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Topic: Algebra[Quad.(Factorisation), Expansion, Ln. Inq.]
T.M: 35
1. Solve the following quadratic equations by factorisation:
a. 3𝑥 + 2 = 2𝑥 2
[3]
b. 𝑥 2 = 7𝑥
c. (𝑥 + 1)(2𝑥 + 3) = 6
[4]
d. 𝑥−2 + 𝑥+1 = 3
[3]
f. 𝑘 2 = 9
e. 𝑥 2 =
𝑥
4
2
4
[3]
[5]
[3]
2. a. Expand: (2p-q)2
a. ………………………………………………. [2]
b. Given that 2p – q = 6, and pq = 10
Using (a) find 4p2 + q2
b. ………………………………………………. [2]
3. Solve the pair of inequalities and write the range of values of x for which both the
inequalities are true:
𝑥+3
5
> −2, and 3 − 2𝑥 < 10
………………………………………………. [3]
4. Given that 1 ≤ 𝑥 ≤ 5 𝑎𝑛𝑑 − 3 ≤ 𝑦 ≤ 1, 𝑓ⅈ𝑛𝑑
a. the greatest possible value of x – y
………………………………………………. [2]
b. the least possible value of x2 + y2
………………………………………………. [2]
5. Graph the inequality: −2 < 𝑥 ≤ 5
………………………………………………. [1]
6. Factorise: 𝑥 2 𝑦 2 + 𝑥 2 + 𝑦 2 + 1
………………………………………………. [2]