SFR Lesson Notes The Winston Churchill School
Algebra Exam Prep
1.
(a)
x2 + 6x + 8
Factorise
……………………… (2)
(b)
x2 + 6x + 8 = 0
Solve
x =……………………… or x =……………………… (1) (Total 3 marks)
2.
3y + y2
Factorise
............................... (Total 2 marks)
3.
(a)
Factorise
x2
2x
15
………………………… (2)
(b)
Hence, or otherwise, solve x2
2x
15 = 0
x = …………
or
x = ……….. (1) (Total 3 marks)
4.
(a)
Solve
6x + 2 = 4(x
7) x = …………………….. (2)
(b)
Solve
15 2 x 3
4 x = …………………….. (3)
(c)
(i)
Factorise
x2
23 x
42
..……………………….. (ii)
Hence solve
x2
23x 42 0
………………………… (3) (Total 8 marks)
5.
Solve x2 – 3x – 18 = 0 …………………………… (Total 3 marks)
6.
x2 + 6x + 8
Factorise
……………………. (Total 2 marks)
7.
Factorise x2 + 7x + 6 .......................... (Total 2 marks)
8.
(i)
Factorise
x2 – 7x + 12
................................. (ii)
Solve the equation x2 – 7x + 12 = 0 ................................. (Total 3 marks)
9.
(a)
Factorise 3x + 6 …………………… (1)
Here is a right-angled triangle.
5x + 10 3x + 6
4x + 8
The lengths of the three sides of the triangle are 3x + 6, 4x + 8 and 5x + 10. All measurements are in centimetres. (b)
Find an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest form.
……………………………. (2)
The perimeter of the triangle is 42 cm. (c)
(i)
Find the value of x. x = ………………………. (1)
(ii)
Find the length of the shortest side of the triangle. …………………………. cm (4) (Total 7 marks)
10.
(a)
Factorise
3t – 12 ………………………… (1)
(b)
Expand and simplify 3(2x – 1) – 2(2x – 3) ………………………… (2) (Total 3 marks)
11.
y2 + 3y – 10
Factorise
........................................ (Total 2 marks)
12.
Factorise
x2
10x ……..………………….. (Total 1 mark)
13.
(a)
Expand and simplify 3(2x – 1) – 2(2x – 3) ………………………… (2)
(b)
Factorise y2 + y ………………………… (1) (Total 3 marks)
14.
Factorise x2 – 3x .......................... (Total 2 marks)
15.
Factorise
x2 – 3x ................................. (Total 2 marks)
16.
(a)
Expand and simplify
(3x + 2)(4x + 1) ............................................ (2)
(b)
Factorise completely
3x2 + 6xy ............................ (2) (Total 4 marks)
17.
(a)
Expand
t(t – 2) .......................... (1)
(b)
Factorise 3y – 12 .......................... (1) (Total 2 marks)
18.
(a)
Solve
4(2x + 1) = 2(3 – x) x = .......................... (3)
(b)
Factorise fully 2p2 – 4pq .......................... (2) (Total 5 marks)
1.
(a)
(x + 2)(x + 4)
(b) –2, –4 2.
y(3 + y)
3.
(a)
(x
5)(x + 3)
(b) 5 or –3 4.
(a)
–15
(b)
1.5
(c)
(i)
(x
(ii)
2 and 21
5.
6,
6.
(x + 2)(x + 4)
7.
(x + 1)(x + 6)
8.
(i)
21)(x
2)
3
(x – 3)(x – 4)
(ii) x = 3, x = 4 9.
(a)
3(x+2)
(b) 12x + 24 (c)
(i)
1.5
(ii)
10.5
10.
(a) (b)
3(t-4) 2x + 3
11.
(y + 5)(y –2)
12.
x (x
10)
13.
(a)
2x + 3
(b)
y (y + 1)
14.
x(x – 3)
15.
x(x – 3)
16.
(a)
12x2 + 11x + 2 (b)3x(x + 2y)
17.
(a)
t2 – 2t
(b) 3(y – 4) 18.
(a)
0.2
(b) 2p(p – 2q)