# Cambridge International AS and A Level Mathematics Pure Mathematics 1

(Michael S) #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)``

##### 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.``