IGCSE Maths Algebraic manipulation topical questions

Simplify each expression.

1. (a)Simplify 7x − 4x + 2x.[1]
2. (b)Simplify 3p × 4p.[1]
3. (c)Expand 5(2y − 3).[1]

Expand and simplify.

1. (a)Expand and simplify 2(3x + 1) + 4(x − 2).[2]
2. (b)Expand and simplify (x + 4)(x + 2).[2]

m = 3 and n = −2. Find the value of each expression.

1. (a)4m + 3n[1]
2. (b)2m² − n[2]
3. (c)m(n + 5)[1]

p = −3 and q = 4. Find the value of each expression.

1. (a)3p + 2q[1]
2. (b)pq[1]
3. (c)p² + q²[2]
4. (d)(q − p)²[1]

Expand and simplify.

1. (a)2x(3x − 5)[2]
2. (b)4(x + 2) − 3(x − 5)[3]

Factorise each expression completely.

1. (a)8x + 12[1]
2. (b)x² − 81[1]
3. (c)x² − 3x − 10[2]
4. (d)3x² − 12x[1]

Expand and simplify (x + 2)(x − 3)(x + 1). (Extended)

1. (a)Expand and simplify (x + 2)(x − 3).[1]
2. (b)Hence expand and simplify (x + 2)(x − 3)(x + 1), writing your answer as a single cubic.[3]

Factorise these quadratics. (Extended)

1. (a)4x² − 25[1]
2. (b)2x² + 5x + 2[2]
3. (c)x² − 4x + 4[2]

Factorise completely.

1. (a)15x² − 20x[2]
2. (b)x² − 100[1]
3. (c)3x² + 10x − 8 (Extended)[3]

Expand and simplify. (Extended)

1. (a)(2x + 5)(3x − 2)[3]
2. (b)(x + 3)³[3]

Complete the square. (Extended)

1. (a)Write x² + 6x + 2 in the form (x + a)² + b.[2]
2. (b)Write x² − 4x + 9 in the form (x + a)² + b.[2]
3. (c)State the coordinates of the minimum point of the curve y = x² + 6x + 2.[1]

Algebraic fractions. (Extended)

1. (a)Express 5/(x − 2) − 3/(x + 1) as a single fraction in its simplest form.[3]
2. (b)Simplify (x² + 7x + 10)/(x² − 25).[3]

Answer this question without a calculator. (Extended)

1. (a)Write x² − 10x + 7 in the form (x − a)² − b.[3]
2. (b)Hence state the minimum value of x² − 10x + 7.[1]
3. (c)Solve x² − 10x + 7 = 0, giving your answers in surd form.[2]

Answer this question without a calculator. (Extended)

1. (a)Simplify (x² − 4x)/(x² − 16).[3]
2. (b)Express 4/(x − 1) − 3/(x + 2) as a single fraction in its simplest form.[3]