Cambridge International AS and A Level Mathematics Pure Mathematics 1

Algebra

P^

1

10 Write the following as single fractions.

(i) xx 4 +^1 + 2 –^1 (ii) 23 xx– 5 –^1 (iii) 35 xx 4 ––+ 67

(iv) 32 ()xx 5 +^1 –^72 (– 2 ) (v) 41 xx 8 + +^7312 –

11 Simplify the following expressions.

(i) 26 xx++^3 (ii) 62 1

32 1

2

5

()

()

x

x

+

+

(iii)

23

83

4

2

xy

xy

(– )

(– )

(iv) (^61) xx–– 22 (v) ()^32664
x^24
x
x
x

+ ×

+

Linear equations

●?^ What is a variable?

You will often need to find the value of the variable in an expression in a

particular case, as in the following example.

EXAMPLE 1.13 A polygon is a closed figure whose sides are straight lines. Figure 1.1 shows a

seven-sided polygon (a heptagon).

An expression for S°, the sum of the angles of a polygon with n sides, is

S = 180(n − 2).

●?^ How is this expression obtained?

Try dividing a polygon into triangles, starting from one vertex.

Find the number of sides in a polygon with an angle sum of (i) 180° (ii) 1080°.

Figure 1.