Worksheet: Intervals

In this worksheet, we will practice determining limited and unlimited intervals.

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:

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

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

Q3:

Which of the following is true?

  • A 1 6 ( 4 , )
  • B 1 6 ( 4 , )
  • C 1 6 ( 4 , )
  • D 1 6 ( 4 , )

Q4:

Which of the following is a closed interval?

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

Q5:

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

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

Q6:

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

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

Q7:

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 , [

Q8:

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 }

Q9:

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

  • A(d)
  • B(a)
  • C(c)
  • D(b)

Q10:

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

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

Q11:

What is [ 5 , 4 ] ?

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

Q12:

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

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q13:

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

Q14:

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 }

Q15:

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

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

Q16:

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

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

Q17:

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

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

Q18:

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

Q19:

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

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

Q20:

Which of the following sets satisfies [ 1 5 , 0 ] 𝑋 = ( 1 5 , 0 ) ?

  • A 𝑋 = [ 1 5 , 0 )
  • B 𝑋 =
  • C 𝑋 = ( 1 5 , 0 ]
  • D 𝑋 = { 1 5 , 0 }
  • E 𝑋 = ( 1 5 , 0 )

Q21:

Which of the following is true?

  • A 1 6 3 ] 9 , 5 [
  • B 1 6 3 ] 9 , 5 [
  • C 1 6 3 ] 9 , 5 [
  • D 1 6 3 ] 9 , 5 [

Q22:

Given that 𝑋 = ( 6 , 6 ) and 𝑌 = { 6 , 1 } , find 𝑋 𝑌 .

  • A { 6 , 1 }
  • B ( 6 , 6 )
  • C { 1 }
  • D [ 6 , 6 )

Q23:

Which of the following is true?

  • A 1 [ 1 , )
  • B 1 [ 1 , )
  • C 1 [ 1 , )
  • D 1 [ 1 , )

Q24:

Which of the following is true?

  • A ( 2 , 7 ) ( , 9 ]
  • B ( 2 , 7 ) ( , 9 ]
  • C ( 2 , 7 ) ( , 9 ]
  • D ( 2 , 7 ) ( , 9 ]

Q25:

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

  • A { 4 , 3 }
  • B [ 6 , 3 ]
  • C { 4 }
  • D [ 6 , 4 ) ( 4 , 3 )

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