Mathelaureate / IGCSE / Extended Mathematics / WS / D J Page no: 1

IGCSE Mathematics - Extended

Topic: Variations & Linear Programming

1. [Maximum marks : 12]

A region R is defined by

[a] on grid paper, graph the region R.

[5marks]

[b] How many points in R have integer coordinates?

[1 mark]

[c] Find all points in R with integer coordinates that lie on the line

[3marks]

[d] Find the maximum value of for the 15 feasible points in R.

[3 marks]

Answer [a]

Mathelaureate / IGCSE / Extended Mathematics / WS / D J Page no: 2

[b] There are 15 points with integer coordinates as shown

[c] the line y = ½ x +3 passes through (2,4) and (4,5)

[d] 5x+4y has maximum value 47 when x = 7

2. [Maximum marks : 5]

Consider the production of 2-drawer and 5-drawer filing cabinets. We only

have 34 drawers, 8 locks, and 42 square meters of sheet metal available.

Each 2-drawer cabinet requires 1 lock and 2 square meters of sheet metal,

while each 5-drawer cabinet requires 1 lock and 4 m2 of sheet metal. Let be

the number of 2-drawer filing cabinets made and be the number of 5-

drawer filing cabinets made of be the number of 5-drawer filing cabinets

made. List the constraints connecting

Answer:

Type Number of cabinets Locks per cabinet Metal per cabinet

2- drawer x 1 2m2

5-drawer y 1 4m2

Since we cannot make negative cabinets.

The total number of drawers :

The total number of locks :

The total number of m2 metal :

Mathelaureate / IGCSE / Extended Mathematics / WS / D J Page no: 3

3. [Maximum marks : 6]

The or time for one completed swing of a pendulum is directly

proportional to the square root of its length. When the length is 25 cm, the

period is 1.00 seconds.

[a] If the length is 70 cm, find the period to 2 decimal places.

[3marks]

[b] What would the length be for a period of 2 seconds?

[3marks]

Answer:

[a] Period is 1.67 seconds

[b] Length 100 cm

4. [Maximum marks : 5]

The velocity V of a body travelling a fixed distance is inversely proportional to

the time taken t to complete the journey. When the velocity is 40cm/s, the

time taken is 280 seconds. Find the time when the velocity is 50 cm/s.

Answer:

Mathelaureate / IGCSE / Extended Mathematics / WS / D J Page no: 4

5. [Maximum marks : 5]

The volume of a cylinder of fixed height varies in direct proportion to the

square of the base radius. Find the change in volume when the base radius is

increased by 18%.

Answer:

V ha increased by 39.24%