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Lesson: Intervals

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

Q1:

The figure shows an interval on the number line. Write an expression for it using interval notation.

  • A [ 3 , 1 ]
  • B ] 3 , 1 ]
  • C ] 3 , 1 [
  • D [ 3 , 1 [

Q2:

Given that ] , 𝑘 [ [ 2 2 , 1 1 ] = [ 2 2 , 9 [ , determine the value of 𝑘 .

Q3:

Which of the following sets satisfies ] 1 7 , 1 5 ] 𝑋 = [ 2 0 , 1 5 ] ?

  • A 𝑋 = [ 2 0 , 1 6 ]
  • B 𝑋 = ] 1 7 , 1 6 [
  • C 𝑋 = [ 2 0 , 1 7 [
  • D 𝑋 = ] 2 0 , 1 8 [
  • E 𝑋 = [ 1 7 , 1 6 ]

Q4:

Express the set of real numbers in the form of an interval.

  • A ] , [
  • B ] 1 , [
  • C ] , 0 [
  • D ] , 1 [
  • E ] 0 , [

Q5:

Which of the following is true?

  • A 1 6 ] 4 , [
  • B 1 6 ] 4 , [
  • C 1 6 ] 4 , [
  • D 1 6 ] 4 , [

Q6:

Which of the following is true?

  • A 4 5 [ 5 , [
  • B 4 5 [ 5 , [
  • C 4 5 [ 5 , [
  • D 4 5 [ 5 , [

Q7:

Which of the following is true?

  • A 8 7 ] , 1 ]
  • B 8 7 ] , 1 ]
  • C 8 7 ] , 1 ]
  • D 8 7 ] , 1 ]

Q8:

Given that 𝑋 = [ 8 , 3 [ and 𝑌 = [ 4 , 3 [ , find 𝑋 𝑌 .

  • A [ 4 , 3 [
  • B [ 8 , 3 [
  • C [ 8 , 4 [ [ 3 , 3 [
  • D

Q9:

Given that 𝑋 = ] 6 , 5 [ and 𝑌 = ] 5 , 8 [ , find 𝑋 𝑌 .

  • A
  • B ] 6 , 5 [
  • C ] 6 , 8 [ { 5 }
  • D ] 5 , 8 [

Q10:

Given that 𝑋 = ] 3 , 4 ] and 𝑌 = [ 6 , 2 [ , find 𝑋 𝑌 .

  • A [ 6 , 4 ]
  • B ] 3 , 4 ]
  • C
  • D [ 6 , 2 [

Q11:

Given that 𝑋 = [ 3 , 1 [ and 𝑌 = [ 0 , 8 ] , find 𝑋 𝑌 .

  • A [ 3 , 8 ] [ 1 , 0 [
  • B [ 3 , 1 [
  • C
  • D [ 0 , 8 ]

Q12:

State the interval that is represented by the following number line.

  • A ] 2 , 4 [
  • B { 2 , 4 }
  • C [ 2 , 4 [
  • D [ 2 , 4 ]
  • E ] 2 , 4 ]

Q13:

State the interval that is represented by the following number line.

  • A ] 4 , 2 ]
  • B { 4 , 2 }
  • C [ 4 , 2 ]
  • D [ 4 , 2 [
  • E ] 4 , 2 [

Q14:

Given that 𝑋 = [ 7 , 2 ] and 𝑌 = ] 2 , [ , find 𝑌 𝑋 .

  • A ] 2 , [
  • B [ 7 , 2 ]
  • C [ 7 , [
  • D

Q15:

Which of the following is a closed interval?

  • A [ 1 , 7 ]
  • B ] 1 , 7 [
  • C { 1 , 7 }
  • D [ 1 , 7 [

Q16:

What is [ 5 , 4 ] ?

  • A [ 5 , 4 ]
  • B [ 5 , 0 ]
  • C ( 0 , 4 ]
  • D [ 5 , 0 )

Q17:

Given that 𝑥 [ 3 5 , [ , which of the following inequalities holds?

  • A 𝑥 3 5
  • B 𝑥 < 3 5
  • C 𝑥 > 3 5
  • D 𝑥 3 5

Q18:

Which of the following expressions represents the set shown on the number line?

  • A ] 4 , 1 ]
  • B ] , 4 ] [ 1 , [
  • C ] 4 , 1 [
  • D [ 4 , 1 [
  • E [ 4 , 1 ]

Q19:

The figure shows an interval on the number line. Write an expression for the interval using set notation.

  • A 𝑋 = { 𝑥 6 < 𝑥 < 3 , 𝑥 }
  • B 𝑋 = { 𝑥 6 𝑥 3 , 𝑥 }
  • C 𝑋 = { 𝑥 6 < 𝑥 3 , 𝑥 }
  • D 𝑋 = { 𝑥 6 𝑥 < 3 , 𝑥 }

Q20:

The figure shows an interval on the number line. Write an expression for the interval using set notation.

  • A 𝑋 = { 𝑥 5 𝑥 < 3 , 𝑥 }
  • B 𝑋 = { 𝑥 5 < 𝑥 3 , 𝑥 }
  • C 𝑋 = { 𝑥 5 𝑥 3 , 𝑥 }
  • D 𝑋 = { 𝑥 5 < 𝑥 < 3 , 𝑥 }

Q21:

Which of the following figures represents the interval ] 1 , 0 ] ?

  • A(b)
  • B(a)
  • C(c)
  • D(d)

Q22:

Which of the following expressions represents the set shown on the number line?

  • A ] 4 , 3 [ { 1 }
  • B ] 4 , 1 [ { 3 }
  • C ] 4 , 3 ] { 1 }
  • D [ 4 , 3 ] { 1 }
  • E [ 4 , 3 [ { 1 }

Q23:

Express the following set using interval notation: 𝑋 = 𝑥 𝑥 8 , 𝑥 3 .

  • A ] , 2 ]
  • B [ 2 , [
  • C ] 2 , [
  • D ] , 2 [

Q24:

If 𝑥 [ 1 , 6 2 5 ) , what interval is 𝑥 in?

  • A [ 2 5 , 1 )
  • B [ 1 , 2 5 )
  • C [ 0 , 2 5 )
  • D [ 1 , 0 )
  • E [ 1 , 2 5 )

Q25:

Which of the following figures represents the set [ 2 , 4 ] ?

  • A(a)
  • B(b)
  • C(d)
  • D(c)
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