Examen de Matemáticas, 8vo Grado

• This document appears to be an exam paper from Colegio Altair Bilingue for a Mathematics class.
• The exam covers topics including statistics and data analysis.

General Information

• Area: Mathematics
• Teacher: Andrea Vega
• Date: March 31, 2025
• Student's Name: Salomé Sierra
• Grade: 8th
• Group: B

Standard

• Resolving and formulating problems by selecting relevant information from data sets obtained from direct sources (press, magazines, television, experiments, consultations, interviews).
• Recognizing tendencies that appear in sets of related variables.

General Instructions

• Unclear or confusing numbers or letters invalidate the point.
• Silence is to be maintained even after finishing the test.
• Detailed justification must be provided for points 4, 5 and 6, showing the corresponding answers and presenting evidence of the processes used in each case. Answers without justification will not be accepted.
• Calculator can be used.

Question 1

• A car dealership sold a certain quantity of the same car over the last six months of the year. The price of the car varied each month as shown in a frequency table.
• The question asks to determine the representative price of the car during the six months.
• The table provides the following information:
  • July: 14 cars sold at $28,250,000
  • August: 22 cars sold at $27,880,000
  • September: 18 cars sold at $27,500,000
  • October: 15 cars sold at $27,220,000
  • November: 24 cars sold at $27,200,000
  • December: 32 cars sold at $27,100,000
• Possible answers:
  • $26,500,340
  • $27,457,280
  • $28,235,660
  • $29,624,900

Question 2

• The following frequency distribution table was constructed from the data of an experiment.
• The question asks which statement is TRUE according to the frequency distribution table.
• The table provides the following data:
  • Class (3,13): frequency 8, relative frequency 12.5%, cumulative frequency 8, cumulative percentage 8
  • Class [14,24]: frequency 10, relative frequency 15.625%, cumulative frequency 18, cumulative percentage 19
  • Class [25,35]: frequency 18, relative frequency 28.125%, cumulative frequency 36, cumulative percentage 30
  • Class [36,46]: frequency 16, relative frequency 25%, cumulative frequency 52, cumulative percentage 41
  • Class [47,57]: frequency 12, relative frequency 18.75%, cumulative frequency 64, cumulative percentage 52
• Possible answers:
  • 15% of the experiment's data belong to class (3,13).
  • 48.75% of the experiment's data belong to class [14, 46).
  • 56.25% of the experiment's data belong to class [3, 35).
  • 74% of the experiment's data belong to class (25, 57).

Question 3

• The teacher observes that only two people pass the evaluation and decides to help the students; for this, he decides that the definitive grade for the students who failed will be the student who represents 50% of the set of grades. To whom does this decision NOT benefit?
• The table provides the following data:
  • Claudia: 28
  • Johan: 31
  • Julián: 20
  • Sara: 44
  • Patricia: 29
  • Lorena: 28
• Possible answers:
  • Claudia
  • Johan
  • Lorena
  • Patricia

Additional Information for Questions 4 to 8

• A study was carried out to analyze the time it takes students from Colegio Altair to get to the educational center from their homes. The main objective of this study was to obtain a detailed view of the students' travel times, which could provide valuable information to optimize school transportation services, adjust class start times, or even improve the planning of extracurricular activities.
• The table with intervals and their values:
  • Interval (3, 14): Class mark 8.5, frequency 8, cumulative frequency 8, percentage 12.5%
  • Interval [14, 25): Class mark 19.5, frequency 10, cumulative frequency 18, percentage 15.625%
  • Interval [25, 36): Class mark 30.5, frequency 18, cumulative frequency 36, percentage 28.125%
  • Interval [36, 47): Class mark 41.5, frequency 16, cumulative frequency 52, percentage 25%
  • Interval [47, 58): Class mark 52.5, frequency 12, cumulative frequency 64, percentage 18.75%

Question 4

• According to the previous information, the representative data with respect to the travel time of the students is:
• Possible answers:
  • 31.40 minutes
  • 25, 5 minutes
  • 30,4 minutes
  • None of the above

Question 5

• The data that represents 50% of the data set is:
• Possible answers:
  • 28,88 minutes
  • 25,56 minutes
  • 34,45 minutes
  • None of the above

Question 6

• The data that has the highest frequency is:
• Possible answers:
  • 27,76 minutes
  • 29,43 minutes
  • 35,3 minutes
  • None of the above

Question 7

• What is the range of the data?
• Possible answers:
  • 9 minutes
  • 55 minutes
  • 44 minutes
  • 11 minutes

Question 8

• How many data are above the interval that represents the median?
• Possible answers
  • 28
  • 46
  • 116
  • 36