Part1: Precalculus
1. Integers: Rational Numbers
2. Circle: Center and Radius
3. 3 ? √7: 3 1√7
4. y = logb x: x = by
5. Even-Degree Polynomial: Horizontal Line Test
6. Nonorigin Point in the Plane: Polar Coordinates (r, θ ) with 0 ≤ θ < 2π
7. am: am?n
8. x = 0: log10 x
9. Degree of a Polynomial: Number of Real Roots
10. ex: ln x
11. Complex Numbers: Real Numbers
12. x2+1 : x = 1
13. y = arctan(x) + 3: y = arctan(x)
14. √ab: √a√b
15. Positive Integers: Prime Numbers and Composite Numbers
16. Polynomial Function: Asymptote
17. x2 = x: x = 1
18. Circle: Ellipse
19. (A ∩ B) ∪ (A ∩ C): A ∪ (B ∩ C)
20. log2 x: ln x
21. tan x: cot x
22. Function: Symmetric about the x-axis
Part2: Calculus
23. Rolle’s Theorem: Mean Value Theorem
24. y = cos x: y ? 1 = √3? 2 (x ? π )
25. Riemann Sum: Definite Integral
26. Critical Point: Local Extremum
27. limx→π sin x: sin x
28. Marginal Cost: Total Cost
29. limx→0 cos x: L’Hopital’s Rule
30. Differentiable : Continuous
31. Maclaurin Series : Taylor Series
32. Concave-Up Function : Minimum
33. Definite Integral : Area
34. Factorials : Polynomials
35. Addition : Arithmetic Sequence
36. 1: ln x
37. Velocity: Position
38. Taylor Polynomials: Smooth Function
39. Chain Rule: Integration by u-substitution
40. Improper Integral: Definite Integrals
41. Everywhere-Zero Derivative: Differentiable Function
42. f (xx) ?f (a): f ′(a)
43. ∞ 3 2 n: 3
44. Intermediate Value Theorem: |x| on the Interval [?2, 1]
Part3: Postcalculus
45. Dot Product: Orthogonal Vectors
46. □□2f
47. Gradient: Level Curve
48. □□2f □□2f ? а □□2f
49. Three Distinct Points: Plane in R3
50. Gradient: Directional Derivative
51. Concavity: Euler’s Method
52. Separation of Variables: Homogeneous Differential Equation
53. Switching Two Rows: Determinant
54. Matrix: Reduced Row Echelon Form
55. Eigenvalue: Eigenvector
56. Determinant: Rank
57. Matrix Multiplication: Square Matrices
58. Permutations: Determinant
59. Event: Sample Space
60. Successive, Independent Coin Flips: Probability of Heads
61. Cumulative Distribution Function: Probability Density Function
62. Geometric Distribution: Exponential Distribution
63. Eulerian Path: Graph
64. Tree: Cycle
65. Bipartite Graph: Three-Colorable
66. Planar Graph: K5 Subgraph