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Sequences, Rational Expressions and Equations - MYP Questionbank | RevisionDojo

Practice Sequences, Rational Expressions and 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

Which of the following best describes a rational function $R(x)$ ?

Question 2

Simplify the following subtraction into a single rational expression:

$\frac{2}{x + 2} - \frac{1}{x}$

Question 3

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 4

True or False: For a rational function $f(x) = \frac{a}{x-h} + k$ , if $a > 0$ , the function is strictly decreasing on both of its disjoint domain intervals $(-\infty, h)$ and $(h, \infty)$ .

Question 5

Which of the following values is a term in the arithmetic sequence defined by $u_1 = 4$ and $d = 0.6$ ?

Question 6

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

Question 7

True or False: A sequence where every term is $7$ ( $7, 7, 7, 7, \dots$ ) is geometric with a common ratio $r = 1$ .

Question 8

Consider the following statement regarding the expression $\dfrac{a^2 + b^2}{a + b}$ , where $a + b \neq 0$ :

"The expression can be simplified to $a + b$ by cancelling the variables $a$ and $b$ in the numerator and denominator."

Determine whether this statement is True or False and identify the correct reasoning.

Question 9

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 10

Solve the rational equation for $x$ :

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

Type

Difficulty

Question 1

Which of the following best describes a rational function $R(x)$ ?

Question 2

Simplify the following subtraction into a single rational expression:

$\frac{2}{x + 2} - \frac{1}{x}$

Question 3

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 4

True or False: For a rational function $f(x) = \frac{a}{x-h} + k$ , if $a > 0$ , the function is strictly decreasing on both of its disjoint domain intervals $(-\infty, h)$ and $(h, \infty)$ .

Question 5

Which of the following values is a term in the arithmetic sequence defined by $u_1 = 4$ and $d = 0.6$ ?

Question 6

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

Question 7

True or False: A sequence where every term is $7$ ( $7, 7, 7, 7, \dots$ ) is geometric with a common ratio $r = 1$ .

Question 8

Consider the following statement regarding the expression $\dfrac{a^2 + b^2}{a + b}$ , where $a + b \neq 0$ :

"The expression can be simplified to $a + b$ by cancelling the variables $a$ and $b$ in the numerator and denominator."

Determine whether this statement is True or False and identify the correct reasoning.

Question 9

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 10

Solve the rational equation for $x$ :

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

Type

Difficulty

Question 1

Which of the following best describes a rational function $R(x)$ ?

Question 2

Simplify the following subtraction into a single rational expression:

$\frac{2}{x + 2} - \frac{1}{x}$

Question 3

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 4

True or False: For a rational function $f(x) = \frac{a}{x-h} + k$ , if $a > 0$ , the function is strictly decreasing on both of its disjoint domain intervals $(-\infty, h)$ and $(h, \infty)$ .

Question 5

Which of the following values is a term in the arithmetic sequence defined by $u_1 = 4$ and $d = 0.6$ ?

Question 6

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

Question 7

True or False: A sequence where every term is $7$ ( $7, 7, 7, 7, \dots$ ) is geometric with a common ratio $r = 1$ .

Question 8

Consider the following statement regarding the expression $\dfrac{a^2 + b^2}{a + b}$ , where $a + b \neq 0$ :

"The expression can be simplified to $a + b$ by cancelling the variables $a$ and $b$ in the numerator and denominator."

Determine whether this statement is True or False and identify the correct reasoning.

Question 9

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 10

Solve the rational equation for $x$ :

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

Sequences, Rational Expressions and Equations Questionbank