Unit 1 of AP Precalculus lays the groundwork for the entire course. Mastering these fundamental concepts is crucial for success. This practice test will help you identify areas where you excel and pinpoint topics needing further review. Remember, consistent practice is key!
This practice test covers common Unit 1 topics, including:
- Functions and their properties: Domain, range, even/odd functions, increasing/decreasing intervals, and function transformations.
- Algebraic manipulations: Simplifying expressions, solving equations and inequalities, working with exponents and logarithms.
- Trigonometry: Unit circle, trigonometric identities, and solving trigonometric equations.
- Analytic Geometry: Equations of lines and conic sections.
Section 1: Multiple Choice
Instructions: Choose the best answer for each question.
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What is the domain of the function f(x) = √(x - 4)? a) All real numbers b) x ≥ 4 c) x > 4 d) x ≤ 4
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If f(x) = x² - 3x + 2, what is f(-2)? a) 12 b) 0 c) -4 d) 1
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Which of the following functions is an even function? a) f(x) = x³ b) f(x) = sin(x) c) f(x) = x² d) f(x) = e^x
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What is the equation of the line passing through (2, 3) and (4, 7)? a) y = 2x - 1 b) y = x + 1 c) y = 2x + 1 d) y = x - 1
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Simplify the expression: (x³y⁻²) / (x⁻¹y⁴) a) x⁴y⁻⁶ b) x²y⁶ c) x⁴y⁶ d) x²y⁻⁶
Section 2: Free Response
Instructions: Show all your work for full credit.
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Find the domain and range of the function f(x) = 1/(x-2). Graph the function. Explain how any asymptotes affect the domain and range.
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Solve the equation: log₂(x+3) + log₂(x) = 2. Show all steps and check for extraneous solutions.
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Transform the function f(x) = x² by shifting it 3 units to the left and 2 units down. Write the equation of the transformed function. Describe the transformation in words.
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Given the equation of a circle: x² + y² - 4x + 6y - 3 = 0. Find the center and radius of the circle. Write your answer in the form (h,k), r.
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Verify the trigonometric identity: (1 + tan²θ)cos²θ = 1.
Answer Key and Solutions
(This section would include the answers and detailed solutions for each multiple-choice and free-response question. Due to the length and complexity of providing fully worked solutions, they have been omitted from this sample. A complete practice test would include them.)
Further Practice and Resources
This practice test is designed to be a starting point. Consider exploring additional resources for further practice, such as:
- Your textbook: Review the examples and exercises within your assigned textbook.
- Online resources: Numerous websites and educational platforms provide practice problems and explanations. (Note: I cannot provide specific links due to the instruction set).
- Collaborate with classmates: Study groups can be an effective way to learn from each other and solidify understanding.
By dedicating time to practice and review, you'll build a strong foundation in AP Precalculus Unit 1 and be well-prepared for success in the course. Good luck!
