IGCSE Math. Algebra.

Expansion

100

Expand the brackets.

y(3 – y³)

3y – y⁴

200

Expand the brackets and simplify.

0.5(6x – 2) – 3(x – 1)

2

300

Expand and simplify

2(x – 3)² – (2x – 3)²

9 – 2x²

400

Expand and simplify.

(x – 2)(x + 5)(2x – 1)

2x³ + 5x² – 23x + 10

Factorization

100

Factorise completely.

2xy – 4yz

2y(x – 2z)

200

Factorise completely

ax + bx + ay + by.

(a+b)(x+y) or (x+y)(a+b)

300

Factorise completely.

p²x – 4q²x

x(p – 2q)(p + 2q)

400

Factorise completely the expression

4x² – 18x – 10.

2(2x + 1)(x – 5)

Equations

100

Solve the equation 

1 + 2x = –15 .

–8

200

Solve the equation 

4x – 12 = 2(11 – 3x).

3.4 (oe)

300

Solve the equation 

2x² + 3x – 6 = 0.

(Give your answers correct to 2 decimal places.)

–2.64, 1.14

400

Solve the equation

7/(x+4) + (2x – 3)/2 = 1

–2.64, 1.14

Algebraic Fractions

100

Write as a single fraction

3a/8 + 4/5

(15a + 32)/40

200

Write as a single fraction in its simplest form.

2/x + 1/2x + 1/2

(x + 5)/2x

300

Write the following as a single fraction in its simplest form.

(x + 1)/(x + 5)  –  x/(x + 1)

(1  –  3x)/(x + 1)(x + 5)

400

Solve the equation

(2x + 3)/(x - 4) + (x + 40)/(x² - 16) = 2

-7

Functions

100

f(x) = 5 – 3x

Find f(6).

–13

200

f(x) = 5 – 3x

Find f(x + 2).

–3x – 1

300

f(x) = 5 – 3x

Find ff(x) in its simplest form.

9x – 10

400

f(x) = x² + x - 1

g(x) = 1 - 2x

Find fg(x). Give your answer in its simplest form.

4x² – 6x + 1