SPS SPS FM Pure 2025 February — Question 9 5 marks

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2025
SessionFebruary
Marks5
TopicNumber Theory
DifficultyChallenging +1.2 This question requires identifying square and cube numbers up to 999, applying inclusion-exclusion principle for sixth powers (numbers that are both squares and cubes), then subtracting from the sum 1 to 999. While it involves multiple steps and careful counting (31 squares, 9 cubes, 3 sixth powers), the techniques are standard A-level: arithmetic series formula and basic set theory. The conceptual demand is moderate—slightly above average due to the inclusion-exclusion aspect and potential for counting errors, but not requiring deep insight.
Spec4.06b Method of differences: telescoping series

In this question, you must show detailed reasoning. Find the sum of all the integers from 1 to 999 inclusive that are not square or cube numbers. [5 marks]

In this question, you must show detailed reasoning.
Find the sum of all the integers from 1 to 999 inclusive that are not square or cube numbers. [5 marks]

\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q9 [5]}}