Algebra 1 Concepts Review

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📊 Part 1: Relationships and Data Analysis

1. A scatterplot shows the relationship between hours of sleep and test scores. The points generally trend upward from left to right. What type of correlation does this represent?

Strong negative correlation

Strong positive correlation

No correlation

Cannot be determined

2. The line of best fit for a data set has the equation y = 3x + 5. What does the slope represent?

3. Which statements are true about correlation and causation? (Check all that apply)

Correlation always implies causation

Strong correlation suggests a relationship between variables

Causation requires additional evidence beyond correlation

No correlation means no relationship exists

4. A quadratic function has vertex at (2, -3) and opens upward. What can you conclude about this function?

The minimum value is -3

The maximum value is -3

The axis of symmetry is y = 2

The function has no real zeros

🔢 Part 2: Problem Solving and Simplification

5. Simplify: √72

6. Solve the system of equations:

2x + y = 7

x - y = 2

7. Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...

First, identify the common difference: d = _______

Using the formula a_n = a₁ + (n-1)d, the 8th term is: _______

8. Graph the inequality y ≥ 2x - 1. Describe two key features of your graph:

💭 Part 3: Critical Thinking and Communication

9. A geometric sequence has first term a₁ = 2 and common ratio r = 3. Write the formula for the nth term and find the 5th term.

Formula: a_n = ________________

5th term: a₅ = ________________

10. Compare exponential growth to linear growth. Give one real-world example of each and explain the key difference in their patterns.

11. Reflection: Choose one algebraic concept from this worksheet (scatterplots, quadratics, systems, sequences, or radicals). Explain how understanding this concept helps you analyze relationships and patterns in mathematics.