This worksheet builds advanced algebraic fluency, teaching students to apply the exponent laws to algebraic terms and expand, factorise and solve non-monic quadratic expressions using the ac method. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- The exponent laws (product, quotient, power, negative exponent) apply to algebraic terms exactly as they do to numbers — combine the numeric coefficients and the variable powers separately.
- Expanding a binomial product like (2x+3)(x+4) uses the distributive property exactly as a monic product does — every term in the first bracket multiplies every term in the second.
- Factorising a non-monic quadratic (ax²+bx+c, a≠1) uses the "ac method": find two numbers that multiply to a×c and add to b, split the middle term using them, then factorise by grouping.
- Every proposed factorisation can (and should) be checked by expanding it back out — it must reproduce the original expression exactly.
- A factorised quadratic equation can be solved using the null factor law, exactly as with monic quadratics — but the coefficient in front of x in each factor must also be accounted for.
What your child will practise:
- Applying the exponent laws to simplify products, quotients and powers of algebraic terms, including with negative exponents.
- Expanding a non-monic binomial product using the distributive property.
- Factorising a non-monic quadratic expression using the ac method (splitting the middle term).
- Verifying a factorisation by expanding it back out and confirming an exact match.
- Solving a non-monic quadratic equation algebraically, using factorisation and the null factor law.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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