Algebra Review — NSW Year 10 Advanced Maths
Algebraic fractions, equations with fractions, worded problems and inequalities, revised and extended. Six subtopics and 120 practice questions with fully worked solutions, aligned to NESA outcomes MA5-ALG-P-02 and MA5-EQU-P-02.
Algebra Review in NSW Year 10 Advanced
Algebra Review gathers the algebra skills that the rest of Year 10 Advanced depends on. It works with algebraic fractions whose denominators contain pronumerals, solves equations with several fractions, sets up equations from worded problems, and solves and graphs linear inequalities such as \(5-\frac{3x}{4}>-2\).
The six subtopics below move from adding and subtracting algebraic fractions to multiplying and dividing them, then to equations with fractions and equation problems, and finish with solving inequalities and graphing them on a number line. Algebra Review is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Number and Algebra strand (NESA outcomes MA5‑ALG‑P‑01, MA5‑ALG‑P‑02, MA5‑EQU‑C‑01, MA5‑EQU‑P‑01 and MA5‑EQU‑P‑02). Fluent work here is needed for quadratics, simultaneous equations, polynomials and Year 11 Advanced.
Subtopics
Algebra Review: common questions
How do you add algebraic fractions with different denominators?
Factorise the denominators, find the lowest common denominator and rewrite each fraction over it. For example, \(\frac{2}{x+3}+\frac{1}{x-1}=\frac{2(x-1)+(x+3)}{(x+3)(x-1)}=\frac{3x+1}{(x+3)(x-1)}\).
How do you divide algebraic fractions?
Multiply by the reciprocal of the second fraction, factorise every numerator and denominator, then cancel common factors. For example, \(\frac{a^2-25}{4a+20}\div\frac{a-5}{8}=\frac{(a-5)(a+5)}{4(a+5)}\times\frac{8}{a-5}=2\).
Why must you check answers to equations with fractions?
A solution that makes any denominator zero is not allowed. In \(\frac{2x}{x-3}=\frac{6}{x-3}+1\) the algebra gives \(x=3\), but that makes the denominators zero, so the equation has no solution.
When do you reverse the sign in an inequality?
Reverse the inequality sign whenever you multiply or divide both sides by a negative number. For example, \(-3x>-28\) becomes \(x<\frac{28}{3}\) after dividing both sides by \(-3\).
Which NESA outcomes does Algebra Review cover?
Algebraic fractions are MA5‑ALG‑P‑01 and MA5‑ALG‑P‑02, equation problems are MA5‑EQU‑C‑01, inequalities are MA5‑EQU‑P‑01, and equations with two or more fractions are MA5‑EQU‑P‑02, all in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).