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Hi parents and students! This is an introduction to what you’ll be needing to know by the end of the first PreCalc semester. My courses cover all of the common core requirements (the syllabus for semester 1 is here, and semester 2 is here!) and prepare my students to think critically. Not only do I want your student to know the material in my class, I want them to succeed in all future classes and opportunities. Please try out this sample test to see what your child will be learning this semester!

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1. Identify the 30-60-90 triangle with the correctly labeled sides of “standard length”
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2. Find tan(B/2) when sinB = -2/5, 3π/2 ≤ B ≤ 2π
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3. Find cos(A/2) when cosA = -4/5, π/2 ≤ A ≤ π.
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4. Determine the domain, x-intercept, and y-intercept for y = (x + 2)/(x² – 16)
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5. Solve 2cosx – 5 + 2secx = 0.
Think of this as a quadratic! ax²+bx+c
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6. Identify the 45-45-90 triangle with the correctly labeled sides of “standard length”
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7. Use the roots and end behavior to identify the graph of [f(x) = -x⁴ + 16x²]
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8. Convert 3π/11 radians to degrees.
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9. Find the horizontal and vertical components of a force vector having an angle of depression of 13° and a magnitude of 202 lb.
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10. Find (f ○ g)(x) where [f(x) = 3x² + 1] & [g(x) = 1/(x+5)]
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11. If cosθ = -5/13 and θ is in the 3rd quadrant, find sinθ and tanθ.
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12. Two ropes are horizontally pulling on a tree The first has a magnitude of 320 newtons and the second, 560 newtons. The angle between the forces is 36°. What is the magnitude of the resultant and what angle does it make with the 560 newton force?
Parallelogram Method for adding vectors!
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13. Solve triangle ABC where a = 5, c = 12, B = 28°.
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14. Based on the graph above, what is the function at x = -2?
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15. Use a calculator to find csc(7π / 9) radians.
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16. Identify the reflection of this function across the y-axis:
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17. Identify [f(x) = (25-x²)^(1/2) – 1]
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18. Find the area of triangle ABC where A = 16°, B = 57° and a = 156.9.
Area = 1/2absinC, use Law of Sines to find your sides!
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19a. Is this a function? (Vertical Line Test)
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19b. What are the Y-intercept(s)?
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19c. What are the zeros?
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19d. f(5) =
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19e. Is the function one-to-one?
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19f. f(0) =
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19g. Increasing intervals
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19h. Decreasing Intervals
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19i. Constant Intervals
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19k. Intervals where f(x) ≥ 0
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20. Find f(-3) where f(x) = (6x – 2)/x²
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21. Find sin(A + B) where sinA = -2/5, π ≤ A ≤ 3π/2; cosB = 1/5, 3π/2 ≤ B ≤ 2π.
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22. What transformation occurs in the graph?
Start with the light gray graph, transform to the black graph.
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23. Use the table to determine if the function f(x) is even, odd, or neither.
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24. Convert 86.4781° to degrees, minutes, and seconds
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25. Identify [f(x) = (x+6)^(1/2) – 5]
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26. (secA + 1)*(secA – 1) simplifies to tan²A. What trig identity is required to prove this?
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27. A cubic contains the point (2,4), has a double root at -2, and a single root at 3. Identify the function.
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28. Give the six trig functions in terms of opp, adj, and hyp.
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