Relations and Functions (Advanced)

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   If (2x + 7, y − 9) = (15, −8), then:

   1. x = 4, y = 1
   2. x = 1, y = 4
   3. x = −4, y = 1
   4. x = 4, y = 3

   Answer

   (a) x = 4, y = 1

   2x + 7 = 15 and y − 9 = −8

2. 2.

   If n(A) = 6 and n(B) = 5, how many relations can be defined from A to B?

   1. 2¹¹
   2. 30²
   3. 30
   4. 2³⁰

   Answer

   (d) 2³⁰

   n(A × B) = 6 × 5 = 30; a relation is any subset: 2³⁰

3. 3.

   If (a, b) = (c, d), then:

   1. a + b = c + d
   2. ab = cd
   3. a = d and b = c
   4. a = c and b = d

   Answer

   (d) a = c and b = d

   ordered pairs are equal only when matching entries are equal

Section B · short answer

1. 4.

   A = {1, 4, 7} and B = {1, 7, 8}. Find (A × B) ∩ (B × A).

   Answer

   {(1, 1), (1, 7), (7, 1), (7, 7)}

   a pair is in both only if each entry is in A ∩ B = {1, 7}; so it is (A ∩ B) × (A ∩ B)

2. 5.

   A = {4, 5, 6} and B = {5, 7, 8, 9}. R = {(a, b) : a divides b; a ∈ A, b ∈ B}. Write R in roster form, and its domain and range.

   Answer

   R = {(4, 8), (5, 5)}; domain {4, 5}; range {5, 8}

   check every pair of A × B against the rule

Section C · long answer

1. 6.

   A = {3, 4}, B = {3, 4, 6} and C = {4, 5, 7}. Find B ∪ C and A × (B ∪ C), and check that A × (B ∪ C) = (A × B) ∪ (A × C). How many elements does it have?

   Answer

   B ∪ C = {3, 4, 5, 6, 7}; A × (B ∪ C) = {(3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7)}; 10 elements

   n = n(A) × n(B ∪ C) = 2 × 5; (A × B) ∪ (A × C) gives the same pairs

Fresh sheets for your child

In the app, every Relations and Functions (Advanced) sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

Coming soon for Android and iPhone.

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