Mathematics 0580 · IGCSE · Algebraic manipulation

Algebraic manipulation — practice question

(a(i))[3]

Factorise the expression $27y^2 - 3$ fully.

(a(ii))[2]

Factorise the expression $2m - pk + 2k - pm$ fully.

(b)[5]

Solve $\dfrac{x - 1}{x + 1} - \dfrac{6}{x - 1} = 1$.

(c)[4]

Solve $4x^2 - 3x - 2 = 0$. Show all the working clearly and give each answer correct to 2 decimal places.

(d)[4]

Make $k$ the subject from the formula $\dfrac{k}{m} = 4 + kp$.

Worked solution & mark scheme

This 18-mark question has a full step-by-step worked solution and mark scheme. One marking point: The factorised form is $3(3y-1)(3y+1)$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI