Are algebraic fractions on the Foundation paper?

No. Algebraic fractions are in the Higher-only part of spec reference A4, so they appear on 1MA1 Higher papers only. Foundation candidates work with numerical fractions and factorise quadratics of the form x^2 + bx + c, but they are never asked to simplify, combine or solve with an algebraic fraction.

How many marks are algebraic fractions worth on Edexcel GCSE Higher?

A 'simplify fully' question is usually 2-3 marks, a 'write as a single fraction in its simplest form' question 3 marks, and an equation containing algebraic fractions 4-5 marks because it ends with a quadratic to solve. Expect something from this topic on most Higher papers, generally in the second half.

Can I use a calculator for algebraic fractions?

Papers 2 and 3 allow one, but it will not do much for you: the answer to most of these questions is an expression rather than a number, and a scientific calculator does not factorise. When the stem says 'show clear algebraic working' or 'you must show your working', an answer with nothing behind it scores zero even if it is right.

Do I have to state the values that x cannot take?

1MA1 does not ask you to write down excluded values, so you will not lose a mark for leaving them out. You do still have to check your solutions when you solve an equation: a value that makes one of the original denominators zero is not a solution and should be rejected.

Algebraic Fractions - Edexcel GCSE Higher Maths

Typically 3-5 marks per paper, and 4-5 in a single question when it is set as an equation · Spec 1MA1

An algebraic fraction is a fraction with a letter on the top, the bottom, or both: $\frac{x+3}{x-2}$ , $\frac{2}{x}$ , $\frac{x^2-9}{x^2+5x+6}$ . All of it sits in the Higher-only part of spec reference A4 on Edexcel's 1MA1, so a Foundation candidate is never asked to simplify one. Nothing in the topic is new machinery. It is factorising, common denominators and solving quadratics, borrowed from three other spec points and pointed at fractions.

The wording Edexcel uses is predictable enough to revise from. 'Simplify fully' means factorise the top and the bottom and cancel; 'Write as a single fraction in its simplest form' means add or subtract over a common denominator; 'Show that it can be written in the form ...' hands you the target and marks the algebra in between; 'Solve the equation' turns the fraction into a linear or quadratic equation, which then falls under A17 or A18. Any of the three papers can carry it. Paper 1 is non-calculator, and on Papers 2 and 3 a calculator is close to useless here because the answer is an expression, not a number, so the phrase 'show clear algebraic working' in the stem means a bare answer scores nothing.

Two moves account for most of the lost marks. The first is cancelling a term instead of a factor, so $\frac{x^2-25}{x^2-x-20}$ gets crossed down to $\frac{25}{x+20}$ ; the $x^2$ is being added to something on both lines, not multiplying the whole of it. The second is subtracting a numerator without bracketing it, which turns $-(x+4)$ into $-x+4$ one line later. Against that, the method marks are there to be taken: a correct common denominator earns one on its own, and so does a correct expansion after multiplying through, so write those lines down even when you can see the simplification will not come out.

Worked example

Solve

\frac{5}{x-1} + \frac{2}{x+2} = 2

[5 marks]

The common denominator is $(x-1)(x+2)$ . Multiply every term by it, the 2 on the right included: $5(x+2) + 2(x-1) = 2(x-1)(x+2)$ .
M1: multiplying through by the common denominator, with the right-hand side treated as a whole
Expand both sides: $5x + 10 + 2x - 2 = 2(x^2 + x - 2)$ , so $7x + 8 = 2x^2 + 2x - 4$ .
M1: correct expansion of each side; the bracket on the right must be multiplied out before doubling
Collect everything on the side that keeps the $x^2$ term positive: $2x^2 - 5x - 12 = 0$ .
A1: correct three-term quadratic set equal to zero
Factorise: $(2x + 3)(x - 4) = 0$ .
M1: any correct method to solve the quadratic, so the formula or completing the square scores here too
So $x = -\frac{3}{2}$ or $x = 4$ . Neither makes $x - 1$ or $x + 2$ zero, so both are genuine solutions.
A1: both values; stopping at $x = 4$ throws this mark away

Practice questions

These are original questions written in Edexcel 1MA1 Higher style, covering simplifying, multiplying and dividing, combining into a single fraction and solving. Type expressions the way you would write them on a line, using a slash for the fraction bar, so $\frac{x+5}{x-1}$ goes in as (x+5)/(x-1); any equivalent form is marked correct. Where a question pins the answer to a stated form, such as $\frac{ax+b}{12}$ , you only enter the numbers.

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 [2 marks]

Write $\frac{2x}{5} - \frac{x}{4}$ as a single fraction in its simplest form.

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

Simplify fully $\frac{x^2 + 8x + 15}{x^2 + 2x - 3}$

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

Simplify fully $\frac{3x^2 - 12x}{x^2 - 16}$

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 4 Exam pace [1 mark]

Which expression is $\frac{x^2 - 25}{x^2 - x - 20}$ in its simplest form?

Answer options for question 4
$\frac{x+5}{x+4}$ $\frac{5}{x+4}$ $\frac{25}{x+20}$ $\frac{x+5}{x-4}$
Question 5 Stretch [3 marks]

Simplify fully $\frac{6x^2 - x - 15}{4x^2 - 9}$

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 6 Stretch [4 marks]

Simplify fully $\frac{x^2 + 7x + 10}{x^2 - 4} \div \frac{x + 5}{x^2 - 2x}$

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)

Common mistakes examiners see

Cancelling a term rather than a factor, for example writing $\frac{x+6}{x} = 6$ , or turning $\frac{x^2-25}{x^2-x-20}$ into $\frac{25}{x+20}$ by crossing out both $x^2$ terms.

Factorise the top and the bottom before you cancel anything. Only a bracket (or a term) that multiplies the whole numerator and the whole denominator can go. If there is still a $+$ or $-$ between you and the thing you want to cancel, you cannot cancel it.
Adding numerators and denominators separately: $\frac{3}{x} + \frac{2}{x+1}$ handed in as $\frac{5}{2x+1}$ .

Rewrite both fractions over $x(x+1)$ first, so the sum becomes $\frac{3(x+1) + 2x}{x(x+1)}$ . Test any suspicious rule on numbers: $\frac{1}{2} + \frac{1}{3}$ is not $\frac{2}{5}$ .
Losing the minus sign across the second numerator, so $\frac{2x-1}{3} - \frac{x+4}{5}$ becomes $\frac{10x-5-3x+12}{15}$ instead of $\frac{10x-5-3x-12}{15}$ .

Write the subtracted numerator in brackets and expand on the next line: $\frac{5(2x-1) - 3(x+4)}{15}$ . The bracket costs a second and protects the accuracy mark.
When solving, multiplying only the fractions by the common denominator and leaving a whole number alone, so $\frac{4}{x} + \frac{1}{x+1} = 3$ turns into $4(x+1) + x = 3$ .

Every term on both sides gets multiplied, including any integer. Draw the multiplier once over the whole line so nothing is skipped, then check the equation is still balanced by trying a value.
Dividing by $x$ at the end of a solving question, so $2x^2 - 8x = 0$ gives $x = 4$ and the root $x = 0$ vanishes.

Factorise instead of dividing: $2x(x - 4) = 0$ gives $x = 0$ and $x = 4$ . The final accuracy mark on these questions is usually for both roots.

Frequently asked questions

Are algebraic fractions on the Foundation paper?: No. Algebraic fractions are in the Higher-only part of spec reference A4, so they appear on 1MA1 Higher papers only. Foundation candidates work with numerical fractions and factorise quadratics of the form $x^2 + bx + c$ , but they are never asked to simplify, combine or solve with an algebraic fraction.
How many marks are algebraic fractions worth on Edexcel GCSE Higher?: A 'simplify fully' question is usually 2-3 marks, a 'write as a single fraction in its simplest form' question 3 marks, and an equation containing algebraic fractions 4-5 marks because it ends with a quadratic to solve. Expect something from this topic on most Higher papers, generally in the second half.
Can I use a calculator for algebraic fractions?: Papers 2 and 3 allow one, but it will not do much for you: the answer to most of these questions is an expression rather than a number, and a scientific calculator does not factorise. When the stem says 'show clear algebraic working' or 'you must show your working', an answer with nothing behind it scores zero even if it is right.
Do I have to state the values that x cannot take?: 1MA1 does not ask you to write down excluded values, so you will not lose a mark for leaving them out. You do still have to check your solutions when you solve an equation: a value that makes one of the original denominators zero is not a solution and should be rejected.

Algebraic Fractions - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics