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Module A-M1

Algebra Consolidation

This module consolidates the algebraic competencies required for success in STRAIT-level mathematics by revisiting linear, quadratic and polynomial manipulation with renewed rigour. Learners strengthen their fluency with exponents, radicals, logarithms and rational expressions while building habits of symbolic reasoning. The emphasis is on accuracy, structure-spotting and transferable algebraic technique rather than isolated drill. By its conclusion, learners can read, re-express and solve algebraic statements with confidence across topics.

Learning Outcomes

1.
Simplify and manipulate algebraic expressions involving powers, roots and rational terms (apply)
2.
Solve linear and quadratic equations and inequalities using algebraic and graphical reasoning (apply)
3.
Factorise polynomials up to degree four using grouping, synthetic division and the factor theorem (apply)
4.
Evaluate and transform logarithmic and exponential expressions using the laws of indices and logs (apply)
5.
Analyse the structure of a problem to select an efficient algebraic strategy (analyse)
6.
Interpret algebraic solutions in context, identifying extraneous and permissible roots (evaluate)
7.
Construct multi-step algebraic arguments with clear logical justification (create)
8.
Compare symbolic, numerical and graphical representations of the same algebraic statement (analyse)

Topics Covered

Real numbers and algebraic axioms
Linear equations and inequalities
Simultaneous linear systems
Quadratic equations: factorisation, formula, completing the square
Discriminant and nature of roots
Polynomial division and the remainder/factor theorems
Rational expressions and partial fractions
Indices and surds
Exponential equations
Logarithms and the change-of-base rule
Absolute-value equations and inequalities
Quadratic inequalities and sign diagrams
Word problems and modelling
Algebraic identities and binomial expansion
Error analysis in symbolic manipulation

Skills Developed

Symbolic manipulation Equation solving and verification Factorisation and expansion Reasoning with inequalities Translation between word problems and algebra Checking solutions against constraints Use of logarithmic/exponential laws Working with surds and rationalisation

Suggested Resources

STRAIT Algebra Consolidation workbook (TutorDA, 2025)
Stewart, J. Precalculus: Mathematics for Calculus (7th ed.), chapters 1-3
Khan Academy: Algebra I and II playlists
Paul's Online Math Notes: Algebra section
Desmos graphing calculator (desmos.com/calculator)
GeoGebra algebraic manipulator (geogebra.org)
TutorDA practice bank: A-M1 drill sets

Assessment

Assessment combines a timed written examination testing accuracy and speed with coursework that rewards reasoning and presentation. Learners must demonstrate both procedural fluency and understanding of underlying structure.

Written examination (2 hr)60%
Coursework portfolio and problem sets40%
Practice bank: 200 MCQs · Timed mock & self-paced modes
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