This 20-lesson unit builds the algebraic foundation for Stage 6 mathematics. You will simplify and expand expressions, master the index laws, and solve linear equations and inequalities — skills essential for every higher maths course.
Simplifies algebraic fractions with numerical denominators and expands algebraic expressions.
Simplifies algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases.
Solves linear equations of up to 3 steps, limited to one algebraic fraction.
Variables, terms, coefficients and substitution
02Like terms, collecting terms and order of operations
03The distributive law and expanding with negatives
04FOIL, perfect squares and difference of two squares
05HCF, grouping and special products
Covers Lessons 1–5
Powers, bases, exponents and prime factorisation
07am × an = am+n and am ÷ an = am−n
08(am)n = amn and a0 = 1
09a−n = 1/an and converting between forms
10Combining all index laws and applications
Covers Lessons 6–10
Balance method and checking solutions
12Reverse operations and variables on one side
13Expanding first and one algebraic fraction
14Solving, graphing and interval notation
15Changing the subject and real-world contexts
Covers Lessons 11–15
Simplifying, expanding and factorising combined
17All equation types and strategy selection
18Number patterns and algebraic rules
19Real-world contexts and geometry applications
20Integrated capstone project
Covers Lessons 16–20
Full unit assessment