      eg 3(2x − 5) = 5x + 7
Quadratics that can be factorised      eg 2x2 − 11x = 21
Polynomials in factorised form   eg 3x2(x − 7)(2x + 6) = 0
Simple logarithmic and exponential     eg Log2x = 2,  2x = 64
Forming and solving linear/linear simultaneous equations.

## Merit

##### Relational thinking involves one or more of:
• selecting and carrying out a logical sequence of steps
• connecting different concepts or representations
• demonstrating understanding of concepts
• forming and using a model;

and also relating findings to a context, or communicating thinking using appropriate mathematical statements

Solve problems involving equations.
Assessment will be based on a selection from:
- quadratics requiring the use of the quadratic formula
- linear/non-linear simultaneous equations
- exponential eg 134x-5 = 6.   N
on-linear equations may be given as appropriate to the complexity of the problem.
Students will be expected to solve problems incontext.

## Excellence

##### Extended abstract thinking involves one or more of:
• devising a strategy to investigate a situation
• identifying relevant concepts in context
• developing a chain of logical reasoning, or proof
• forming a generalisation;

and also using correct mathematical statements, or communicating mathematical insight.

Choose algebraic techniques and strategies to solve problems.
Where appropriate, interpretation of a solution will be expected and may involve the nature of the roots of a quadratic.