Questions covered in Unit Test: Sets and Functions (Standard)

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If $n(A) = 17$, $n(B) = 23$ and $n(A \cup B) = 38$, then $n(A \cap B)$ is
2. The domain of the function $f(x) = \frac{x^2+2x+1}{x^2-8x+12}$ is
3. Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is
4. The range of $f(x) = 1 - |x-2|$ is
5. If $A = \{1, 2\}$, then the power set $P(A)$ is
6. Find the domain and range of the real function $f(x) = \sqrt{9-x^2}$.
7. If $A \times B = \{(p, q), (p, r), (m, q), (m, r)\}$, find $A$ and $B$.
8. Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Write $R$ in roster form.
9. In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.
10. Find the domain and range of the real function $f(x) = \frac{|x-1|}{x-1}$.
11. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
    (i) the number of people who read at least one of the newspapers.
    (ii) the number of people who read exactly one newspaper.
12. Case Study: A linear function is defined by $f(x) = mx + c$. Given $f(1) = 3$ and $f(2) = 5$.
    (i) Find the values of $m$ and $c$.
    (ii) Find $f(5)$.
    (iii) Find $x$ when $f(x) = 11$.