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SAT Unit Conversion and Physics Change Analysis Quiz (Hard)

SAT Unit Conversion and Physics Change Analysis Quiz (Hard)

1 / 15

A function \( E(w) = \\frac{5}{8}(w - 600) + 100 \) converts weight \( w \) in kilograms to a new scale. If the weight increases from 650 kg to 700 kg, what is the increase in the new scale, and what is the final value in the new scale?

2 / 15

The function \( D(s) = \\frac{2}{3}(s - 500) + 90 \) converts speed \( s \) in kilometers per hour to a new scale. If the speed increases from 550 km/h to 600 km/h, calculate the increase in the new scale and the final value in the new scale.

3 / 15

A function \( C(p) = \\frac{7}{6}(p - 400) + 80 \) converts pressure \( p \) in Pascals to a new scale. If the pressure increases from 450 Pascals to 500 Pascals, what is the final value in the new scale?

4 / 15

The function \( B(t) = \\frac{3}{5}(t - 300) + 70 \) converts time \( t \) in hours to a new scale. If the time increases from 350 hours to 370 hours, what is the increase in the new scale?

5 / 15

Given the function \( A(x) = \\frac{5}{4}(x - 200) + 50 \), which converts temperature in degrees Celsius to a new scale, calculate the new scale value if the temperature increases by 12 degrees Celsius from an initial temperature of 250 degrees Celsius.

6 / 15

The function \( Q(r) = \\frac{3}{8}(r - 450) + 100 \) translates a rate \( r \) in seconds to a new unit. Find the increase in the new unit if \( r \) increases by 16 seconds.

7 / 15

Given \( P(q) = \\frac{4}{7}(q - 500) + 90 \) for converting a quantity \( q \) in liters to a new scale, determine the increase in the new scale if \( q \) increases by 21 liters.

8 / 15

If the function \( O(p) = \\frac{5}{6}(p - 700) + 60 \) changes a pressure \( p \) in Pascals to a new scale, what is the increase in the new scale if \( p \) increases by 18 Pascals?

9 / 15

For the function \( N(s) = \\frac{3}{5}(s - 600) + 80 \), which converts a distance \( s \) in miles to a new scale, calculate the increase in the new scale if \( s \) increases by 25 miles.

10 / 15

The function \( M(v) = \\frac{1}{2}(v - 400) + 50 \) transforms a speed \( v \) in kilometers per hour to a different unit. What is the increase in the transformed unit if \( v \) increases by 20 kilometers per hour?

11 / 15

The function \( L(w) = \\frac{2}{3}(w - 500) + 70 \) converts weight \( w \) in kilograms to a new scale. How much does the new scale increase if the weight increases by 15 kilograms?

12 / 15

Given \( K(z) = \\frac{7}{5}(z - 300) + 40 \) where \( z \) is measured in meters, what is the increase in \( K(z) \) when \( z \) increases by 10 meters?

13 / 15

If the function \( J(y) = \\frac{3}{4}(y - 400) + 50 \) represents a conversion from a unit \( y \) to another unit, how much does the second unit increase if \( y \) increases by 12 units?

14 / 15

The function \( H(x) = \\frac{5}{2}(x - 250) + 100 \) converts a temperature in degrees Celsius to a unique scale \( x \). By how much does the unique scale increase if the temperature increases by 8 degrees Celsius?

15 / 15

A function \( G(t) = \\frac{4}{3}(t - 200) + 30 \) converts time from minutes to a special unit \( t \). If the time increases by 6 minutes, by how many units does \( G(t) \) increase?

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About This Quiz

The core concept tested in this quiz revolves around the transformation and analysis of changes in units through linear functions. Each question involves a function that converts one unit to another, typically represented as F(x) = a(x - b) + c, where:

  • a is the scaling factor that determines how the input unit is converted to the output unit.
  • b is a constant that shifts the input unit to align with the output unit's reference point.
  • c is another constant that adjusts the output value to fit the desired scale.

The main task in each problem is to calculate the change in the output unit given a specific change in the input unit. This requires understanding how the scaling factor a affects the change. For instance, if the input unit increases by \u0394x, then the output unit will increase by a \u00d7 \u0394x.

  1. Identify the Scaling Factor: Always identify the coefficient a in the function, as this is the key to determining how changes in the input unit translate to changes in the output unit.
  2. Understand the Reference Point: Pay attention to the constant b, which helps you understand the reference point for the input unit. However, for calculating the change, focus mainly on the scaling factor.
  3. Calculate the Change: Multiply the change in the input unit by the scaling factor to find the corresponding change in the output unit. This step is crucial for most of the questions.
  4. Handle Initial Values: Some questions require calculating both the initial value and the final value after the change. Start by plugging the initial input into the function to get the initial output, then apply the change calculation to find the final output.
  5. Check Your Work: After solving, verify your calculations by ensuring they make logical sense within the context of the problem. Double-check the arithmetic operations and the application of the function.

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