$$\begin{gathered} The sponsors of a golf tournament have provided \$232,500 for the total prizes for the first 15 places. The prize for the winner is to be \$26,000 and, from there down, each prize decreases by a cons\tan t amount \\ find \\ i) the prize for finishing 15th \\ ii) the prize for finishing 2nd \end{gathered}$$

$The population P, in thousands of small city is given by P\left(t\right)=\frac{500t}{2t^2+9}, where t is the time in years$

$$\begin{gathered} Find the population after 10 months. \\ Find the rate of change of the population with respect to time. \\ Find the rate of change in the population at t=12years. \\ Find the average rate of change in the population from t=10 minths and t=4years. \end{gathered}$$

$$\begin{gathered} A gold coin is biased so that the probability of tos\sin g a head is 2/3 . A silver coin is \text{'}fair\text{'} with an equal chance of tos\sin g a head or a tail. \\ \left(i\right) The two coins are tos\sin g together . what is the probability of tos\sin g \\ \left(\alpha \right) 2 heads. \\ \left(\beta \right) a head and a tail. \\ \left(\gamma \right) at least 1 tail. \\ \left(ii\right) One of the coins is selected at random and then tossed twice. What is the probability tos\sin g 2 tails. \end{gathered}$$

$The data in the following table relates study time and test scores$

Find the regression line for the above, using accuracy to two decimal places.

$$\begin{gathered} \text{ Mary decided to contribute to a superannuation fund by investing }\mathrm{\$}3000\text{ each year at the beginning of }1990\text{. The interest was paid at a rate of }7\mathrm{\%}\mathrm{p}.\mathrm{a}\text{. for }10\text{ years after which it was changed to }8\mathrm{\%}\text{ p.a. starting January }1,2000.\text{ She plans to continue to invest in this fund until }the year 2010. \\ \left(i\right) Show that after 10 years her investment is worth \$44350.80. \\ \left(ii\right) How much is her investment worth at the end of the {11}^{th} year ? \\ \left(iii\right) How much is her investment worth at the end of 2010 ? \end{gathered}$$

$$\begin{gathered} \text{ Merrilvn a oraduate engineer earns }\mathrm{\$}60000\text{ in her first vear of employment and in each of the following years her annual salary is increased by }5\mathrm{\%}\text{ of the previous year's salary. } \\ \text{(i) What is Merrilyn's annual salary in her }5\text{ th year of employment? } \\ \text{(ii) Calculate her total earnings for the first ten years of her employment. } \\ \text{(iii) At the end of each year of employment Merrilyn invests }\mathrm{\$}5000.\mathrm{Her}\text{ investment earns interest at a rate of }4\mathrm{\%}\text{ per annum, compounded annually. Calcuate the total amount she has accrued by the end of her first }10\text{ years of employment. } \end{gathered}$$

The world population was approximately 6.04 billion at the beginning of 2000. It has been estimated that the population is growing exponentially at the rate of 0.016 per year. The world population P is modelled by the equation P = Pekt, where k and Po are constants and it is the amount of time (in years) since the beginning of 2000.

Estimate the world population at the end of 2030

A large class takes an exam, and the students' scores are normally distributed. The mean score is 72 and the standard deviation is o-4.5. Students who score in the top 10%. receive an A grade. What is the minimum score needed to get an A grade?

$$\begin{gathered} \underset{n=5}{\overset{20}{\sum \left(2n-1\right) =}} \\ A. 59 \\ B. 50 \\ C. 884 \\ D. 85 \end{gathered}$$

$$\begin{gathered} On the first day of each month for 12 months, starting 1st January 2012, \\ Eleni deposited \$200 into a special savings account, which was paying \\ 6\% per annum interest, compounded monthly. \\ i) What was the monthly rate of interest \\ ii) What was the value of the \$200 she deposited at 31st December 2012? \\ iii) What was the total of her savings account at 31st December 20 12? \end{gathered}$$