MAT1501 Oct/Nov 2023 exam paper — questions

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  1. Question 1(a) · Sets, intervals and number lines · 1 mark

    Consider the two sets A and B defined as follows: A is the set of all real numbers x such that x is greater than -3 (written A = {x ∈ R : x > -3}), and B is the interval (-4; 5], meaning all real numbers greater than -4 and up to and including 5. For the sets A = {x ∈ R : x > -3} and B = (-4; 5], draw a separate number line for A and another separate number line for B, showing each set clearly.Show the full question

  2. Question 1(b) · Sets, intervals and number lines · 1 mark

    Consider the two sets A and B defined as follows: A is the set of all real numbers x such that x is greater than -3 (written A = {x ∈ R : x > -3}), and B is the interval (-4; 5], meaning all real numbers greater than -4 and up to and including 5. Using set builder notation, write down the union of A and B, that is A ∪ B, where A = {x ∈ R : x > -3} and B = (-4; 5].Show the full question

  3. Question 1(c) · Sets, intervals and number lines · 1 mark

    Consider the two sets A and B defined as follows: A is the set of all real numbers x such that x is greater than -3 (written A = {x ∈ R : x > -3}), and B is the interval (-4; 5], meaning all real numbers greater than -4 and up to and including 5. On a separate number line, sketch the union A ∪ B for the sets A = {x ∈ R : x > -3} and B = (-4; 5].Show the full question

  4. Question 1(d) · Sets, intervals and number lines · 1 mark

    Consider the two sets A and B defined as follows: A is the set of all real numbers x such that x is greater than -3 (written A = {x ∈ R : x > -3}), and B is the interval (-4; 5], meaning all real numbers greater than -4 and up to and including 5. Write down the intersection A ∩ B on a separate number line, where A = {x ∈ R : x > -3} and B = (-4; 5].Show the full question

  5. Question 1(e) · Sets, intervals and number lines · 1 mark

    Consider the two sets A and B defined as follows: A is the set of all real numbers x such that x is greater than -3 (written A = {x ∈ R : x > -3}), and B is the interval (-4; 5], meaning all real numbers greater than -4 and up to and including 5. Again write down the intersection A ∩ B on a separate number line, for the sets A = {x ∈ R : x > -3} and B = (-4; 5].Show the full question

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