Topics Topic 1—Algebra un u1 (n 1)d Sn n (2u1 (n 1)d ) 2 The nth term of a geometric sequence un u1r n The sum of n terms of a finite geometric sequence Sn u1 (r n 1) r 1 The sum of an infinite geometric sequence S Exponents and logarithms ax Laws of logarithms 1.2 The nth term of an arithmetic sequence The sum of n terms of an arithmetic sequence 1.1 log c a log c b log c ab a log c a log c b log c b log c a r r log c a Change
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Core 1 Linear Graphs and Equations For any straight line‚ the gradient (M) is: dy/dx or difference in y/difference in x which is (y2-y1)/(x2-x1) Equation of a line: y=mx+c which is used when the gradient and intercept is known or y-y1=m(x-x1) when the gradient and the co-ordinates (x1‚y1) of a single point that the line passes through is known. You’ll need to learn this equation. [The equation of the line can be kept in this form unless stated in the exam. (reduces error chance) Also
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John Wallis—Infinity John Wallis was born at Ashford on November 22‚ 1616‚ and died at Oxford on October 28‚ 1703. He was educated at Felstead school‚ and one day in his holidays‚ when fifteen years old‚ he happened to see a book of arithmetic in the hands of his brother; struck with curiosity at the odd signs and symbols in it he borrowed the book‚ and in a fortnight‚ with his brother’s help‚ had mastered the subject. As it was intended that he should be a doctor‚ he was sent to Emmanuel College
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the third term of a geometric progression is 20 and the sum of its first three terms is 26. Find the progression. (a) 2‚ 6‚ 18… (b) 18‚ 6‚ 2‚… (c) Both of these (d) Cannot be determined 4. The sum of 5 numbers in AP is 30 and the sum of their squares is 220. Which of the following is the third term? (a) 5 (b) 6 (c) 8 (d) 9 5. Find the general term of the GP with the third term 1 and the seventh term 8. (a) (23/4)n-3 (b) (23/2)n-3 (c) (23/4)3-n (d) None of these Four geometric means are inserted
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ASSIGNMENT 1 1. For a given arithmetic sequence‚ the sum of the third term and the sixth term is 86. The eleventh term is 56. Find the a) first term and the common difference. (6m) b) nth term. (2m) 2. A couple estimates that the expense of caring for their baby will increase by RM1.80 from the previous month’s expenses. The cost for the first month when the baby was born was RM22. What a) were the expenses for the 10th month and the 15th month after the baby was born? (4m) b) were the
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statement of equality between two expressions. 2. An equation in two or more variables. 3. A polynomial with more than three terms. 4. A monomial that does not contain variable. 5. Is a special type of sequence in which the reciprocal of each term forms an arithmetic sequence. 6. Is a statement indicating the equality of two ratios. 7. A polynomial with exactly two terms. 8. A pair of numbers in which the order is specified. 9. A comparison between two quantities. 10
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the finalists. Solution:The prizes are RM860‚RM800 ‚RM740….. It is an arithmetic progression .The first term a=rm860 ‚ common difference d=-60 and n=20. The total amount given is Sn = n/2[ 2a + (n-1)] S26 =20/2[ 2(860) +(20-1)(-60)] =RM5800 The amount is RM 5800 2. Find the minimum number of terms that must be taken from the sequence : 4‚16‚6‚256…so that the sum is more than 400. Solution: This is a geometric sequence with a=4 and r =4 Let the minimum number of terms be n. From Sn= a(rn-1)/r-1
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Introduction: In this following assignment‚ I will be considering geometric shapes that lead to special numbers. The simplest examples of these are square numbers (1‚ 4‚ 9‚ 16‚ etc)‚ which are derived from squaring 1‚ 2‚ 3‚ and 4. From this I got the equation y= x2. This equation is illustrated in the table below. y=x2 |x |y | |1 |1 | |2 |4 | |3
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1. The nth term of an arithmetic sequence is given by un = 5 + 2n. (a) Write down the common difference. (1) (b) (i) (ii) Given that the nth term of this sequence is 115‚ find the value of n. For this value of n‚ find the sum of the sequence. (5) (Total 6 marks) 2. A sum of $ 5000 is invested at a compound interest rate of 6.3 % per annum. (a) Write down an expression for the value of the investment after n full years. (1) (b) What will be the value of the investment at
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impossible to implement. | 3.03 points Question 3 1. In measuring the comparative performance of different fund managers‚ the preferred method of calculating rate of return is __________. Answer | | internal rate of return | | | arithmetic average | | | dollar-weighted | | | time-weighted | | | None of these is correct | 3.03 points Question 4 1. Active portfolio management consists of __________. Answer | | market timing | | | security analysis |
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