Mathematics · 2nd preparatory · First Term

Numbers and Their Operations — Intervals and Their Operations

About this lesson

This unit introduces the concept of intervals as subsets of the real numbers, distinguishing between bounded intervals (closed, open, half-open/half-closed) and unbounded intervals. It explains how to represent intervals on the number line and how to perform set operations—union, intersection, difference, and complement—on intervals. The unit uses real-life contexts such as diving depths in the Red Sea, university lecture schedules, job age requirements, temperature ranges for food storage, and caring for an elderly mother to illustrate the application of intervals. By the end, students should be able to write sets as intervals, represent them on a number line, perform operations on intervals, and solve problems involving intervals.

Main topics in this lesson

  • Intervals as subsets of real numbers
  • Bounded and unbounded intervals
  • Operations on intervals (union, intersection, difference, complement)
  • Representation on the number line
  • Real-life applications of intervals

Key terms and vocabulary

  • interval
  • bounded interval
  • open interval
  • closed interval
  • half-open interval
  • half-closed interval
  • unbounded interval
  • union
  • intersection
  • difference
  • complement
  • universal set
  • infinity
  • number line
  • real numbers

Questions and answers on Numbers and Their Operations — Intervals and Their Operations - practice and revision

Multiple choice questions on this lesson in Mathematics for 2nd preparatory, First Term, with practice exercises for revision and exam preparation.

1

إذا كان أ = ]−٢ ، ٣] ، ب = ]١ ، ٦] ، فإن أ ∪ ب =

  • 1 ]−٢ ، ٦]
  • 2 [−٢ ، ٦]
  • 3 ]١ ، ٣]
  • 4 ]−٢ ، ١[ ∪ ]٣ ، ٦]
2

إذا كان أ = ]−٤ ، ٠] ، ب = [٠ ، ٣[ ، فإن أ ∩ ب =

  • 1 {٠}
  • 2 ∅
  • 3 ]−٤ ، ٣[
  • 4 [٠ ، ٠]
3

إذا كان أ = [١ ، ٧] ، ب = [٣ ، ٩] ، فإن أ ∩ ب =

  • 1 [٣ ، ٧]
  • 2 ]٣ ، ٧[
  • 3 [١ ، ٩]
  • 4 [١ ، ٣[
4

الفترة التي تمثل جميع الأعداد الحقيقية هي:

  • 1 ]−∞ ، ∞[
  • 2 [−∞ ، ∞]
  • 3 ]٠ ، ∞[
  • 4 [٠ ، ∞[
5

إذا كان أ = ]−∞ ، ٥[ ، ب = ]٢ ، ∞[ ، فإن أ − ب =

  • 1 ]−∞ ، ٢]
  • 2 ]−∞ ، ٢[
  • 3 [٢ ، ٥[
  • 4 ]٥ ، ∞[
6

إذا كانت ش = ح وكانت أ = [−١ ، ٤] ، فإن أ′ =

  • 1 ]−∞ ، −١[ ∪ ]٤ ، ∞[
  • 2 ]−∞ ، −١] ∪ [٤ ، ∞[
  • 3 ]−١ ، ٤[
  • 4 [−∞ ، −١] ∪ [٤ ، ∞[

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