IGCSE maths tutor in Peru, live online

Source: Cambridge International, Cambridge IGCSE Mathematics 0580 syllabus for 2025, 2026 and 2027 (Version 3), assessment overview, read on 9 November 2026. Core candidates take Papers 1 and 3 and can be awarded grades C to G; Extended candidates take Papers 2 and 4 and can be awarded grades A* to E. Exams run in the June and November series, plus a March series for schools in India only.

Cambridge also states that the syllabus and its assessment materials exist in English only, and it designs each IGCSE subject around roughly 130 guided learning hours, a figure it calls guidance rather than a rule. Private candidates may enter for 0580 through a centre that accepts them, and a candidate can retake the whole qualification as often as they wish. One administrative trap is worth a parent's attention: once the entries deadline passes, an entry on the A* to G grading scale cannot be switched to the 9 to 1 scale.

Schools decide tier, entry and series; we do not enter candidates, and we are not a Cambridge school or exam centre. Our job is to make sure the student is ready for whichever papers the school chooses.

from math import floor, log10

def sf3(x):
    # round x to 3 significant figures
    return round(x, 2 - floor(log10(abs(x))))

value = 2500
half = value / 2

hasty = value
year = 0
while hasty >= half:
    year += 1
    hasty = sf3(hasty * 0.87)   # rounded every single year
    print("Year", year, int(hasty))
print("Hasty answer: year", year)

careful = value
year = 0
while careful >= half:
    year += 1
    careful = careful * 0.87    # every digit kept until the end
print("Careful answer: year", year)
print("Value then:", round(careful, 2), "which is", int(sf3(careful)), "to 3 s.f.")

The lesson we want students to keep is short: compare the unrounded value, then round only what you write down. On paper that means keeping the full calculator display, or the exact expression 2500 × 0.87⁵, until the last line. In Python it means rounding inside the print, never inside the loop.

We then turn it round. Students change the rate to 12% and predict, before running anything, whether the two versions will still disagree. They also explain in two English sentences why the loop condition says >= and what would change with >. Reasoning about the program is the point; Python simply makes the error impossible to argue with.

1. Core warm-up, no calculator. A price rises by 10% and then falls by 10%. Is it back where it started? Show it with 200 as the starting value.
2. Core, calculator. A population of 8,000 grows by 5% a year. Find it after 3 years to 3 significant figures, keeping full accuracy in between.
3. Extended, by trial. Starting at 2,500 and losing 13% a year, find the first whole year in which the value is below 1,000. Write each trial with the full calculator display.
4. Extended, in Python. Edit Version 2 to find the first year below 1,000, then add a line that prints the value to 3 significant figures only after the loop ends.

All four problems are ours, written for this page; none comes from a Cambridge paper. Answers: no, 198; 9,260; year 7 (the value then is about 943); the program agrees, year 7.

We do not hand students answers to copy, from a tutor or from an AI tool. Younger students do not use adult chatbot accounts in class, and older students may use AI only to question their own reasoning after they have solved a problem. Cambridge gives teachers at registered schools access to its own large resource bank, which we do not have and do not claim; we work from the public syllabus and from problems we write ourselves. We are not connected with Cambridge International.