Cambridge International Examinations Cambridge ... · Meena invests her $6000 at a rate of 1.5% per year compound interest. Eisha invests her $6000 in a bank that pays simple interest.
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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 fluid.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 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.
MATHEMATICS 0580/42
Paper 4 (Extended) February/March 2016
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional)
Cambridge International ExaminationsCambridge International General Certificate of Secondary Education
(c) Meena and Eisha both invest their $6000. Meena invests her $6000 at a rate of 1.5% per year compound interest. Eisha invests her $6000 in a bank that pays simple interest. After 8 years, their investments are worth the same amount.
Calculate the rate of simple interest per year that Eisha received.
10 (a) The ten circles in the diagram each have radius 1 cm. The centre of each circle is marked with a dot.
Calculate the height of triangle PQR. NOT TOSCALE
Q R
P
8 cm
............................................. cm [3]
(b) Mr Patel uses whiteboard pens that are cylinders of radius 1 cm.
(i) The diagram shows 10 pens stacked in a tray. The tray is 8 cm wide. The point A is the highest point in the stack.
Find the height of A above the base, BC, of the tray.
NOT TOSCALE
B C
A
8 cm
............................................ cm [1]
(ii) The diagram shows a box that holds one pen. The box is a prism of length 12 cm. The cross section of the prism is an equilateral triangle. The pen touches each of the three rectangular faces of the box.
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11 f(x) = 2 − 3x g(x) = 7x + 3
(a) Find
(i) f(−3),
........................................ [1]
(ii) g(2x).
........................................ [1]
(b) Find gf(x) in its simplest form.
........................................ [2]
(c) Find x when 3f(x) = 7.
x = ................................................. [3]
(d) Solve the equation. f(x + 4) − g(x) = 0
x = ................................................. [3]