Free SATs Math Questions and Answers 1 — Questions and Answers
Question 1: Is there a function in this relation?
- no
- yes (Correct answer)
Correct answer: yes
A relation is considered a function if and only if every input (x-value) corresponds to exactly one output (y-value). If the provided relation (which is missing from the prompt but implied by the question) adheres to this rule, meaning no x-value is paired with more than one distinct y-value, then it represents a function. The "yes" answer indicates that, whatever the specific relation was, it satisfied this fundamental condition for a function.
Question 2: Is there a function in this relation?
- no
- yes (Correct answer)
Correct answer: yes
For a relation to be a function, each input value (typically represented by 'x') must be associated with only one output value (typically 'y'). If the given relation (which is not explicitly shown in the prompt) ensures that no single input maps to multiple different outputs, then it correctly defines a function. The answer "yes" confirms that the relation in question meets this criterion.
Question 3: What is the effect on the graph of f(x) of the transformation f(x)→f(4x)?
- reduces its horizontal size (Correct answer)
- reduces it vertically
- extends it vertically
- extends it laterally
Correct answer: reduces its horizontal size
The transformation f(x)→f(4x) involves a change to the input variable, x. When the input x is multiplied by a factor greater than 1 (like 4), the graph undergoes a horizontal compression. This means the graph is squeezed towards the y-axis, effectively reducing its horizontal size by a factor of 1/4.
Question 4: Is there a function in this relation?
- no
- yes (Correct answer)
Correct answer: yes
A relation is considered a function if every input value (x-value) corresponds to exactly one output value (y-value). This means that for any given x, there should not be two or more different y-values associated with it. Since the correct answer is 'yes', the unspecified relation must adhere to this rule, ensuring each input has a unique output.
Question 5: Which quadrant, in standard position, contains the terminal side of a 315° angle?
- Quadrant IV (Correct answer)
- Quadrant III
- Quadrant II
- Quadrant I
Correct answer: Quadrant IV
In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 315° angle falls between 270° and 360°, placing its terminal side in Quadrant IV.
Question 6: Which quadrant, in standard position, contains the terminal side of a 135° angle?
- Quadrant III
- Quadrant IV
- Quadrant I
- Quadrant II (Correct answer)
Correct answer: Quadrant II
In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 135° angle falls between 90° and 180°, placing its terminal side in Quadrant II.
Question 7: Which quadrant, in standard position, corresponds to the terminal side of a 225° angle?
- Quadrant III (Correct answer)
- Quadrant I
- Quadrant IV
- Quadrant II
Correct answer: Quadrant III
In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 225° angle falls between 180° and 270°, placing its terminal side in Quadrant III.
Question 8: Which quadrant, in standard position, contains the terminal side of a 45° angle?
- Quadrant II
- Quadrant III
- Quadrant IV
- Quadrant I (Correct answer)
Correct answer: Quadrant I
In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 45° angle falls between 0° and 90°, placing its terminal side in Quadrant I.
Question 9: The terminal side of a 690° angle in standard position lies in which quadrant?
- Quadrant IV (Correct answer)
- Quadrant I
- Quadrant III
- Quadrant II
Correct answer: Quadrant IV
To find the quadrant for an angle greater than 360°, subtract multiples of 360° until you get an angle between 0° and 360°. For 690°, 690° - 360° = 330°. Since 330° lies between 270° and 360°, its terminal side is in Quadrant IV.
Question 10: The terminal side of a 480° angle in standard position lies in which quadrant?
- Quadrant II (Correct answer)
- Quadrant IV
- Quadrant I
- Quadrant III
Correct answer: Quadrant II
To find the quadrant for an angle greater than 360°, subtract multiples of 360° until you get an angle between 0° and 360°. For 480°, 480° - 360° = 120°. Since 120° lies between 90° and 180°, its terminal side is in Quadrant II.
Question 11: Which quadrant, in standard position, corresponds to the terminal side of a 150° angle?
- Quadrant IV
- Quadrant III
- Quadrant II (Correct answer)
- Quadrant I
Correct answer: Quadrant II
In standard position, angles are measured counterclockwise from the positive x-axis. Quadrant I spans 0° to 90°, Quadrant II 90° to 180°, Quadrant III 180° to 270°, and Quadrant IV 270° to 360°. A 150° angle falls between 90° and 180°, placing its terminal side in Quadrant II.
Free SATs Math Questions and Answers 1
Is there a function in this relation?