Equations — NSW Year 9 Advanced Maths
Linear equations with brackets and fractions, formulas, word problems, ax² = c and changing the subject. Eight subtopics and 160 questions with worked solutions, aligned to NESA outcomes MA5-EQU-C-01 and MA5-EQU-P-02.
Equations in NSW Year 9 Advanced
An equation is solved by doing the same thing to both sides until the pronumeral stands alone. Year 9 Advanced takes this further, with pronumerals on both sides, brackets and several algebraic fractions, substitution into formulas, word problems, quadratic equations of the form \(ax^2 = c\), and rearranging formulas to change the subject.
The eight subtopics below move from variables on one side and on both sides to equations with brackets, using formulae and equation problems, then equations with algebraic fractions, quadratic equations and changing the subject of a formula. Equations is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Number and Algebra strand (NESA outcomes MA5‑EQU‑C‑01 and MA5‑EQU‑P‑02, with the quadratic equations extending MA4‑EQU‑C‑01). These skills are used throughout the course, from money formulas to solving quadratics by factorising.
Subtopics
Equations: common questions
How do you solve an equation with pronumerals on both sides?
Move the pronumeral terms to one side and the numbers to the other, then divide. For \(8x + 7 = 4x - 5\), subtract \(4x\) and 7 from both sides to get \(4x = -12\), so \(x = -3\).
How do you solve an equation with fractions?
Multiply every term by the lowest common denominator to clear the fractions, then solve as usual. For \(\frac{a}{2} + \frac{a}{3} = 5\), multiplying by 6 gives \(3a + 2a = 30\), so \(a = 6\).
How do you solve a simple quadratic equation?
Make \(x^2\) the subject, then take the square root, remembering both signs. For \(3k^2 = 192\), \(k^2 = 64\), so \(k = \pm 8\). If the square equals a negative number, there is no real solution.
How do you rearrange a formula to change its subject?
Undo the operations around the new subject in reverse order, doing the same to both sides. For \(v = u + at\), subtract \(u\) and then divide by \(t\) to get \(a = \frac{v - u}{t}\).
Which NESA outcomes cover Year 9 Advanced equations?
Linear equations of up to three steps with one algebraic fraction are the Stage 5 Core outcome MA5‑EQU‑C‑01. Equations with two or more fractions and changing the subject are the Path outcome MA5‑EQU‑P‑02. Equations of the form \(ax^2 = c\) extend the Stage 4 outcome MA4‑EQU‑C‑01.