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