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Formula manipulation - MYP Questionbank | RevisionDojo

Practice Formula manipulation with authentic MYP MYP Standard 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

Variables $x$ and $y$ are in an inverse proportion relationship given by $y = \frac{k}{x}$ , where $k$ is a non-zero constant.

Which of the following statements is true for all valid values of $x$ and $y$ ?

Question 2

A variable $y$ is directly proportional to $x$ . If the graph of this relationship passes through the point $(5, 2)$ , what is the value of $y$ when $x = 1$ ?

Question 3

Consider the function $y = \frac{3}{2x-8}$ . For which value of $x$ is the function undefined?

Question 4

True or False: The formula $\frac{V}{R + r}$ can be correctly rewritten as $\frac{V}{R} + \frac{V}{r}$ by distributing the division across the addition in the denominator.

Question 5

The intensity of light $L$ is inversely proportional to the square of the distance $d$ from the source. Which equation correctly models this relationship using a constant $k$ ?

Question 6

Which of the following equations correctly represents a relationship where $y$ is inversely proportional to the square of $x$ ?

Question 7

In the context of formula manipulation, what does it mean for a variable to be the 'subject' of the formula?

Question 8

Rearrange the equation $y = \frac{1}{3}x^2 + 3$ to make $x$ the subject.

Question 9

Rearrange $a = \frac{k}{x^2+c}$ to make $x$ the subject (assuming all variables represent positive real numbers).

Question 10

True or False: In pure algebra, to make $x$ the subject of the formula $y = (x - h)^2$ , the result must be written as $x = h \pm \sqrt{y}$ to account for both possible roots.

Type

Difficulty

Question 1

Variables $x$ and $y$ are in an inverse proportion relationship given by $y = \frac{k}{x}$ , where $k$ is a non-zero constant.

Which of the following statements is true for all valid values of $x$ and $y$ ?

Question 2

A variable $y$ is directly proportional to $x$ . If the graph of this relationship passes through the point $(5, 2)$ , what is the value of $y$ when $x = 1$ ?

Question 3

Consider the function $y = \frac{3}{2x-8}$ . For which value of $x$ is the function undefined?

Question 4

True or False: The formula $\frac{V}{R + r}$ can be correctly rewritten as $\frac{V}{R} + \frac{V}{r}$ by distributing the division across the addition in the denominator.

Question 5

The intensity of light $L$ is inversely proportional to the square of the distance $d$ from the source. Which equation correctly models this relationship using a constant $k$ ?

Question 6

Which of the following equations correctly represents a relationship where $y$ is inversely proportional to the square of $x$ ?

Question 7

In the context of formula manipulation, what does it mean for a variable to be the 'subject' of the formula?

Question 8

Rearrange the equation $y = \frac{1}{3}x^2 + 3$ to make $x$ the subject.

Question 9

Rearrange $a = \frac{k}{x^2+c}$ to make $x$ the subject (assuming all variables represent positive real numbers).

Question 10

True or False: In pure algebra, to make $x$ the subject of the formula $y = (x - h)^2$ , the result must be written as $x = h \pm \sqrt{y}$ to account for both possible roots.

Type

Difficulty

Question 1

Variables $x$ and $y$ are in an inverse proportion relationship given by $y = \frac{k}{x}$ , where $k$ is a non-zero constant.

Which of the following statements is true for all valid values of $x$ and $y$ ?

Question 2

A variable $y$ is directly proportional to $x$ . If the graph of this relationship passes through the point $(5, 2)$ , what is the value of $y$ when $x = 1$ ?

Question 3

Consider the function $y = \frac{3}{2x-8}$ . For which value of $x$ is the function undefined?

Question 4

True or False: The formula $\frac{V}{R + r}$ can be correctly rewritten as $\frac{V}{R} + \frac{V}{r}$ by distributing the division across the addition in the denominator.

Question 5

The intensity of light $L$ is inversely proportional to the square of the distance $d$ from the source. Which equation correctly models this relationship using a constant $k$ ?

Question 6

Which of the following equations correctly represents a relationship where $y$ is inversely proportional to the square of $x$ ?

Question 7

In the context of formula manipulation, what does it mean for a variable to be the 'subject' of the formula?

Question 8

Rearrange the equation $y = \frac{1}{3}x^2 + 3$ to make $x$ the subject.

Question 9

Rearrange $a = \frac{k}{x^2+c}$ to make $x$ the subject (assuming all variables represent positive real numbers).

Question 10

True or False: In pure algebra, to make $x$ the subject of the formula $y = (x - h)^2$ , the result must be written as $x = h \pm \sqrt{y}$ to account for both possible roots.

Formula manipulation Questionbank