CAIE IGCSE Mathematics Extended E2.2 Algebraic Manipulation Topic Practice

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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

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 ]

Question 2

[Maximum number: 7]

Question (a)

(a)

Expand and simplify.

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

[ 2 ]

Question (b)

(b)

Factorise completely.

[ 5 ]

Question (i)

(i)

6 x^2 y+9 x y

[ 2 ]

Question (ii)

(ii)

4 x^2-y^2+8 x+4 y

[ 3 ]

Question 3

[Maximum number: 2]

Write x2+8x−7x^2+8x-7 in the form (x+a)2+b(x+a)^2+b.

Question 4

[Maximum number: 4]

Expand and simplify.

Question (a)

(a)

7(x+2)+4(3 x-5)

[ 2 ]

Question (b)

(b)

(3 x-y)(5 x+2 y)

[ 2 ]

Question 5

[Maximum number: 2]

Factorise completely.

6 x^2 y+9 x y

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