IGCSE Mathematics – Extended Topic: Algebra- Manipulation Worksheet Student Name: Date: Expanding Brackets 1. (a) Expand the bracket and simplify the expression 7x + 5 – 3(x – 4). Answer (a) ……….…………………….…… [2] (b) Factorise 5x2 – 7x. Answer (b) ……….…………………….…… [1] 2. (x + 4) cm 4x cm R Q (x + 12) cm (a) (i) (x + 2) cm NOT TO SCALE Write down an expression for the area of rectangle R. Answer (a) (i) …….…………………. cm2 [1] (ii) Show that the total area of rectangles R and Q is 5x2 + 30x + 24 square centimetres. [1] Mathelaureate / IGCSE / Revision Worksheet / DJ 1 (b) The total area of rectangles R and Q is 64 cm2. Calculate the value of x correct to 1 decimal place. Answer (b) x = ……………………………. [4] 3. Expand the brackets and simplify 3x2 – x(x – 3y). Answer …………….………….. [2] 4. Expand the brackets and simplify 4x2 – x(x – 2y). Answer ………………..………. [2] 5. Expand the brackets and simplify 5x – 6(3x – 2). Answer …..….……….………… [2] 6. Expand the brackets and simplify 3x – 5(4x – 2). Answer ………………………… [2] 7. (a) Expand and simplify 5(3c – 4d) – 8c. Answer (a) …….…………………… [2] (b) Factorise pq – q2. Answer (b) ………….……………… [1] Mathelaureate / IGCSE / Revision Worksheet / DJ 2 8. (a) Expand and simplify 4(5c – 3d) – 7c. Answer (a) ………………………… [2] (b) Factorise m2 – mn. Answer (b) ………………………… [1] Factorization 9. Factorise 3xy – 2x. Answer …………………….…………… [1] 10. Factorise completely (a) 7ac + 14a, Answer (a) ………….……….…………… [1] (b) 12ax3 + 18xa3. Answer (b) ………….……….…………… [2] 11. Factorise completely 2x2 – 6xy. Answer ……………..…………………… Mathelaureate / IGCSE / Revision Worksheet / DJ 3 [2] 12. Factorise (a) 4x2 – 9, Answer (a) ……………………………… [1] (b) 4x2 – 9x, Answer (b) ……..…..…………………… [1] (c) 4x2 – 9x + 2. Answer (c) ……..…..…………………… [2] 13. Factorise completely 2a2b – 6a. Answer …….………….………………… [2] 14. Factorise completely xy2 – x2y. Answer …………………….. [2] 15. Factorise completely 4xy – 2x. Answer ………………………… [2] Mathelaureate / IGCSE / Revision Worksheet / DJ 4 16. Factorise completely 2pq – 4q. Answer ….……………………… [2] 17. Factorise completely 6x – 9x2y. Answer ……….….………..…… [2] 18. (i) Factorise x2 – x – 20. [2] (ii) Solve the equation x2 – x – 20 = 0. [1] 19. y = m2 – 4n2. (i) Factorise m2 – 4n2. [1] (ii) Find the value of y when m = 4.4 and n = 2.8. [1] (iii) m = 2x + 3 and n = x – 1. Find y in terms of x, in its simplest form. [2] Mathelaureate / IGCSE / Revision Worksheet / DJ 5 (iv) Make n the subject of the formula y = m2 – 4n2. [3] 20. (i) m4 – 16n4 can be written as (m2 – kn2)(m2 + kn2). Write down the value of k. [1] (ii) Factorise completely m4n – 16n5. [2] 21. (a) Factorise ax2 + bx2. Answer (a) ……….….………… [1] (b) Make x the subject of the formula ax2 + bx2 – d2 = p2 Answer (b) x = ………………… [2] Mathelaureate / IGCSE / Revision Worksheet / DJ 6 Simplification 22. Simplify the following expressions. (a) 9r – 4s – 6r + s Answer (a) ……….…………….………… [1] (b) q4 ÷ q3 Answer (b) ……….…………….………… [1] (c) p6 × p–2 Answer (c) ……….…………….………… [1] 23. Simplify (a) p 2 × p 3, Answer (a) ……………..………………… [1] (b) q3 ÷ q–4, Answer (b) ………..……………………… [1] (c) (r2)3. Answer (c) ………………………..……… [1] Mathelaureate / IGCSE / Revision Worksheet / DJ 7 24. Simplify the expression 5p – 2q – (p + q). Answer ……………………………… [2] 25. Simplify 3x2y × x4y2. Answer …….……...…..………………… [2] 26. Simplify x 5x 5x . 3 9 18 Answer ……….….…….……… [2] 27. Simplify x 7x 7x . 3 9 18 Answer ……….….……………. [2] Mathelaureate / IGCSE / Revision Worksheet / DJ 8