EOC Warm-Up Quiz

Instructions: Answer the following questions to the best of your ability. Show your work!

1. Algebra: Solving Equations
   Solve for x:
   3x - 7 = 14
   
   
   
   
   
   
   

2. Functions: Identifying a Function
   Is the following set of ordered pairs a function? Explain why or why not.
   {(1, 2), (2, 4), (3, 6), (1, 5)}
   
   
   
   
   
   
   

3. Statistics: Interpreting Scatter Plots
   Describe the correlation shown in a scatter plot where as the x values increase, the y values generally decrease.
   
   
   
   

EOC Quick Check Answer Key

Question 1: Which of the following equations represents a linear function?

Correct Answer: C) y = 5x - 4

Thought Process:

• A linear function has a constant rate of change and its graph is a straight line. The equation for a linear function can typically be written in the form y = mx + b.
• A) y = x² + 3 is a quadratic function (parabola).
• B) y = 2ˣ is an exponential function.
• C) y = 5x - 4 is in the form y = mx + b where m=5 and b=-4, making it a linear function.
• D) y = |x| is an absolute value function (V-shape).

Question 2: Solve the system of equations:

y = 2x + 1
x + y = 10

Correct Answer: x = 3, y = 7

Thought Process:

1. Substitution Method: Since the first equation is already solved for y, substitute (2x + 1) for y in the second equation.
   x + (2x + 1) = 10
2. Solve for x: Combine like terms and solve the resulting equation.
   3x + 1 = 10
3x = 9
x = 3
3. Solve for y: Substitute the value of x back into either original equation. Using y = 2x + 1:
   y = 2(3) + 1
y = 6 + 1
y = 7
4. Check: Verify the solution by substituting both x and y values into the second equation:
   3 + 7 = 10 (True)

Question 3: What is the domain of the function f(x) = sqrt(x - 4)?

Correct Answer: C) x >= 4

Thought Process:

• The domain of a function refers to all possible input values (x-values) for which the function is defined.
• For a square root function, the expression under the square root symbol cannot be negative, as we cannot take the square root of a negative number in the real number system.
• Therefore, x - 4 must be greater than or equal to 0.
• x - 4 >= 0
• Add 4 to both sides: x >= 4
• This means x must be 4 or any number greater than 4.

Question 4: A scatter plot shows a strong positive correlation between the number of hours studied and test scores. Does this imply that studying causes higher test scores? Explain your reasoning.

Correct Answer: No, correlation does not imply causation.

Thought Process:

• Correlation indicates a relationship or association between two variables. A strong positive correlation means that as one variable increases, the other tends to increase as well.
• Causation means that one event is the result of the occurrence of the other event; i.e., there is a cause-and-effect relationship.
• While there is a strong correlation between studying and test scores, we cannot definitively say that studying causes higher test scores based solely on correlation. There could be other factors involved (confounding variables) that influence both, such as a student's natural aptitude, prior knowledge, good nutrition, or effective test-taking strategies. While studying is likely a significant contributing factor, correlation alone isn't enough to prove direct causation.