Questions covered in 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 $A = \{1, 2\}$ and $B = \{3, 4\}$, then the number of relations from $A$ to $B$ is
2. The domain of the function $f(x) = \frac{1}{\sqrt{x-1}}$ is
3. If $f(x) = x^3 - \frac{1}{x^3}$, then $f(x) + f(1/x)$ is equal to
4. Let $R = \{(x, x^3) : x \text{ is a prime number less than 5}\}$. Then $R$ is
5. The range of the function $f(x) = |x|$ is
6. Find the domain of the function $f(x) = \frac{x^2+3x+5}{x^2-5x+4}$.
7. If $f(x) = x^2$, find $\frac{f(1.1) - f(1)}{1.1 - 1}$.
8. Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Depict this relation using an arrow diagram.
9. Find the domain and range of the real function $f(x) = \sqrt{9-x^2}$.
10. Let $f, g: R \to R$ be defined by $f(x) = x+1$ and $g(x) = 2x-3$. Find $f+g, f-g$ and $f/g$.
11. Define the function $f: R \to R$ by $y = f(x) = x^2, x \in R$. Draw the graph of $f(x)$. Find the domain and range. Also draw graph of $g(x) = x^3$.
12. Case Study: The relation between the height of a plant $y$ (in cm) with respect to exposure to sunlight $x$ (in hours) is given by $y = 4x - \frac{1}{2}x^2$.
    (i) Find the height when sunlight is 2 hours.
    (ii) Find the height when sunlight is 0 hours.
    (iii) What is the domain of $x$ if height cannot be negative?