REVISE PAPER GRADE 7 2ND SEMESTER Part 1. ALGEBRA 1. Expand the following: a. 6(𝑎 − 2𝑏 + 3𝑐) 1 b. 2 𝑎(2𝑎 + 4𝑐 − 4𝑑) 2. Expand and simplify the following: a. 3(𝑚 + 2) − 5 2 1 b. 3 (6𝑥 + 3𝑦) + 3 (3𝑥 − 9𝑦) c. (2𝑎 + 5)(𝑎 − 3) d. (𝑥 − 7)(𝑥 − 9) e. (𝑥 + 1)(𝑥 − 2)(𝑥 + 3) 3. Factorise the following: a. 3𝑎𝑏 + 6𝑎𝑐 b. 12𝑥 2 𝑦 − 36𝑥𝑦 2 4. Evaluate the following expressions if 𝑎 = 5, 𝑏 = 3, 𝑐 = −1, 𝑑 = −2 a. 𝑎 − 𝑏 + 𝑐 − 𝑑 b. 𝑎𝑐 − 𝑏𝑑 c. (𝑎 + 𝑑)(𝑏 − 𝑐) 5. In the following questions, make the letter in red the subject of the formula: a. 𝑎𝑐 + 𝑑 = 𝑓 b. 𝑝𝑞(𝑟 + 𝑠) = 𝑡 c. 𝑎2 + 𝑏 2 = 𝑐 2 𝑝 d. 𝑎𝑐 = 𝑓√ 𝑠 6. Factorise the following by grouping: a. 𝑚𝑛 + 4𝑚 + 2𝑛 + 8 b. 𝑥 2 − 𝑥𝑦 − 2𝑥 + 2𝑦 7. Factorise the following: a. 𝑎2 − 𝑐 2 b. 25 − 9𝑎2 1 4 c. 9 𝑥 2 − 25 𝑦 2 d. 𝑝6 − 𝑞 6 8. Factorise the following quadratic expression: a. 𝑥 2 + 5𝑥 − 24 b. 𝑥 2 − 6𝑥 + 9 c. 𝑥 2 + 8𝑥 + 15 d. 3𝑥 2 + 9𝑥 + 6 9. Simplify the following algebraic fractions: a. b. 𝑎2 𝑏 𝑐 9𝑎𝑏 4 × ÷ 𝑐𝑓 𝑎 3𝑎 2 𝑒𝑑 × 𝑏𝑓 10. Simplify the following algebraic fractions: 2𝑝 a. 𝑝 + 5 b. 11𝑥 − 5𝑥 3 2 2(𝑏−2) 4(𝑏−1) c. + 2 3 11. Simplify the following: 2 3 a. 𝑥+1 + 𝑥−2 b. c. 𝑎2 −64 𝑎2 +8𝑎 (𝑥+2)(𝑥−5) (𝑥+1)(𝑥+2) 12. Simplify the following: a. (2𝑝2 )3 × (3𝑝)2 b. 𝑎0 ÷𝑎−5 (𝑎2 )−2 𝑛 13. Simplify the following algebraic expression, giving your answer in the form ( √𝑏) 1 a. √𝑏×𝑏3 2 (𝑏 2 )3 3 b. 𝑏 −2 ×( √𝑏) 𝑏 −1 2 𝑚