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READ THESE INSTRUCTIONS FIRST
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 an HB pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correction fl uid.DO NOT WRITE IN ANY BARCODES.
Answer all questions.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 specifi ed in the question, and if the answer is not exact, give the answer to three signifi cant fi gures. 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.
MATHEMATICS 0580/43
Paper 4 (Extended) May/June 2014
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional)
(c) There were 3 different fl avours of fruit juice. The number of bottles sold in each fl avour was in the ratio apple : orange : cherry = 3 : 4 : 2. The total number of bottles sold was 45 981.
Calculate the number of bottles of orange juice sold.
Answer(b) a = ................................................ [4]
(c) sin x = cos 40°, 0° Y x Y 180°
Find the two values of x.
Answer(c) x = .................. or x = .................. [2]__________________________________________________________________________________________
P, Q, R and S are points on a circle and PS = SQ. PR is a diameter and TPU is the tangent to the circle at P. Angle SPT = 63°.
Find the value of
(i) x,
Answer(b)(i) x = ................................................ [2]
(ii) y.
Answer(b)(ii) y = ................................................ [2]__________________________________________________________________________________________
Answer(d) f –1(x) = ................................................ [2]
(e) Solve the equation gf(x) = 1.
Answer(e) x = ................................................ [3]__________________________________________________________________________________________
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Everyreasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the publisher will be pleased to make amends at the earliest possible opportunity.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
11
Diagram 1 Diagram 2 Diagram 3
The fi rst three diagrams in a sequence are shown above. Diagram 1 shows an equilateral triangle with sides of length 1 unit.
In Diagram 2, there are 4 triangles with sides of length 21 unit.
In Diagram 3, there are 16 triangles with sides of length 41 unit.
(a) Complete this table for Diagrams 4, 5, 6 and n.