Year 11

Answers to the first 10 questions of the algebra revision are attached.
If you need to check the remainder, please send a comment and I will upload.

Algebra revision answers, don't know how to do powers so ^2 means squared etc.

1
a) t^8
b) 12a^2b
c) 30a^4b
d) a^6b^3
e) 24p^2q^4
f) a^3b^3c^3
g) 4x^2
h) 27x^6y^3

2
a) a^2
b) a^2b
c) 4a^-3b^3
d) a^4
e) a^4c^-1
f) 2a^2b^2c

3
a) 2p + p^2
b) 10x + 15
c) -21x^2 + 12x
d) 3y^2 – 2y^5
e) 2x^3 – 5x^2
f) 3x^3 – 2x^2 + 5x

4
a) 4a + 3a + 2 = 7a + 2
b) 3p + 10p – 6 = 13p – 6
c) 9t – 6t – 12 = 3t – 12
d) 5r – 6 + 12r = 16r – 6
e) 2x + 2 + 3x + 12 = 5x + 14
f) 3x + 18 – 3x – 12 = 6x + 6
g) 7 + 5x + 10 = 5x + 17
h) 11 – 2x + 10 = 21 – 2x
i) 12t – 20 – 8 + 12t = 24t – 28

5
a) 4(x + 2)
b) 6(x – 3)
c) 4(x2 + 5)
d) x(3x – 1)
e) 5y(2y – 1)
f) 4x(x + 3)
g) 5y(3y – 4z^2)
h) xy(y – x)
i) 2x^2y^2(2yz + 3x)

6
a) (x + 3)(x – 3)
b) (z + 1)(z – 1)
c) (2x + y)(2x – y)
d) (3w + 5y)(3w – 5y)
e) (6x + 2)(6x – 2)
f) 2x^2 so can’t be difference of two squares

7 factorise then solve
a) x(x – 9) = 0 so x = 0 or x = 9
b) x(x – 5) = 0 so x = 0 or x = 5
c) x(5x – 3) = 0 so x = 0 or 5x – 3 = 0, x = 0.6 (three fifths)
d) x(x – 7) = 0 so x = 0 or x = 7
e) 2x(x – 4) = 0 so x = 0 or x = 4
f) 3x(x – 2) = 0 so x = 0 or x = 2

8
a) x^2 + 8x + 15
b) x^2 + 8x + 7
c) x^2 + x – 30
d) x^2 + 5x – 36
e) x^2 – 5x + 6
f) x^2 – 10x + 9
g) x^2 + 10x + 25
h) x^2 – 16x + 64
i) 2x^2 + 5x + 3
j) 8x^2 + 10x – 3
k) 9x^2 – 9x + 2
l) 16x^2 – 24x + 9

9 Factorise then solve
a) (x + 2)(x + 3) = 0 so x = -2 or x = -3
b) (x + 6)(x + 1) = 0 so x = -6 or x = -1
c) (x + 3)(x – 2) = 0 so x = -3 or x = 2
d) (x – 7)(x + 3) = 0 so x = 7 or x = -3
e) (x – 5)(x – 1) = 0 so x = 5 or x = 1
f) (x – 7)(x – 5) = 0 so x = 7 or x = 5
g) (x – 1)(x – 1) = 0 so x = 1
h) (x + 3)(x + 3) = 0 so x = -3
i) (x + 7)(x – 4) = 0 so x = -7 or x = 4

10 Factorise then solve
a) (2x + 1)(x + 3) = 0 so x = -0.5 or x = -3
b) (3x – 1)(x + 2) = 0 so x = 0.33333… or x = -2
c) (5x - 2)(x – 3) = 0 so x = 2/5 or x = 3
d) (2x - 1)(2x + 3) = 0 so x = 0.5 or x = -3/2
e) (4x + 3)(x + 5) = 0 so x = -3/4 or x = -5
f) Simplify first and you get 3x^2 – 7x + 2 = 0, so (3x – 1)(x – 2) = 0, x = 0.33333… or x = 2