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Non-linear inequalities - MYP Questionbank | RevisionDojo

Practice Non-linear inequalities with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

Consider the inequality $y > \ln(4 - x)$ . What is the primary domain restriction that must be reflected in the shaded solution region?

Question 2

True or False: The point $(-3, 10)$ is part of the solution region for the inequality $y \ge x^2 + 2$ .

Question 3

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y > x^2 + x$ .

Question 4

A system of inequalities is defined by:

\begin{cases} y > x^2 \\ y < 4 \end{cases}

Which description best fits the feasible region?

Question 5

Fill in the blank: In the rational inequality $y \le \frac{2x}{x+4}$ , even though the inequality is non-strict, the vertical asymptote at $x = -4$ is always drawn as a ________ line.

Question 6

What is the feasible region for the following system?

\begin{cases} y > x^2 + 1 \\ y < 1 \end{cases}

Question 7

A student uses the test point $(0,0)$ to solve the inequality $y < x^2 - 2x - 3$ . Upon substitution, the student finds that the inequality results in $0 < -3$ . What should the student conclude?

Question 8

True or False: For the inequality $y \ge x^2 + 2x + 1$ , the point $(-1, 0)$ is included in the solution set.

Question 9

True or False: For the inequality $y < \frac{1}{x^2 + 1}$ , the entire solution region lies strictly below the horizontal asymptote $y = 0$ .

Question 10

To solve the system of inequalities $y < -x^2 + 4$ and $y > x^2 - 4$ , the feasible region is the area ________ the parabola $y = -x^2 + 4$ and ________ the parabola $y = x^2 - 4$ .

Type

Difficulty

Question 1

Consider the inequality $y > \ln(4 - x)$ . What is the primary domain restriction that must be reflected in the shaded solution region?

Question 2

True or False: The point $(-3, 10)$ is part of the solution region for the inequality $y \ge x^2 + 2$ .

Question 3

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y > x^2 + x$ .

Question 4

A system of inequalities is defined by:

\begin{cases} y > x^2 \\ y < 4 \end{cases}

Which description best fits the feasible region?

Question 5

Fill in the blank: In the rational inequality $y \le \frac{2x}{x+4}$ , even though the inequality is non-strict, the vertical asymptote at $x = -4$ is always drawn as a ________ line.

Question 6

What is the feasible region for the following system?

\begin{cases} y > x^2 + 1 \\ y < 1 \end{cases}

Question 7

A student uses the test point $(0,0)$ to solve the inequality $y < x^2 - 2x - 3$ . Upon substitution, the student finds that the inequality results in $0 < -3$ . What should the student conclude?

Question 8

True or False: For the inequality $y \ge x^2 + 2x + 1$ , the point $(-1, 0)$ is included in the solution set.

Question 9

True or False: For the inequality $y < \frac{1}{x^2 + 1}$ , the entire solution region lies strictly below the horizontal asymptote $y = 0$ .

Question 10

To solve the system of inequalities $y < -x^2 + 4$ and $y > x^2 - 4$ , the feasible region is the area ________ the parabola $y = -x^2 + 4$ and ________ the parabola $y = x^2 - 4$ .

Type

Difficulty

Question 1

Consider the inequality $y > \ln(4 - x)$ . What is the primary domain restriction that must be reflected in the shaded solution region?

Question 2

True or False: The point $(-3, 10)$ is part of the solution region for the inequality $y \ge x^2 + 2$ .

Question 3

True or False: The point $(0,0)$ can be used as a valid test point to determine the shading region for the inequality $y > x^2 + x$ .

Question 4

A system of inequalities is defined by:

\begin{cases} y > x^2 \\ y < 4 \end{cases}

Which description best fits the feasible region?

Question 5

Fill in the blank: In the rational inequality $y \le \frac{2x}{x+4}$ , even though the inequality is non-strict, the vertical asymptote at $x = -4$ is always drawn as a ________ line.

Question 6

What is the feasible region for the following system?

\begin{cases} y > x^2 + 1 \\ y < 1 \end{cases}

Question 7

A student uses the test point $(0,0)$ to solve the inequality $y < x^2 - 2x - 3$ . Upon substitution, the student finds that the inequality results in $0 < -3$ . What should the student conclude?

Question 8

True or False: For the inequality $y \ge x^2 + 2x + 1$ , the point $(-1, 0)$ is included in the solution set.

Question 9

True or False: For the inequality $y < \frac{1}{x^2 + 1}$ , the entire solution region lies strictly below the horizontal asymptote $y = 0$ .

Question 10

To solve the system of inequalities $y < -x^2 + 4$ and $y > x^2 - 4$ , the feasible region is the area ________ the parabola $y = -x^2 + 4$ and ________ the parabola $y = x^2 - 4$ .

Non-linear inequalities Questionbank