1. 1
   During the early stages of an outbreak of a disease, 5 new cases are recorded in week 1, and the number of new cases recorded each week is double the number recorded the week before.

   (a)

   Find the number of new cases recorded in week 8.

   [1 mark]

   • A1280
   • B640
   • C80
   • D320

   (b)

   Find the total number of new cases recorded in the first 8 weeks.

   [1 mark]

   • A2560
   • B1280
   • C2555
   • D1275

   (c)

   Find the first week in which more than 10 000 new cases are recorded.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A geometric sequence $u_1, u_2, u_3, \dots$ has $u_2 = 12$ and $u_5 = -96$.

   (a)

   Find the common ratio of the sequence.

   [1 mark]

   • A$-2$
   • B$2$
   • C$-8$
   • D$-36$

   (b)

   Find the first term, $u_1$.

   [1 mark]

   • A$-24$
   • B$6$
   • C$-6$
   • D$24$

   (c)

   Find the value of $\displaystyle\sum_{k=1}^{7}u_k$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Amira starts a job with an annual salary of 48 000 USD in her first year. Her salary increases by 4% at the start of each following year. A calculator may be used in this question.

   (a)

   Find Amira's salary in her 10th year, correct to the nearest dollar.

   [3 marks]

   (b)

   Another employer offers Amira a fixed salary of 58 000 USD every year instead. Determine which offer pays more in total over the first 10 years, and by how much.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   At the start of 2025, town A has a population of 25 000, which is decreasing by 3% each year. At the same time, town B has a population of 12 000, which is increasing by 5% each year. Assume these rates continue. A calculator may be used in this question.

   (a)

   (i) Show that the population of town A after $n$ years is $25\,000(0.97)^{n}$, and write down a similar expression for the population of town B after $n$ years.
   (ii) Find the population of town A after 10 years.
   (iii) Find the decrease in the population of town A during the 10th year.

   [6 marks]

   (b)

   (i) Find the number of complete years after which the population of town B first exceeds the population of town A. Justify your answer.
   (ii) The council of town A claims that, at this rate of decrease, its population will have fallen to half of its 2025 value within 20 years. Determine whether the claim is correct.

   [6 marks]

   Total for question 4: 12 marks

End of questions