TJC 2024 IP3 Integrated and Advanced Math June Hol HW.pdf

Temasek Junior College (IP) 2024 IP3 Intermediate & Advanced Mathematics June Holiday Homework Instructions to all students 1. Complete all working on foolscap paper. Present all working clearly. 2. After completing all questions, self-mark using the answers provided on the last page. 3. For all incorrect answers, you are to re-attempt the question s by doing the necessary corrections. 5. If you require clarification for any errors made, p lease take the initiative to consult your Mathematics tutor via email or when you are back in College. 6. Submit your solutions and corrections to your tutor for checking during the first Mathematics lesson in Term 3 2024. Intermediate Mathematics 1. Kesamet Bank offers two types of deposit accounts, the SimSaver account and the ComSavers account. The SimSavers account offers a simple interest at 5% per annum and the ComSavers account offers an interest at 4.8% per annum, compounded half-yearly. Jay opened and deposited $10 000 into a ComSavers account. (i) Find, to the nearest dollar, the amount of money Jay will have at the end of 4 years. Tee opened and deposited $10 000 into a SimSavers account. (ii) Find, to the nearest dollar, the amount of money Tee will have at the end of 4 years. At the end of 4 years, Tee intends to transfer all the money in her SimSaver account to the ComSaver account for another year. (iii) Explain, with supporting calculations, whether it is worthwhile for Tee to do so as compared to leaving her money in her SimSaver account. Show all working clearly. 2. Sketch the following graphs. (a) ( ) 2 3 2 3yx= − − (b) 2 3yx=− − (c) 2 6 13y x x= + + This study source was downloaded by 100000857398866 from CourseHero.com on 11-15-2024 00:10:30 GMT -06:00 https://www.coursehero.com/file/237245029/2024-IP3-IMAM-June-Hol-HW-v10-1pdf/

3. (i) A quadratic graph has a minimum point at ( )3, 2− and cuts the y-axis at ( )0,16 . Find the equation of the curve. (ii) Another quadratic graph cuts the x-axis at ( )4, 0− and ( )6, 0 and passes through 213, 2   . Find the equation of the curve. 4. Show that the expression 2 22 5 25xx− + − is always negative. Hence, explain the implications of your results on the number of possible solutions of x for the equation 2 22 05 25xx− + − = . 5. In 2018, the price of water was $x per litre and a factory spent $100 on its water bill in January. (i) Express, in terms of x, the volume of water used in January. In February, the price of water was reduced by $0.14 per litre but the factory continued to spend $100 on its water bill. (ii) Express, in terms of x, the volume of water used in February. (iii) If the difference in the volumes of water used in both months is 6 litres, formulate an equation in x and show that it simplifies to 26 0.84 14 0xx− − = . (iv) Hence, find the price of water per litre in February, showing your working clearly. In 2019, a water conservation tax of