Maths tutor in Arequipa, Peru

INEI: Censos Nacionales 2025, Indicadores demográficos, Cuadro 1 (15 September 2025), and Perfil Sociodemográfico 2017, Cuadro N° 1.9 (22 October 2017). Units overlap, so the rows are not added.

Competencies and hours from MINEDU's national curriculum document (CNEB), area Matemática and its plan de estudios. The two right-hand columns record our tutors' experience, not MINEDU's.

Sources: UGEL 06, Oficio Múltiple 164-2026 on the XXII ONEM; El Peruano report of 11 October 2026. We describe the contest; we never reproduce its problems or solutions.

Olympiad problems reward a few habits more than any formula: trying small cases, looking for what stays the same, counting carefully, and writing a short argument. Our ONEM preparation in English page explains our approach in detail, and maths olympiad coaching for Peru covers the international route.

A problem of ours, in the olympiad spirit. How many whole numbers from 1 to 999 start with the digit 1? And how many start with 9? (Ours. Answer: 111 each, since 1, 10 to 19 and 100 to 199 give 1 + 10 + 100. So why do real-life lists of amounts so often start with 1 far more than 9? The lesson below is about exactly that.)

import csv

counts = [0] * 10
with open("prociencia-arequipa.csv", encoding="utf-8") as fh:
    for row in csv.DictReader(fh):
        amount = float(row["monto"] or 0)
        if amount > 0:
            first = int(str(amount).lstrip("0.")[0])
            counts[first] += 1

total = sum(counts)
print("Amounts:", total)
for d in range(1, 10):
    print(d, counts[d], f"{100 * counts[d] / total:.1f}%")

The digit 1 leads 29.6% of the 270 non-zero amounts, almost exactly Benford's 30.1%. But 3, 4 and 5 are each well above the prediction, and 6 and 7 well below. Version 2 lines the two up, reads the first digit more safely from scientific notation, and checks one suspicion: grants set by competition rules are often round numbers.

import csv
import math

counts = [0] * 10
round_ones = 0
with open("prociencia-arequipa.csv", encoding="utf-8") as fh:
    for row in csv.DictReader(fh):
        amount = float(row["monto"] or 0)
        if amount > 0:
            counts[int(f"{amount:e}"[0])] += 1
            if amount % 10000 == 0:
                round_ones += 1

total = sum(counts)
gap = 0
for d in range(1, 10):
    expected = math.log10(1 + 1 / d)
    seen = counts[d] / total
    gap += abs(seen - expected)
    print(d, f"seen {seen:.3f}", f"Benford {expected:.3f}")
print("Total gap:", round(gap, 3))
print("Multiples of 10,000:", round_ones, "of", total)

Data from the GORE Arequipa file of Prociencia co-financed projects, 2013 to 2024, under ODC-By. We did every count and share. Six rows have no positive amount; most amounts are in soles and eight rows in other currencies, which does not change the idea, because Benford's law does not depend on the unit.

So what happened? 109 of the 270 amounts are exact multiples of 10,000. When a call for projects offers a fixed ceiling, many applicants ask for exactly that, and a few popular ceilings starting with 3, 4 or 5 lift those digits above the curve. The sample is also small: with 270 numbers, a difference of two or three percentage points can be chance. The honest conclusion is that the data follows Benford on the digit 1, departs from it where rules shape the amounts, and proves nothing about anyone. Auditors use Benford's law as a reason to look closer, never as evidence on its own.

1. Primaria, 9 to 11. Write the populations from the table above and the ages of everyone in your family. Which list starts with 1 more often? Why might ages not follow the law?
2. 1° to 3° de secundaria. Without a calculator, show that log10(2) is between 0.3 and 0.31, using 2 to the power 10 = 1,024.
3. 4° and 5° de secundaria. Add the nine Benford shares log10(1 + 1/d). Why do they add to exactly 1? (Hint: the logarithm of a product.)
4. Statistics students. Remove the 109 round amounts and count again. Does the gap shrink? Is 161 numbers enough to say?
5. Going further. Multiply every amount by 3.7 and recount the first digits. Benford's law predicts the shares hardly move. Test it.

Students who enjoy the data side of maths often take up programming as well. Our coding classes in Arequipa page shows a Python project on the region's tourist inventory, and families comparing options may also find our Spanish guide to online private maths tutors useful.

Peru keeps UTC minus 5 hours without daylight saving (tz database, America/Lima); India keeps UTC plus 5 hours 30 minutes; the gap is 10 hours 30 minutes all year.

A class time agreed once does not drift, because neither country changes its clocks. You choose in Arequipa time and the tutor sees the India equivalent. Lessons carry on through school breaks unless you ask to pause, and the long summer break from January is a good time to rebuild a weak topic before the new school year.