Questions covered in Basic

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 $n(A) = p$ and $n(B) = q$, then $n(A \times B)$ is
2. If $(x+1, y-2) = (3, 1)$, then the values of $x$ and $y$ are
3. Which of the following relations is a function?
4. The domain of the function $f(x) = \frac{1}{x}$ is
5. If $f(x) = x^2 - 2x + 1$, then $f(-1)$ is
6. Let $A = \{1, 2\}$ and $B = \{3, 4\}$. Write $A \times B$.
7. A relation $R$ is defined on the set $A = \{1, 2, 3\}$ by $R = \{(x, y) : y = 2x, x \in A\}$. Write $R$ in roster form.
8. Find the domain of the real function $f(x) = \sqrt{x-2}$.
9. Let $f(x) = x + 1$ and $g(x) = 2x - 3$. Find $(f+g)(x)$, $(f-g)(x)$ and $(fg)(x)$.
10. Find the range of the function $f(x) = 2 - 3x$ for $x > 0$.
11. Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ on $A$ by $R = \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$.
    (i) Write $R$ in roster form.
    (ii) Find the domain of $R$.
    (iii) Find the range of $R$.
12. Case Study: The temperature in degrees Celsius ($C$) and degrees Fahrenheit ($F$) are related by the formula $F = \frac{9}{5}C + 32$.
    (i) Find $F$ when $C = 0$.
    (ii) Find $C$ when $F = 212$.
    (iii) Find the temperature where the value is same in both scales ($F = C$).