Review practice · Section 4 of 4

A class has $16$ boys with AP heights and $10$ girls with GP heights. The shortest boy and girl are each $150.0$ cm. The tallest boy is $180.0$ cm, and the fourth-shortest girl is $157.5$ cm.

(i) Show the girls’ common ratio is $1.05^{1/3}$ and find the tallest girl’s height to 1 d.p.2 marks

(ii) Find how many girls are taller than $164.0$ cm.3 marks

(iii) Find the girls’ mean height to 1 d.p.3 marks

(iv) Find the class mean to 1 d.p.2 marks

(i) Swimmer A swims $50$ m on day one and increases each subsequent day’s distance by $10\%$ of the previous day’s distance for $30$ days.

(a) Show her day-30 distance is $793$ m to the nearest metre.2 marks

(b) Find her total in 30 days to the nearest metre.2 marks

(ii) Swimmer B starts at $50$ m and adds $5$ m each day. Find the least number of days for B’s total to exceed A’s total in (i)(b).5 marks

A grain facility holds $10000$ bushels at the end of December 2013. Insurance pay-outs purchase extra grain, increasing the stock by $2\%$ before the end of every month.

(a) Find the stock at the end of December 2014.1 mark

(b) During January–December 2014 the facility supplies x bushels to a laboratory each month, before the $2\%$ addition.

(i) For $x=100$, show the end-March stock is $10299.9$ bushels to 1 d.p.2 marks

(ii) Find the maximum monthly supply.4 marks

A man enters a coma after an accident on 10 January 2013 and misses payment of his credit-card balance M dollars due on 27 January. On each monthly 27th, unpaid balances first receive $2\%$ interest and then an additional late fee L dollars.

(a) Express his balance on 1 February 2013 in terms of M and L.1 mark

(b) Show that exactly n months after the accident, on the same day of the month, the accumulated balance is $(1.02)^nM+50L[(1.02)^n-1]$.3 marks

(c) For $M=1000$, $L=55$, find the least n for which the balance first exceeds $2010.2 marks