2012 A-level H2 Mathematics (9740) Paper 2 Question 4 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
$\frac{n}{2} [2(100) + 10(n-1)] > 5000$

Using the graphing calculator, smallest n = 24.

Thus, Mrs A’s account will have more than 5000 dollars on 1 December 2002.

(ii)
Amount at the end of 1st month $= 100 \times 1.005$

Amount at the end of 2nd month $= (100 \times 1.005 + 100) \times 1.005 = 100 \times 1.005^2 + 100 \times 1.005$

Amount at the end of nth month $= 100 \times 1.005^n + \ldots 100 \times 1.005$

$= 20100 (1.005^n - 1)$

Mr B’s account will be more than 5000 dollars on September 2004.

(iii)
$100x \frac{x^{35} - 1}{x-1} + 100 = 5000$

Using Graphing Calculator, $x = 1.01796$

Thus the interest rate is 1.80% per month.

KS Comments:

Students should reproduce the table (with its succeeding and preceding values) to substantiate their answers for (i) and (ii). For (i), its necessary to identify the month; just use your fingers to count.

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

2012 A-level H2 Mathematics (9740) Paper 2 Question 4 Suggested Solutions

KS Comments:

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