CAIE IGCSE Mathematics Extended E2.2 Algebraic Manipulation Question Bank

Practise collecting terms, expanding multiple brackets and factorising common, grouped or square-difference expressions.

Syllabus
2028–2030
Topic
E2.2
Level
Extended

Exam points

  • collect like terms while keeping different variables and powers separate
  • expand two or three brackets before combining the resulting polynomial terms
  • factorise by common factors, grouping or recognising a difference of two squares

Covered syllabus points

E2.2.1 Simplify expressions by collecting like terms.E2.2.2 Expand products of algebraic expressions.E2.2.3 Factorise by extracting common factors.E2.2.4 Factorise expressions of the form: • ax + bx + kay + kby • a2x2 − b2y2E2.2.5 Complete the square for expressions in the form ax2 + bx + c

E2.2 Algebraic manipulation question 1

[Maximum number: 4]

Question (a)

(a)

Simplify.

[ 4 ]

Question (i)

(i)

3 m-5 n-4 m+8 n

[ 2 ]

Question (ii)

(ii)

4x5−3x10+2x15\frac{4 x}{5}-\frac{3 x}{10}+\frac{2 x}{15}

[ 2 ]

E2.2 Algebraic manipulation question 2

[Maximum number: 4]

Question (a)

(a)

Factorise.
a2−9a^2-9

[ 1 ]

Question (b)

(b)

Expand and simplify.
(2x+3)(x-1)(x+3)

[ 3 ]

E2.2 Algebraic manipulation question 3

[Maximum number: 4]

Question (a)

(a)

Expand and simplify.

4(2 x-1)-6(3-x)

[ 2 ]

Question (b)

(b)

Factorise completely.

[ 2 ]

Question (i)

(i)

6 x^2 y+9 x y

[ 2 ]
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