Multiple Choice

1. Which of the following relations is non-linear and has a degree of $2$?

   $y = 7 - 2x$

   $y = 3x^2 - 5x + 1$

   $y = x^3 + 4x^2 - x$

   $y = -5$

2. In mathematics, what is a relation?

   A type of equation that only uses addition.

   A set of ordered pairs showing a connection between two sets of data.

   The answer to a math problem.

   A single number.

3. In the scenario ``The amount of money earned depends on the number of hours worked,'' which variable is the dependent variable?

   The number of hours worked.

   The employer.

   The type of job.

   The amount of money earned.

4. Which of the following equations represents a linear relation?

   $y = 2x - 1$

   $y = \sqrt{x}$

   $y = x^2 + 5$

   $y = 3/x$

5. Which of these equations represents a non-linear relation?

   $y = x + 7$

   $y = x^3 + x$

   $y = 5x$

   $y = -3x + 2$

6. How does the graph of a linear relation appear?

   As a straight line.

   As a parabola.

   As a wavy line.

   As a disconnected set of points.

7. Which description best fits the graph of a non-linear relation?

   It has a constant slope.

   It can only be a horizontal line.

   It is a curve or a broken line that is not straight.

   It is always a straight line passing through the origin.

8. Based on the table of values below, is the relation linear?

   Yes, because the x-values are consecutive.

   No, because it does not include negative numbers.

   No, because the y-values are increasing.

   Yes, because the first differences in the y-values are constant.

9. What is the degree of the relation $y = 4x - 7$?

   4

   7

   0

   1

10. What is the degree of the relation $y = 2x^2 + 3x - 1$?

    -1

    2

    1

    3

11. If a relation has a degree of 1, what can you conclude about its graph?

    It will pass through the origin.

    It will be a straight line.

    It will be a horizontal line.

    It will be a curve.

12. A student tracks their plant's height over several weeks. Which statement correctly identifies the independent and dependent variables in this relation?

    The number of weeks is the dependent variable, and the plant's height is the independent variable.

    The plant's height is the independent variable, and the number of weeks is the dependent variable.

    The student is the independent variable, and the plant's height is the dependent variable.

    The number of weeks is the independent variable, and the plant's height is the dependent variable.

13. Consider the following relations. Which one is a linear relation?

    $y = 2x^2 - 5x + 1$

    $y = \dfrac{6}{x} + 2$

    $y = 3x(x - 1) + 3x^2$

    $y = (x+2)(x-1) - x^2$

14. What is the degree of the relation $y = 5x^2 - 3x^3 + 7 - 2x^2 + x$?

    0

    3

    2

    1

15. The equation $y = 4^x$ represents a non-linear relation. What is the primary reason it is classified as non-linear?

    The independent variable is in the exponent.

    The constant term is missing.

    The independent variable is multiplied by a constant.

    The $y$-values are always positive.

16. Which graph represents a linear relation?

    A graph that decreases rapidly at first, then flattens out towards zero.

    A parabola opening upwards.

    A straight line passing through the points $(0, 2)$ and $(3, 5)$.

    A curve that starts flat and then steepens upwards.

17. A relation is defined by the set of ordered pairs $\{(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)\}$. Which statement about this relation is true?

    The range of the relation is $\{-2, -1, 0, 1, 2\}$.

    It is a linear relation.

    The domain of the relation is $\{0, 1, 2, 4\}$.

    It is a non-linear relation with a degree of 2.

18. What is the degree of the relation represented by $y = (x+2)^2 - (x-1)(x+3)$?

    2

    0

    Not applicable (non-polynomial)

    1

19. Which of the following best describes a non-linear relation?

    A relation where the $y$-values have a constant difference for equal intervals of $x$.

    A relation whose equation can be written in the form $y = mx + b$.

    A relation whose graph is a straight line.

    A relation where the rate of change between variables is not constant.

20. A car is accelerating at a constant rate. Its speed $v$ (in m/s) over time $t$ (in seconds) can be described by the relation $v = at + v_0$, where $a$ is acceleration and $v_0$ is initial speed. Which statement about this relation is true?

    This relation is non-linear because it models real-world physics.

    This is a non-linear relation because the speed is changing.

    The degree of this relation is 2 because acceleration involves $t^2$ in distance equations.

    This is a linear relation because the highest power of the independent variable $t$ is 1.