RevisionDojo

Rational equations - MYP Questionbank | RevisionDojo

Practice Rational equations 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 equation:

\frac{5}{x^2-9} = \frac{2}{x-3}

Which of the following describes all values of $x$ that must be excluded from the domain?

Question 2

Which of the following is NOT a rational equation according to the definition that rational expressions must be ratios of polynomials?

Question 3

True or False: The rational equation $\frac{x-1}{x^2-1} = \frac{1}{x+1}$ is satisfied by all real numbers except $x = 1$ and $x = -1$ .

Question 4

Solve the rational equation for $x$ :

\frac{x}{x+2} - \frac{8}{x^2-4} = \frac{2}{x-2}

Question 5

Find the solution set for the following equation:

\frac{2}{x-1} = \frac{x}{x-1} - 1

Question 6

The operation of cross-multiplication on the equation $\frac{a}{b} = \frac{c}{d}$ results in the equation $ad = bc$ . This process is an application of the method of clearing denominators. Identify the multiplier that, when applied to both sides of the original equation, results in this form.

Question 7

Determine whether the following statement is true or false:

'If the graphs of two rational functions $f(x)$ and $g(x)$ do not intersect, then the equation $f(x) = g(x)$ has no real solutions.'

Question 8

True or False: If an algebraic step in solving a rational equation leads to $x=2$ , but the original equation had a term $\frac{5}{x^2-4}$ , then $x=2$ must be rejected as an extraneous solution.

Question 9

Identify all domain restrictions for the following rational equation:

\frac{x}{x^2+x-6} = \frac{x-1}{x^2-4}

Question 10

The speed of a boat in still water is $x\text{ km h}^{-1}$ . To travel $1\text{ km}$ upstream against a $1\text{ km h}^{-1}$ current and then $1\text{ km}$ downstream, the boat takes a total of $\frac{3}{4}\text{ hour}$ . Find $x$ by solving: $\frac{1}{x-1} + \frac{1}{x+1} = \frac{3}{4}$

Type

Difficulty

Question 1

Consider the equation:

\frac{5}{x^2-9} = \frac{2}{x-3}

Which of the following describes all values of $x$ that must be excluded from the domain?

Question 2

Which of the following is NOT a rational equation according to the definition that rational expressions must be ratios of polynomials?

Question 3

True or False: The rational equation $\frac{x-1}{x^2-1} = \frac{1}{x+1}$ is satisfied by all real numbers except $x = 1$ and $x = -1$ .

Question 4

Solve the rational equation for $x$ :

\frac{x}{x+2} - \frac{8}{x^2-4} = \frac{2}{x-2}

Question 5

Find the solution set for the following equation:

\frac{2}{x-1} = \frac{x}{x-1} - 1

Question 6

Question 7

Determine whether the following statement is true or false:

'If the graphs of two rational functions $f(x)$ and $g(x)$ do not intersect, then the equation $f(x) = g(x)$ has no real solutions.'

Question 8

True or False: If an algebraic step in solving a rational equation leads to $x=2$ , but the original equation had a term $\frac{5}{x^2-4}$ , then $x=2$ must be rejected as an extraneous solution.

Question 9

Identify all domain restrictions for the following rational equation:

\frac{x}{x^2+x-6} = \frac{x-1}{x^2-4}

Question 10

Type

Difficulty

Question 1

Consider the equation:

\frac{5}{x^2-9} = \frac{2}{x-3}

Which of the following describes all values of $x$ that must be excluded from the domain?

Question 2

Which of the following is NOT a rational equation according to the definition that rational expressions must be ratios of polynomials?

Question 3

True or False: The rational equation $\frac{x-1}{x^2-1} = \frac{1}{x+1}$ is satisfied by all real numbers except $x = 1$ and $x = -1$ .

Question 4

Solve the rational equation for $x$ :

\frac{x}{x+2} - \frac{8}{x^2-4} = \frac{2}{x-2}

Question 5

Find the solution set for the following equation:

\frac{2}{x-1} = \frac{x}{x-1} - 1

Question 6

Question 7

Determine whether the following statement is true or false:

'If the graphs of two rational functions $f(x)$ and $g(x)$ do not intersect, then the equation $f(x) = g(x)$ has no real solutions.'

Question 8

True or False: If an algebraic step in solving a rational equation leads to $x=2$ , but the original equation had a term $\frac{5}{x^2-4}$ , then $x=2$ must be rejected as an extraneous solution.

Question 9

Identify all domain restrictions for the following rational equation:

\frac{x}{x^2+x-6} = \frac{x-1}{x^2-4}

Question 10

Rational equations Questionbank