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Worksheet: Intervals

Q1:

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

  • A
  • B
  • C
  • D

Q2:

Given that ( βˆ’ ∞ , π‘˜ ) ∩ [ βˆ’ 2 2 , 1 1 ] = [ βˆ’ 2 2 , 9 ) , determine the value of π‘˜ .

Q3:

Which of the following sets satisfies ?

  • A
  • B
  • C
  • D
  • E

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is true?

  • A
  • B
  • C
  • D

Q6:

Which of the following is true?

  • A
  • B
  • C
  • D

Q7:

Which of the following is true?

  • A
  • B
  • C
  • D

Q8:

Given that and , find .

  • A
  • B
  • C
  • D

Q9:

Given that and , find .

  • A
  • B
  • C
  • D

Q10:

Given that and , find .

  • A
  • B
  • C
  • D

Q11:

Given that and , find .

  • A
  • B
  • C
  • D

Q12:

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

  • A
  • B
  • C
  • D
  • E

Q13:

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

  • A
  • B
  • C
  • D
  • E

Q14:

Given that and , find .

  • A
  • B
  • C
  • D

Q15:

Which of the following is a closed interval?

  • A
  • B
  • C
  • D

Q16:

What is ?

  • A
  • B
  • C
  • D

Q17:

Given that , which of the following inequalities holds?

  • A
  • B
  • C
  • D

Q18:

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

  • A
  • B
  • C
  • D
  • E

Q19:

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

  • A 𝑋 = { π‘₯ ∢ βˆ’ 6 ≀ π‘₯ < βˆ’ 3 , π‘₯ ∈ ℝ }
  • B 𝑋 = { π‘₯ ∢ βˆ’ 6 ≀ π‘₯ ≀ βˆ’ 3 , π‘₯ ∈ ℝ }
  • C 𝑋 = { π‘₯ ∢ βˆ’ 6 < π‘₯ ≀ βˆ’ 3 , π‘₯ ∈ ℝ }
  • D 𝑋 = { π‘₯ ∢ βˆ’ 6 < π‘₯ < βˆ’ 3 , π‘₯ ∈ ℝ }

Q20:

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

  • A 𝑋 = { π‘₯ ∢ βˆ’ 5 < π‘₯ < 3 , π‘₯ ∈ ℝ }
  • B 𝑋 = { π‘₯ ∢ βˆ’ 5 < π‘₯ ≀ 3 , π‘₯ ∈ ℝ }
  • C 𝑋 = { π‘₯ ∢ βˆ’ 5 ≀ π‘₯ ≀ 3 , π‘₯ ∈ ℝ }
  • D 𝑋 = { π‘₯ ∢ βˆ’ 5 ≀ π‘₯ < 3 , π‘₯ ∈ ℝ }

Q21:

Which of the following figures represents the interval ?

  • A(d)
  • B(a)
  • C(c)
  • D(b)

Q22:

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

  • A
  • B
  • C
  • D
  • E

Q23:

Express the following set using interval notation: .

  • A
  • B
  • C
  • D

Q24:

If , what interval is in?

  • A
  • B
  • C
  • D
  • E

Q25:

Which of the following figures represents the set ?

  • A(c)
  • B(b)
  • C(d)
  • D(a)