Calculus: Key Concepts, Applications, and Foundations
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1. What is the formula for the area of A = 1/2 bh
a triangle?
2. What is the formula for the circum- C = 2πr
ference of a circle?
3. What is the formula for the volume V = 4/3 πr³
of a sphere?
4. What is the formula for the volume V = πr²h
of a cylinder?
5. What is the formula for the volume V = 1/3 πr²h
of a cone?
6. What is the distance formula be- d = ((x2 - x1)² + (y2 - y1)²)
tween two points (x1, y1) and (x2,
y2)?
7. What is the midpoint formula for Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
two points (x1, y1) and (x2, y2)?
8. What is the quadratic formula? x = (-b ± (b² - 4ac)) / (2a)
9. What is the slope-intercept form of y = mx + b
a linear equation?
10. What is the point-slope form of a y - y1 = m(x - x1)
linear equation?
, Calculus: Key Concepts, Applications, and Foundations
Study online at https://quizlet.com/_j5fxwc
11. What is the Law of Sines? a/sin(A) = b/sin(B) = c/sin(C)
12. What is the Law of Cosines? c² = a² + b² - 2ab * cos(C)
13. What is the formula for the area of A = 1/2 r²θ (in radians)
a sector of a circle?
14. What is the formula for the area of A = πr²
a circle?
15. What is the relationship between sin(θ) = cos(90° - θ)
sine and cosine for complementary
angles?
16. What is the double angle formula sin(2x) = 2sin(x)cos(x)
for sine?
17. What is the double angle formula cos(2x) = cos²(x) - sin²(x)
for cosine?
18. What is the definition of tangent in tan(θ) = opposite/adjacent
a right triangle?
19. What is the definition of cotangent cot(θ) = adjacent/opposite
in a right triangle?
20. What is the formula for the area of A = length × width
a rectangle?
21. What is the formula for the area of A = base × height
a parallelogram?
22. What is the formula for the area of A = 1/2 (b1 + b2)h
a trapezoid?
, Calculus: Key Concepts, Applications, and Foundations
Study online at https://quizlet.com/_j5fxwc
23. What is the formula for the volume V = length × width × height
of a rectangular prism?
24. What is the relationship between 1 : 3 : 2 (short leg : long leg : hypotenuse)
the sides of a 30-60-90 triangle?
25. What is the relationship between 1 : 1 : 2 (legs : hypotenuse)
the sides of a 45-45-90 triangle?
26. What is the formula for the surface A = 4πr²
area of a sphere?
27. What is a function? A relation that assigns exactly one output for each
input.
28. What are the four ways to represent Graphically, numerically, analytically, and verbally.
a function?
29. What is a mathematical model? A representation of a system using mathematical con-
cepts and language.
30. What are exponential functions? Functions of the form f(x) = a * b^x, where b > 0 and
b `1.
31. What are inverse functions? Functions that reverse the effect of the original func-
tion.
32. What is a limit in calculus? The value that a function approaches as the input
approaches some value.
33. What is continuity? A function is continuous if there are no breaks, jumps,
or holes in its graph.
34. What is the derivative?
Study online at https://quizlet.com/_j5fxwc
1. What is the formula for the area of A = 1/2 bh
a triangle?
2. What is the formula for the circum- C = 2πr
ference of a circle?
3. What is the formula for the volume V = 4/3 πr³
of a sphere?
4. What is the formula for the volume V = πr²h
of a cylinder?
5. What is the formula for the volume V = 1/3 πr²h
of a cone?
6. What is the distance formula be- d = ((x2 - x1)² + (y2 - y1)²)
tween two points (x1, y1) and (x2,
y2)?
7. What is the midpoint formula for Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
two points (x1, y1) and (x2, y2)?
8. What is the quadratic formula? x = (-b ± (b² - 4ac)) / (2a)
9. What is the slope-intercept form of y = mx + b
a linear equation?
10. What is the point-slope form of a y - y1 = m(x - x1)
linear equation?
, Calculus: Key Concepts, Applications, and Foundations
Study online at https://quizlet.com/_j5fxwc
11. What is the Law of Sines? a/sin(A) = b/sin(B) = c/sin(C)
12. What is the Law of Cosines? c² = a² + b² - 2ab * cos(C)
13. What is the formula for the area of A = 1/2 r²θ (in radians)
a sector of a circle?
14. What is the formula for the area of A = πr²
a circle?
15. What is the relationship between sin(θ) = cos(90° - θ)
sine and cosine for complementary
angles?
16. What is the double angle formula sin(2x) = 2sin(x)cos(x)
for sine?
17. What is the double angle formula cos(2x) = cos²(x) - sin²(x)
for cosine?
18. What is the definition of tangent in tan(θ) = opposite/adjacent
a right triangle?
19. What is the definition of cotangent cot(θ) = adjacent/opposite
in a right triangle?
20. What is the formula for the area of A = length × width
a rectangle?
21. What is the formula for the area of A = base × height
a parallelogram?
22. What is the formula for the area of A = 1/2 (b1 + b2)h
a trapezoid?
, Calculus: Key Concepts, Applications, and Foundations
Study online at https://quizlet.com/_j5fxwc
23. What is the formula for the volume V = length × width × height
of a rectangular prism?
24. What is the relationship between 1 : 3 : 2 (short leg : long leg : hypotenuse)
the sides of a 30-60-90 triangle?
25. What is the relationship between 1 : 1 : 2 (legs : hypotenuse)
the sides of a 45-45-90 triangle?
26. What is the formula for the surface A = 4πr²
area of a sphere?
27. What is a function? A relation that assigns exactly one output for each
input.
28. What are the four ways to represent Graphically, numerically, analytically, and verbally.
a function?
29. What is a mathematical model? A representation of a system using mathematical con-
cepts and language.
30. What are exponential functions? Functions of the form f(x) = a * b^x, where b > 0 and
b `1.
31. What are inverse functions? Functions that reverse the effect of the original func-
tion.
32. What is a limit in calculus? The value that a function approaches as the input
approaches some value.
33. What is continuity? A function is continuous if there are no breaks, jumps,
or holes in its graph.
34. What is the derivative?
