Is the quadratic formula given on Edexcel GCSE papers?

Yes, for the 2025 to 2027 assessment windows. The Exam Aid sheet issued with every 1MA1 paper carries x = (-b ± sqrt(b^2 - 4ac))/(2a). What it does not do is tell you which values are a, b and c, and a sign error there is the usual reason this question scores 1 out of 3.

How do I know which method Edexcel wants?

Read the answer format: 'solve' with whole-number-friendly coefficients suggests factorising; 'give your answers to 2 decimal places' signals the formula; 'write in the form (x+a)^2+b' is completing the square. Marks are awarded for any valid method unless the form is specified.

Do quadratic equations appear on the non-calculator paper?

Yes. Factorisable quadratics and completing the square are regularly set on Paper 1, where surd and fraction answers must be left exact. Formula questions needing decimal answers sit on the calculator papers.

Quadratic Equations - Edexcel GCSE Higher Maths

Typically 5-8 marks across the three papers · Spec 1MA1

Quadratic equations are equations with an $x^2$ term, and on Edexcel's 1MA1 Higher tier you are expected to solve them three ways: factorising (spec ref A18), the quadratic formula, and completing the square, plus using them inside problems about areas, graphs and the Higher-only quadratic simultaneous equations.

Edexcel typically gives factorising questions in the middle of a paper for 3 marks, while formula and completing-the-square questions appear later, often asking for answers 'to 2 decimal places' (a strong hint to use the formula) or 'in the form $(x+a)^2 + b$ '. The quadratic formula itself comes with the paper on the Exam Aid sheet for the 2025 to 2027 windows, so the marks are in substituting into it accurately rather than in recalling it.

Examiners' reports repeatedly flag the same losses: candidates who divide through by $x$ and lose a root, sign slips inside the formula when $b$ is negative, and answers left unfinished at $(x-3)(x+2)$ without stating the solutions. Every question below is built to practise the full 'solve and state both roots' habit.

Worked example

Solve

2x^2 - 7x + 3 = 0

[3 marks]

Look for a factorisation of $2x^2 - 7x + 3$ : the outer/inner pairs must add to $-7x$ , giving $(2x - 1)(x - 3)$ .
M1: brackets that expand to give two correct terms
Set each bracket to zero: $2x - 1 = 0$ or $x - 3 = 0$ .
M1: using the factorised form to create two equations
State both solutions: $x = \frac{1}{2}$ and $x = 3$ . A quick check: $2(\frac{1}{4}) - \frac{7}{2} + 3 = 0$ ✓
A1: both roots, including the fractional one

Practice questions

Original questions in Edexcel 1MA1 Higher style. Factorising questions are fair game on non-calculator Paper 1, and give exact fractions where they arise (type 1/2). The quadratic formula is on the Exam Aid sheet, but the marks are in identifying $a$ , $b$ and $c$ and substituting without sign errors.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

Which of these is the correct factorisation of $x^2 - x - 12$ ?

Answer options for question 1
$(x - 4)(x + 3)$ $(x + 4)(x - 3)$ $(x - 6)(x + 2)$ $(x - 12)(x + 1)$
Question 2 Warm-up [2 marks]

Expand and simplify $(x + 3)(x - 4)$

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 3 Exam pace [3 marks]

Solve $2x^2 - 5x - 3 = 0$ Give exact answers.

smaller x = larger x =
Question 4 Exam pace [2 marks]

$x^2 + 6x + 2$ can be written in the form $(x + a)^2 + b$ . Find the value of $b$ .

Your answer (fractions like 1/2 are fine)
Question 5 Stretch [3 marks]

Solve $x^2 - 6x + 2 = 0$ . Give the larger solution correct to 2 decimal places.

Your answer (fractions like 1/2 are fine)
Question 6 Stretch [4 marks]

A rectangle has length $x$ cm and width $(x - 3)$ cm. Its area is $40 \text{ cm}^2$ . Find the value of $x$ .

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Dividing both sides by $x$ in equations like $x^2 - 4x = 0$ , which silently throws away the root $x = 0$ .

Never divide by the unknown. Factorise instead: $x(x - 4) = 0$ gives both $x = 0$ and $x = 4$ .
Sign errors substituting a negative $b$ into the quadratic formula, such as writing $-b$ as $-7$ when $b = -7$ .

Write the substitution line in full with brackets before evaluating: $x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(3)}}{2(2)}$ . Edexcel awards the method mark for exactly this line.
Stopping at the factorised form $(x - 3)(x + 2) = 0$ without stating the solutions.

The question says solve, so the final line must be values of $x$ . Factorising alone leaves the accuracy marks on the table.
Halving $b$ incorrectly (or forgetting to subtract the square) when completing the square on $x^2 + 6x + 2$ .

Follow the two-step routine every time: $(x + 3)^2$ deals with $x^2 + 6x$ , then subtract $3^2$ and bring back the constant: $(x + 3)^2 - 7$ .
Rounding answers when the question asked for exact values, or giving 1 decimal place when it asked for 2.

Match the answer format to the instruction word for word: 'exact' means surds or fractions, '2 d.p.' means use the formula and keep intermediate digits.

Frequently asked questions

Is the quadratic formula given on Edexcel GCSE papers?: Yes, for the 2025 to 2027 assessment windows. The Exam Aid sheet issued with every 1MA1 paper carries $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . What it does not do is tell you which values are $a$ , $b$ and $c$ , and a sign error there is the usual reason this question scores 1 out of 3.
How do I know which method Edexcel wants?: Read the answer format: 'solve' with whole-number-friendly coefficients suggests factorising; 'give your answers to 2 decimal places' signals the formula; 'write in the form $(x+a)^2+b$ ' is completing the square. Marks are awarded for any valid method unless the form is specified.
Do quadratic equations appear on the non-calculator paper?: Yes. Factorisable quadratics and completing the square are regularly set on Paper 1, where surd and fraction answers must be left exact. Formula questions needing decimal answers sit on the calculator papers.