For teachers · Cambridge IGCSE 0580 Extended · Syllabus 2025 to 2027

Algebra repair: teacher sample

A bounded intervention for Extended candidates who lose algebra method marks on Papers 2 and 4. All content is original and mapped to the 2025 to 2027 syllabus, on the Cambridge International website.

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Scope

Free
12-question diagnostic, a distinct 12-question retry, and one lesson matched to the student's biggest gap.
Pack (£79, 12 months)
6 lessons, 72 marked tasks, two 20-mark practice sections (Paper 2 and Paper 4 conditions).
Not included
E2.4 Indices; E2.7 Sequences; E2.8 Proportion; E2.9 to E2.11 Graphs; E2.12 Differentiation; E2.13 Functions. Core, 0980 and 2028 onwards.

Syllabus map

Task counts include every diagnostic, retry, practice and section question tagged to the statement.

Ref	Statement (our wording)	Module	Tasks
E2.1.2	Substitute numbers into expressions and formulas	Expanding and rearranging	2
E2.2.1	Simplify expressions by collecting like terms	Expanding and rearranging	6
E2.2.2	Expand products of algebraic expressions, including more than two brackets	Expanding and rearranging	9
E2.2.3	Factorise by taking out common factors	Factorising	7
E2.2.4	Factorise by grouping, difference of two squares, perfect squares, ax² + bx + c and ax³ + bx² + cx	Factorising	14
E2.2.5	Complete the square for ax² + bx + c	Quadratics	7
E2.3.1	Add, subtract, multiply and divide algebraic fractions	Algebraic fractions	8
E2.3.2	Factorise and simplify rational expressions	Algebraic fractions	6
E2.5.1	Construct expressions, equations and formulas, including simultaneous equations	Linear and simultaneous equations	6
E2.5.2	Solve linear equations in one unknown	Linear and simultaneous equations	9
E2.5.3	Solve equations with numerical and linear algebraic denominators	Algebraic fractions	5
E2.5.4	Solve simultaneous linear equations in two unknowns	Linear and simultaneous equations	8
E2.5.5	Solve simultaneous equations, one linear and one non-linear, with powers no higher than two	Quadratics	3
E2.5.6	Solve quadratics by factorising, completing the square and the formula, including surd form	Quadratics	16
E2.5.7	Change the subject of a formula, including when it appears twice or under a power or root	Expanding and rearranging	8
E2.6.1	Represent and interpret inequalities, including on a number line	Inequalities and regions	5
E2.6.2	Construct, solve and interpret linear inequalities	Inequalities and regions	14
E2.6.3	Represent and interpret linear inequalities in two variables graphically	Inequalities and regions	1
E2.6.4	List the inequalities that define a region	Inequalities and regions	1

Used without being taught, as on the papers: Rounding to decimal places and significant figures (E1.9); Perimeter and area of a rectangle (E5.2).

Diagnostic skills

One question per skill; the retry tests the same skill with a new question, so improvement is measured on unseen work.

Expanding with a minus outside a bracket (Expanding and rearranging)
Changing the subject with a square (Expanding and rearranging)
Factorising fully (Factorising)
Factorising ax² + bx + c (Factorising)
Subtracting algebraic fractions (Algebraic fractions)
Simplifying a rational expression (Algebraic fractions)
Solving a linear equation with brackets (Linear and simultaneous equations)
Solving simultaneous equations (Linear and simultaneous equations)
Solving a quadratic by factorising (Quadratics)
Completing the square (Quadratics)
Solving an inequality with a negative coefficient (Inequalities and regions)
Integer solutions of a double inequality (Inequalities and regions)

Lesson outline: Linear and simultaneous equations

By the end, you will solve linear equations without moving-term slips and choose whether to add or subtract to eliminate.

Solve $7 - 2x = 3x + 22$ .
Solve $3x + 2y = 16$ and $5x - 2y = 0$ .
To eliminate $y$ , add or subtract?
A student solved $2x + y = 9$ and $x - y = 3$ . Tap the slip.
Three consecutive even numbers add to 54. The smallest is $n$ .
Solve $\dfrac{x}{2} + \dfrac{x}{5} = 14$ .
Solve $3x - 2y = 4$ and $x + 2y = 12$ .

Two complete tasks

3 marksNo calculatorE2.5.4

Solve the simultaneous equations $2x + 3y = 13$ and $3x + 2y = 7$ . Give your answer as $(x, y)$ . [3]

Answer: $x = -1$ , $y = 5$

Make the $x$ coefficients match. $6x + 9y = 39, \quad 6x + 4y = 14$
Subtract: the matching terms have the same sign. $5y = 25, \quad y = 5$
Substitute into $2x + 3y = 13$ . $2x + 15 = 13, \quad x = -1$

Mark	Earned for	Usually lost by
M1	Both equations multiplied to match one coefficient.	Multiplying only the left-hand side.
M1 dep	The correct operation to eliminate: $5y = 25$ or $5x = -5$ .	Adding equations whose matching terms have the same sign. Feedback: Elimination sign
A1 dep	$x = -1$ and $y = 5$ .	Substituting $y$ into the wrong equation and slipping. Feedback: Stopping at one unknown

3 marksNo calculatorE2.3.1

Write $\dfrac{2x + 1}{3} - \dfrac{x - 4}{2}$ as a single fraction in its simplest form. [3]

Answer: $\dfrac{x + 14}{6}$

Use the common denominator 6. $\frac{2(2x + 1) - 3(x - 4)}{6}$
Expand. The minus multiplies the whole second numerator. $\frac{4x + 2 - 3x + 12}{6}$
Collect. $\frac{x + 14}{6}$

Mark	Earned for	Usually lost by
M1	A common denominator with both numerators multiplied correctly: $\frac{2(2x + 1) - 3(x - 4)}{6}$ .	Adding numerators and denominators. Feedback: Adding fractions straight across
M1 dep	The numerator expanded with the sign handled: $4x + 2 - 3x + 12$ .	Writing $-3x - 12$ , so the top becomes $x - 10$ . Feedback: Minus sign over a numerator
A1 dep	$\frac{x + 14}{6}$ .	Giving $\frac{x - 10}{6}$ after the sign slip. Feedback: Minus sign over a numerator

How the answers were checked

Every task was written for this pack and solved independently three times (two separate Claude runs and one GPT run, each from the question text alone). Each method mark carries evidence that the marker matches in a student's working, and every scheme is tested: its own working earns full marks, a blank earns none, and each named slip loses marks.

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