Name______________________________ Grade___________ Date____________
1
Factorise completely
(a) 21a2 – 14a,
(b) x2 – 3x – 40.
Given that y = 3 is a solution of the equation 2y2 + ky – 27 = 0, find the other solution.
3
Solve the equation
4
Expand and simplify
5
Factorise completely
3( y + 2) = 2(2y – 7) + y.
( p – 5)( p + 4).
(a) 4x2 + 12xy + 9y2,
(b) 3m2 – 48.
6
Solve the equations
(a)
24 = 1,
x–4
(b) 12 – 2(5 – y) = 5y.
7 Factorise completely
(a) 15a2 + 12a3,
(b) 1 – 16b2,
(c) 6cx – 3cy – 2dx + dy.
8
Simplify
9
Solve
25x 2 ÷ 5x– 4.
(2x – 3)(x + 2) = 0.
10 (a) Factorise fully
5x2 – 10x.
(b) Solve
3y + 6 = 7y – 10.
(c) Solve
3p(p + 2) = 0.
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2
Name______________________________ Grade___________ Date____________
11
Solve the equations
(a) 2y = 8,
(b) 3p + 4 = 8 – 2( p – 3),
(c)
18 – 16
q q+2
(d) 5x2 + x – 7 = 0, giving each solution correct to 2 decimal places.
13
Simplify 3b(b – 1) – 2(b – 2)(b + 2).
14 (a) Solve the equation 3x2 – 4x
(b) Remove the brackets and simplify (3a – 4b)2.
(c) Factorise completely 12 + 8t – 3y – 2ty.
15 Given that 3h + 2x = 2f – gx, express x in terms of f, g and h.
16 Solve the equation 2x 2 + x –12 = 0, giving the solutions correct to 3 decimal places
17 Solve the equation 3x2 + 11x − 7 = 0 , giving each answer correct to 2 decimal places.
18 (a) Remove the brackets and simplify
(q+3r) (2q–r).
(b) Given that m = –2 and n = 4, evaluate
(i) 5m3,
(ii) –m– + –n– .
n
m
(c) Factorise completely
3y 2–3.
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12 Solve the equation x2 + 30x – 64800 = 0.