IGCSE Mathematics - International (0607) — October–November 2023, Paper 61

Here is a table of the first nine terms of an F-type sequence: F1 = 5, F2 = 3, giving 5, 3, 8, 11, 19, 30, 49, 79, 128. Calculate the 10th term F10.

In another F-type sequence the first term is 3 and the second term is 1. Complete the first five terms: 3, 1, ?, ?, ?

In another F-type sequence the 2nd term is 3 and the 12th term is 652. Use your answer to Question 1(e) to find the sum of the first 10 terms.

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …. Use this information and your answers to Question 1(c) to simplify this sum: F1 + F3 + F5 + … + F(2n−1).

The first four terms of an F-type sequence are a, b, c and d. There is a relationship between c² − b² and a simple combination of a and d. Investigate this relationship by making…

The life expectancy for a human is 73.5 years. The life expectancy for a goat is 10.5 years, which matches a biological life expectancy of 73.5 years for a human (when a = 10.5…

A goat that is 2 years old has a biological age of 24 years (and at a = 0, b = 0). Find a straight-line model for b in terms of a for 0 ≤ a ≤ 2.

The most recent research gives a graph for a model of b in terms of a. Use the graph to write down the biological age of a goat that is: 2 years old; 10 years old.

A goat lives until it is 18 years old, which is old for a goat. For each model (M: b = 7a; N: b = 4a + 16; P: b = 37 log a + 31) calculate the biological age of the goat at a =…

Find the ages between which: biological age from Model N < biological age from Model P < biological age from Model M. (Model N: b = 4a + 16; Model P: b = 37 log a + 31; Model M: b…