# IGCSE Mathematics Paper-1: Specimen Questions with Answers 17 - 20 of 324

## Question number: 17

Essay Question▾

### Describe in Detail

The diagram shows a cube of side ‘a’ of 6 cm.

(a) Calculate the area of the cube.

(b) Calculate the volume of the cube in meter.

### Explanation

Here, side a = 6 cm.

(a) **Area of cube**:

(b) **Volume of the cube**:

Now,

So,

So,

## Question number: 18

Essay Question▾

### Describe in Detail

Solve

In the diagram BC is parallel to DE.

(a) Complete the following statement; Triangle ABC is ________ to triangle ADE.

(b) AB = 12 cm, BC = 8 cm and DE = 10 cm. Find length of AD.

(c) Angle ABC = . Find size of the reflex angle at D.

### Explanation

Here,

(a) BC is parallel to DE, which means it is a side splitter theorem.

In which .

So, Triangle ABC is **similar** to triangle ADE.

(b) AB = 12 cm, BC = 8 cm and DE = 10 cm.

Now,

So, for

For

So, from (I) and (II),

(c) Angle ABC = . So, size of the reflex angle at D is similar to angle ABC because and so both triangles are similar.

So, size of reflex angle at D is

## Question number: 19

Short Answer Question▾

### Write in Short

Solve the equations

(a) ,

(b)

### Explanation

Here,

(a)

(b)

## Question number: 20

Essay Question▾

### Describe in Detail

The population of a city is . It is expected that this population will increase by 42 % by the year 2008. Calculate the expected population in 2008.

### Explanation

Here, Population is .

Expected population will increase by 42%.

So, increment in population will: .

So, expected population will be