Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#9

Question A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive. Scheme 1: Salary in Year 1 is £P. Salary increases by £(2T) each year, forming an arithmetic sequence. Scheme 2: Salary in Year 1 is £(P+1800). Salary increases by £T each year, forming an arithmetic sequence. a.   Show that the total earned under […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#5

Question The first term of a geometric progression is  and the fourth term is  . Find     i.       the common ratio,    ii.       the sum to infinity. Solution From the given information, we can compile following data for Geometric Progression (G.P); i.   Expression for the general term  in the Geometric Progression (G.P) is: Expressions for 4th term can be written as; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#8

Question a)   In a geometric progression, all the terms are positive, the second term is 24 and the fourth term  is . Find i.       the first term, ii.      the sum to infinity of the progression. b)  A circle is divided into n sectors in such a way that the angles of the sectors are in arithmetic  progression. The […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#1

Question The first term of an arithmetic progression is 61 and the second term is 57. The sum of the first n  terms is n. Find the value of the positive integer n. Solution   From the given information, we can compile following data for Arithmetic Progression (A.P); The expression for difference  in Arithmetic Progression (A.P) is: For the given case; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#6

Question The first term of an arithmetic progression is 12 and the sum of the first 9 terms is 135.      i.       Find the common difference of the progression. The first term, the ninth term and the nth term of this arithmetic progression are the first term, the  second term and the third term respectively of a geometric progression.    ii.       Find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/12) | Q#7

Question a)   In an arithmetic progression, the sum of the first  terms, denoted by , is given by . Find the first term and the common difference. b)  In a geometric progression, the second term is 9 less than the first term. The sum of the second  and third terms is 30. Given that all the terms of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#7

Question a)   The first two terms of an arithmetic progression are 1 and  respectively. Show that the sum  of the first ten terms can be expressed in the form , where a and b are constants to be  found. b)  The first two terms of a geometric progression are 1 and  respectively, where . i.       Find the […]