Variables, monomials, systems of equations and the quadratic formula
Learn algebra from variables and monomials to quadratic equations and systems. The exam covers: simplifying expressions, linear equations with brackets, verifying solutions, factorisation, notable identities and the quadratic formula with the discriminant.
Algebra is the part of mathematics that uses letters (variables) to represent unknown numbers and express general relationships. Moving from arithmetic to algebra —from concrete numbers to ‘x’ and ‘y’— is one of the great leaps of Secondary school, and the basis of almost all higher mathematics.
The key content ranges from expressions and monomials to first-degree equations (isolating the unknown), special products, factoring, systems of equations and, finally, quadratic equations solved with the quadratic formula and its discriminant.
Revise everything from simple equations to the quadratic formula with the exam below, with the full working in each question.
Mathematics · Secondary
The exam starts with simple equations (3x=12) and progresses to equations with brackets, quadratics and systems. Every step is explained with the full procedure.
x = (−b ± √(b²−4ac)) / 2a. The exam includes calculating the discriminant and interpreting it: Δ>0 two solutions, Δ=0 one solution, Δ<0 no real solutions.
Difference of squares (a²−b²=(a+b)(a−b)) and perfect square trinomial ((a+b)²=a²+2ab+b²). Essential skills for upper secondary maths.
"A student who expanded (x+4)² as x²+16 learns the identity (a+b)²=a²+2ab+b² and correctly gets x²+8x+16."
Tricks and techniques to master this topic faster:
Linear equation: isolate the unknown by doing the same to both sides. 2x+3=11 → 2x=8 → x=4.
Quadratic equation: try factorising first. If that fails, use x=(−b±√(b²−4ac))/2a.
Discriminant Δ=b²−4ac: Δ>0 gives 2 solutions, Δ=0 gives 1, Δ<0 gives no real solutions.
Systems by elimination: multiply equations so one term cancels when you add them.
If you are studying Algebra — 1st and 2nd Degree Equations, these curriculum topics complement each other:
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