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Bahamas General Certificate of Secondary Education: Mathematics: Paper 3

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These are the solutions to the BGCSE Mathematics Paper 3 questions.
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Ministry of Education National Examinations
Bahamas General Certificate of Secondary Education
Mathematics
Paper 3 (Core/Extended)

Time: 1:00 pm – 2:30 pm

Instructions to Candidates
(1.) Do not open this booklet until you are told to do so.
(2.) Write your school number, candidate number, surname and initials in the spaces provided on each answer booklet.
(3.) Remove the graph paper from the question paper. Write your school number, candidate number, surname and initials, signature and date on the graph paper. Place the graph paper in the answer booklet.
(4.) Answer ALL questions in the answer booklet.
(5.) ALL working must be shown.
(6.) ALL working must be done in blue or black ink, except for drawings, lines and constructions which may be done in pencil.

Information for Candidates
(1.) Calculators may be used. (No Graphing Calculators allowed).
(2.) Tracing paper and geometrical instruments may be used.
(3.) The mark for each question, or part question, is shown in brackets [ ].
(4.) The total number of marks for this paper is 100.

Formula Sheet: Information and Formulae
(1.) Mathematics of Finance: $4750 earns $1068.75 simple interest when invested for 4 years 6 months.
Calculate the rate percent per annum.


$ \text{principal, } P = \$4750 \\[3ex] \text{simple interest, } SI = \$1068.75 \\[3ex] \text{time, } t = 4\text{ years } 6\text{ months} \\[3ex] t = 4 + \dfrac{6}{12} \\[5ex] t = 4 + 0.5 \\[3ex] t = 4.5\text{ years} \\[3ex] \text{rate, } r = ? \\[5ex] SI = P \times r \times t \\[3ex] r = \dfrac{SI}{P \times t} \\[5ex] r = \dfrac{1068.75}{4750 \times 4.5} \\[5ex] r = \dfrac{1068.75}{21375} \\[5ex] r = 0.05 \\[3ex] r = 0.05 \times 100\% \\[3ex] r = 5\% $
(2.) Mensuration: The sum of the interior angles of a regular polygon is 2,340°.
Determine the size of an exterior angle.


$ \underline{\text{Regular Polygon}} \\[3ex] \text{side} = n \\[3ex] \text{sum of interior } \angle s = 180(n - 2) \\[3ex] 180(n - 2) = 2340 \quad\text{Given} \\[3ex] n - 2 = \dfrac{2340}{180} \\[5ex] n - 2 = 13 \\[3ex] n = 13 + 2 \\[3ex] n = 15 \\[5ex] \text{an exterior } \angle = \dfrac{360}{n} \\[5ex] = \dfrac{360}{15} \\[5ex] = 24^\circ $
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