# MATH PROBLEM

Jul 8th, 2015
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1.1 Solve for x, correct to TWO decimal places, where necessary:

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Mathematicsby Mlungicy-Kalvin 1.1Solve for x, correct to TWO decimal places, where necessary:1.1.1(3)1.1.2(4)1.1.3(4)1.2Solve for x and y simultaneously:(7)1.3Simplify completely, without the use of a calculator:(3) [21]QUESTION 2The sequence 3 ; 9 ; 17 ; 27 ; is a quadratic sequence.2.1Write down the next term.(1)2.2Determine an expression for the term of the sequence.(4)2.3What is the value of the first term of the sequence that is greater than 269?(4)[9]QUESTION 33.1The first two terms of an infinite geometric sequence are 8 and . Prove, without the use of a calculator, that the sum of the series to infinity is .(4)3.2The following geometric series is given: x = 5 + 15 + 45 + to 20 terms.3.2.1Write the series in sigma notation.(2)3.2.2Calculate the value of x.(3)[9]QUESTION 44.1The sum to n terms of a sequence of numbers is given as: 4.1.1Calculate the sum to 23 terms of the sequence.(2)4.1.2Hence calculate the 23rd term of the sequence.(3)4.2The first two terms of a geometric sequence and an arithmetic sequence are the same. The first term is 12. The sum of the first three terms of the geometric sequence is 3 more than the sum of the first three terms of the arithmetic sequence.Determine TWO possible values for the common ratio, r, of the geometric sequence.(6)[11]QUESTION 5Consider the function 5.1Write down the equations of the asymptotes of f.(2)5.2Calculate

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