Numerical reasoning
PAES M1 maths practice for 2027 admission
Mathematical Competency 1 (M1) is a required test for Chile’s centralised university admissions process. The regular 2026 sitting for 2027 admission takes place on Wednesday 2 December. Start with a worked percentage example, then try four original questions in nine minutes.
When PAES M1 takes place
The Ministry of Education lists M1 at 09:00 on 2 December 2026, with an 08:00 start in Rapa Nui. Check DEMRE’s test instructions for your local time and venue.
Regular registration closed on 27 July 2026 after an extension. Scores come out on 4 January 2027 and centralised applications run from 4 to 7 January.
Bring your ID document, test registration card, a No. 2 graphite pencil or HB mechanical pencil, and an eraser. Calculators are prohibited.
M1 format and syllabus
You have 2 hours and 20 minutes for 65 questions. Each has four options and one correct answer. Sixty questions count towards the score. Dividing 140 minutes by 65 gives an average of about 2 minutes and 9 seconds per question.
The syllabus draws on Chile’s curriculum from seventh grade (7.º básico) through the second year of secondary school (2.º medio). It covers numbers, algebra and functions, geometry, and probability and statistics. You solve problems, build models, interpret representations and justify methods.
The regular 2026 syllabus adds similarity and proportionality of figures, including scale drawings, and material on cylinders. Review how scale affects lengths and areas. For cylinders, identify the radius before you calculate.
Worked percentage example
When the total changes, work out each percentage using its own denominator.
How to plan your next practice session
Record how many questions you attempted and how many you got right. Retry mistakes and guesses without the timer. If you used the wrong total, write the denominator before calculating. If you mixed units, label each step. If you solved it on the second try, identify the decision that slowed you down.
In Cognik, use Proportional Reasoning to practise rates and Statistics & Percentages to work on shares and changes in the denominator. For a full session, find the 2027 admission winter M1 paper and its answer key in the ministry’s practice materials. Use the regular syllabus as well, especially the new geometry topics.
Four questions in nine minutes
Set a nine-minute timer and work without a calculator. If you get stuck, mark the question and move on. Return to it if you have time. Open the answer key at the end. Nine minutes is a practice target based on the average pace of the exam.
A shop reduces a product’s price by 20%. A voucher then takes 10% off the reduced price. If the final price is 25,200 Chilean pesos, what was the original price?
- 31,500 pesos
- 32,760 pesos
- 35,000 pesos
- 36,000 pesos
Three identical printers together print 180 labels in 12 minutes. Every printer runs at the same constant rate when active. Five are available for an order of 480 labels, but one is idle for the first four minutes. All five then run. How long does the order take from the start?
- 16 minutes
- 20 minutes
- 19 minutes and 12 seconds
- 24 minutes
The graph shows how long a group waited at a bus stop. The intervals are in minutes and each block represents two people. What percentage waited at least 10 minutes?
0–4 ██ 4 5–9 ████ 8 10–14 ██████ 12 15–19 ███ 6- 20%
- 40%
- 50%
- 60%
A rectangular garden measures 3 cm by 5 cm on a 1:200 plan. The same garden is drawn on a 1:100 plan. What area does it take up on the new plan?
- 60 cm²
- 15 cm²
- 30 cm²
- 120 cm²
Show answers and explanations
- C. The first discount leaves 80% of the original price. The voucher leaves 90% of that amount. You pay 0.8 × 0.9 = 0.72 of the original price. Divide 25,200 by 0.72 to get 35,000 pesos. Option D comes from adding discounts that apply to different amounts.
- B. Each printer produces 180 ÷ (3 × 12) = 5 labels per minute. Four printers produce 4 × 4 × 5 = 80 labels at the start. Five printers produce the remaining 400 at 25 per minute in 16 minutes. Add the first 4 minutes to get 20.
- D. At least 10 minutes includes the last two intervals. Add 12 + 6 = 18. The group total is 4 + 8 + 12 + 6 = 30. The share is 18 ÷ 30 = 60%. The 40% answer is the share who waited less than 10 minutes.
- A. Each centimetre on the second plan represents half the real distance it represented on the first. Double both sides to draw the same garden: 6 cm by 10 cm. The area is 60 cm². Doubling the original area to 30 cm² would account for only one side changing.
Put it into practice
Explore more questions and step-by-step explanations in Cognik.
