IGCSE Mathematics 0580/42 Paper 4 Feb/Mar 2022 - XtremePapers

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Cambridge IGCSETM

MATHEMATICS Paper 4 (Extended)

You must answer on the question paper. You will need: Geometrical instruments

0580/42 February/March 2022

2 hours 30 minutes

INSTRUCTIONS

Answer all questions. Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. Write your name, centre number and candidate number in the boxes at the top of the page. Write your answer to each question in the space provided. Do not use an erasable pen or correction fluid. Do not write on any bar codes. You should use a calculator where appropriate. You may use tracing paper. You must show all necessary working clearly. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in

degrees, unless a different level of accuracy is specified in the question.

For r, use either your calculator value or 3.142.

INFORMATION The total mark for this paper is 130. The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Any blank pages are indicated.

DC (CE/FC) 301926/4 ? UCLES 2022

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2 1 A company employed 300 workers when it started and now employs 852 workers.

(a) Calculate the percentage increase in the number of workers.

............................................. % [2] (b) Of the 852 workers, the ratio part-time workers : full-time workers = 5 : 7.

Calculate the number of full-time workers.

................................................. [2]

(c) The company makes 40 600 headphones in one year.

Write this number

(i) in words,

........................................................................................ [1]

(ii) in standard form.

................................................. [1]

(d) In one month, the company sells 3 000 headphones.

Of

these,

48%

are

exported,

3 8

are

sold

to

shops

and

the

rest

are

sold

online.

Calculate the number of headphones that are sold online.

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0580/42/F/M/22

................................................. [3]

3 (e) One year, sales increased by 15%.

The following year sales increased by 18%. Calculate the overall percentage increase in sales.

............................................. % [3]

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0580/42/F/M/22

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4

2

The

table

shows

some

values

for

y

=

x2 -

1 3x

,

x ! 0.

The y-values are rounded to 1 decimal place.

x

-2

-1.5

-1

-0.75

-0.5

-0.25

-0.1

y

4.2

2.5

1.3

1.4

3.3

(a) Complete the table.

[2]

(b) On the grid, draw the graph of

y

=

x2

-

1 3x

for -2 G x G-0.1 .

The

graph

of

y

=

x2 -

1 3x

for

x

2

0

has

been

drawn

for

you.

y

4

3

2

1

? 2

? 1

0

? 1

1

2x

? 2

[4]

(c)

By

drawing

a

suitable

line

on

the

grid,

solve

the

equation

x2

-

1 3x

+1

=

0.

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x = ................................................ [2]

0580/42/F/M/22

3 (a) Find (i) gf(3),

f (x) = 1 + 4x

5 g (x) = x2

(ii) fg(x), (iii) f -1f (x). (b) Find the value of x when f (x) = 15.

................................................. [2] ................................................. [1] ................................................. [1]

x = ................................................ [2]

? UCLES 2022

0580/42/F/M/22

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