# The Grid and Examiner

Topics: The Grid, University of Cambridge, Decimal Pages: 37 (2427 words) Published: April 6, 2013
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education

*4849274249*

0580/42

MATHEMATICS

October/November 2012

Paper 4 (Extended)

2 hours 30 minutes
Candidates answer on the Question Paper.

Electronic calculator
Mathematical tables (optional)

Geometrical instruments
Tracing paper (optional)

Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.
If working is needed for any question it must be shown below that question. Electronic calculators should be used.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 130.

This document consists of 20 printed pages.
IB12 11_0580_42/2RP

[Turn over

2
1

A factory produces bird food made with sunflower seed, millet and maize.

For
Examiner's
Use

(a) The amounts of sunflower seed, millet and maize are in the ratio sunflower seed : millet : maize = 5 : 3 : 1 .
(i) How much millet is there in 15 kg of bird food?

kg [2]

(ii) In a small bag of bird food there is 60 g of sunflower seed. What is the mass of bird food in a small bag?

g [2]

(b) Sunflower seeds cost \$204.50 for 30 kg from Jon’s farm or €96.40 for 20 kg from Ann’s farm. The exchange rate is \$1 = €0.718.
Which farm has the cheapest price per kilogram?
You must show clearly all your working.

0580/42/O/N/12

[4]

3
(c) Bags are filled with bird food at a rate of 420 grams per second.

For
Examiner's
Use

How many 20 kg bags can be completely filled in 4 hours?

[3]

(d) Brian buys bags of bird food from the factory and sells them in his shop for \$15.30 each. He makes 12.5% profit on each bag.
How much does Brian pay for each bag of bird food?

[3]

(e) Brian orders 600 bags of bird food.

1

.
50
How many bags would Brian expect to be damaged?

The probability that a bag is damaged is

0580/42/O/N/12

[1]

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4
2

For
Examiner's
Use

A
32 m
B

43 m

NOT TO
SCALE
64 m

D

C

The diagram represents a field in the shape of a quadrilateral ABCD. AB = 32 m, BC = 43 m and AC = 64 m.
(a) (i) Show clearly that angle CAB = 37.0° correct to one decimal place. Answer(a)(i)

[4]
(ii) Calculate the area of the triangle ABC.

m2 [2]

(b) CD = 70 m and angle DAC = 55°.
Calculate the perimeter of the whole field ABCD.

0580/42/O/N/12

m [6]

5
3

(a) (i) Factorise completely the expression 4x2 O 18x O 10 .

For
Examiner's
Use

[3]

(ii) Solve 4x2 O 18x O 10 = 0.

or x =

[1]

(b) Solve the equation 2x2 O 7x O 10 = 0 .

or x =

(c) Write

6
3x − 1

O=

2
x−2

as a single fraction in its simplest form.

[4]

0580/42/O/N/12

[3]

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6
4

(a)

For
Examiner's
Use

B

A

32°

143°
NOT TO
SCALE
D

O

C

Points A, C and D lie on a circle centre O.
BA and BC are tangents to the circle.
Angle ABC = 32° and angle DAB = 143°.
(i) Calculate angle AOC in quadrilateral AOCB.