S3 Algebra Homework
Exercise 1
1. Expand the following expressions;
a) 3(4x + 7)
b) 4(3x – 5y)
c) x(4x – 5x2)
d) 3xy(5x – 2 +y)
Exercise 2
1. Solve the following equations;
a) 3x + 6 = 15
b) 6x – 9 = 6
c) 3(x – 5) = 12
d) 7(2x - 3) = 49
e) 6x – 5 = 4x + 8
f) 5x + 6 = 2x – 9
g) 5(2x + 6) = 2(x + 3)
h) 15 -2(x+ 3) = 1
2. Expand and simplify the following expressions;
a) 4(x + 3) + 7(x -2)
b) 6(x – 1) + 4(2x + 1)
c) 2(x – 3) – 7(x – 5)
d) x(x – 6) – 2x(4 – x)
2. Change the subject of the formula to x
a) y = mx + c
b) P = x + 9
c) S = 4 + 8x
d) F = 2(x + 10)
e) V = mx
f) L = 4(x – 3) + x
𝑥
g) Y = 𝐵
3. Factorise the following expressions;
a) 6x + 18
b) 8x – 12
c) 9x – 12y
d) x2 – 4x
e) 6x2 – 9x
4. Expand and simplify;
a) (x + 2)(x + 5)
c) (x – 4)(x + 3)
e) (2x + 3)(3x + 8)
g) (x + 8)(x – 8)
i) (x + 4)2
k) (3x – 2)2
Exercise 3
b) (x + 6)(2x + 1)
d) (x – 5)(x – 7)
f) (x + y)(x – y)
h) (2x – 6)(2x + 6)
j) (x – 9)2
l) (x – y)2
𝑃
h) 𝑉 = 𝑥
3. For each of the following rules, copy and complete a
table like the one shown below.
x
0
1
2
3
y
a) y = 4x - 2
c) y = x – 5
b) y = 2x + 3
d) y = 8 – x
4. On the same graph, plot the 4 lines given in Qu. 3
Exercise 4
1. Expand the following expressions;
a) 3(5 + 7x)
b) 12(x – 5y)
c) x(4 – 7x2)
d) 9xy(5y – 2 +3x)
1. Solve the following equations;
a) 2x + 1 = 4
b) 4x – 9 = 6
c) 4(x – 8) = 40
d) 7(2x + 9) = 21
e) 6x – 7 = 3x + 8
f) 7x + 6 = 3x – 12
g) 3(2x - 6) = 2(x - 3)
h) 10 – 2(x + 3) = 8
2. Expand and simplify the following expressions;
a) 2(x + 3) + (x - 2)
b) 5(x – 1) + 2(2x + 1)
c) 3(x – 3) – 3(x – 3)
d) x(x – 1) – 2x(4 – 3x)
2. Change the subject of the formula to x
a) y = 2x + c
b) 5P = x + 9
c) S = 1 – 8x
d) F = 2(x – 10)
e) V = 10x
f) L = 2(x – 3) + x
2𝑥
g) a = 𝑤
3. Factorise the following expressions;
a) 9x + 12
b) 8x – 24
c) 12x – 18y
d) 2x2 – 6x
e) 66x2 – 99x
4. Expand and simplify;
a) (x + 7)(x + 10)
c) (x – 2)(x + 3)
e) (2x + 7)(x – 8)
g) (x + 1)(x – 1)
i) (x + 1)2
k) (2x – 5)2
b) (2x + 3)(x + 1)
d) (x – 3)(x – 3)
f) (m + n)(m – n)
h) (6 – x)(6 + x)
j) (x – 7)2
l) (2x – y)2
2𝑃
h) 𝑉 = 3𝑥
3. For each of the following rules, copy and complete a
table like the one shown below.
x
0
1
2
3
y
a) y = 3x - 1
c) y = 4x – 7
b) y = 2x – 3
d) y = 3 – x
4. On the same graph, plot the 4 lines given in Qu. 3
Exercise 5
1. Expand and simplify the following expressions;
Exercise 6
1. Solve the following equations;
a) (x + 3) – 7(x - 2)
b) x(x – 1) + x(2x + 1)
c) x(3x – 3) – 2x(x – 5)
d) x(x – 6) – 2x(4 – x) – 3(x + 1)
a) 6x – 5 = 3x +13
c) 6x – 5 = 9x + 10
e) 5(2x – 6) = 2(x + 3)
2. Factorise the following expressions;
a) 6x + 24
c) 9ab – 12a2b
b) 8xy – 12y
d) 9x2 – 4x
b) 6(2x - 3) = 66
d) 5x + 14 = 2 – x
f) 10 – 2(x+ 3) = 1
2. Solve the following inequations;
a) 2x + 5 > 15
b) 3x – 9 < 6
c) 3(x – 5) < 12
d) 7(2x - 3) > 49
e) 6x – 5 ≤ 4x + 8
f) 5x + 6 ≥ 2x – 9
3. Change the subject of the formula to y
3. Expand and simplify;
a) (x + 6)(x + 5)
c) (x – 5)(x + 9)
e) (2x + 3)(x – 8)
g) (x + a)(x – a)
i) (2x + 5)2
b) (x + 7)(x + 2)
d) (x – 2)(x – 4)
f) (2x + y)(x – 2 y)
h) (5x – 3)(2x + 1)
j) (3x – 2)2
4. Factorise the following expressions;
a)9x2 – 4
c) 16m2 – 49
e) x2 + 5x + 6
g) x2 + x + 6
b) y2 – 64
d) p2 – 36
f) x2 –5x + 6
h) x2 – x + 6
a) T = 7y + x
c) S = 4 + 8y
e) V = 3my
5𝑦
g) W = 𝐵
b) P = 3y – 9
d) F = 2(y + 5)
f) L = 2(y – 3) + y
𝑃
h) 𝐺 = 𝑦
4. For each of the following rules, copy and complete a
table like the one shown below.
x
0
1
2
3
y
a) y = 3x - 2
c) y = x – 3
b) y = 2x + 1
d) y = 5 – x
5. On the same graph, plot the 4 lines given in Qu. 4
Exercise 7
1. Expand and simplify the following expressions;
Exercise 8
1. Solve the following equations;
a) (x + 2) – 3(x - 1)
b) x(x – 1) + x(3x + 2)
c) x(7x – 2) – 3x(x – 2)
d) x(x – 9) – 2x(2 – x) – 3(x – 1)
a) x – 4 = 3x +13
c) 6x – 5 = x + 10
e) 5(2x – 1) = 2(x + 1)
2. Factorise the following expressions;
a) 7x + 21
c) 8a – 12a2b
b) 12xy – 10y
d) 10x2 – 15x
b) 9(2x - 3) = 63
d) 5x + 1 = 1 – x
f) 16 – 2(x+ 3) = 1
2. Solve the following inequations;
a) 2x + 3 > 11
b) 3x – 5 < 4
c) 4(x – 3) < 12
d) 4(2x - 5) > 44
e) 5x – 3 ≤ 4x – 8
f) 4x + 6 ≥ 2x – 9
3. Change the subject of the formula to y
3. Expand and simplify;
a) (x + 6)(x + 5 – y))
c) (x – 9)(x + 2)
e) (2x + 1)(3x – 2)
g) (x + 3a)(x – 3a)
i) (5x + 2)2
b) (2x + 7)(x + 2 + t)
d) (x – 6)(x – 5)
f) (2x + 3y)(x – 2y)
h) (5x – 2)(5x + 2)
j) (4x – 3)2
4. Factorise the following expressions;
a) x2 –144
c) 25m2 – 9
e) x2 + 6x + 5
g) x2 + 7x + 6
b) y2 – 1
d) p2 – 4
f) x2 –4x + 4
h) x2 – 6x – 7
a) P = x + 7y
c) S = 4y + 3
e) V = 8my
9𝑦
g) W = 𝐵
b) G = 9 – 3y
d) F = 2(6 + y)
f) L = 2(y – 3) + 1
𝑃
h) 𝐺 = 4𝑦
4. For each of the following rules, copy and complete a
table like the one shown below.
x
0
1
2
3
y
a) y = 4x - 6
c) y = ½ x – 2
b) y = 2x – 2
d) y = 5 – 3x
5. On the same graph, plot the 4 lines given in Qu. 4