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CLEP Pre - Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Major Axis
n(A u B0 = n(A) + n(B) - n(A n B)
the longest axis of an ellipse 2a
m X N - rows by columns
If two actions are mutually exclusive and the first can be done in n1 ways and the second in n2 ways- then one action OR the other can be done in n1 + n2 ways.

2. If A is acute a<h
1
No triangle
(x-h)^2 + (y-k)^2 = r^2
2b²/a

3. Equation of Parabola
m X N - rows by columns
sec2 t
1/ cos t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

4. Law of Cosines
one triangle
If an action can be performed in n1 ways - and for each of these ways another action can be performed in n2 ways - then the two actions can be performed together in n1n2 ways.
Length of one vertex to the other 2a
c²=a²+b²-2abcosC

5. If A is obtuse a> b
length from one covertex to the other 2b
one triangle
1
(x-h)^2 - (y-k)^2/a^2 b^2 = 1 - (y-k)^2 - (x-h)^2/a^2 b^2 = 1 - a is always positive term

6. If A is acute h<a<b
m X N - rows by columns
one triangle
Two Triangles
y= +-(a/b) (x-h) + k

7. Multiply Matrices
center - p
sin2 t + cos2 t =
Multiply Row By Column - Columns of first must be equal to rows of second
y= +-(a/b) (x-h) + k

8. Focus of Hyperbola
c^2 = a^2 + b^2
2 events that can't be done together.
c²=a²+b²-2abcosC
sinA/a=sinB/b=sinC/c

9. matrices order
c²=a²+b²-2abcosC
m X N - rows by columns
1
one triangle

10. Conjugate Axis
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
2 events that can't be done together.
length from one covertex to the other 2b

11. distance between focus and directrix
2p
No triangle
1
n(A u B0 = n(A) + n(B) - n(A n B)

12. Transverse Axis
Length of one vertex to the other 2a
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
c^2 = a^2 + b^2
ad - bc

13. 1=
length from one covertex to the other 2b
sin2 t + cos2 t =
If an action can be performed in n1 ways - and for each of these ways another action can be performed in n2 ways - then the two actions can be performed together in n1n2 ways.
4p

14. Law of Sines
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sinA/a=sinB/b=sinC/c
one triangle
ratio

15. If A is obtuse a=< b
the likehood of an event happening m/n - nCr (ratio)^raised to the times desired * (ratio)^raised to the times desired - n is total r is desired
No triangle
Order Matters
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

16. Directrix
(side adjacent to given angle) sin (given angle) - h = b(sina)
center - p
one triangle
If an action can be performed in n1 ways - and for each of these ways another action can be performed in n2 ways - then the two actions can be performed together in n1n2 ways.

17. Inverse of 2X2 matrix
(side adjacent to given angle) sin (given angle) - h = b(sina)
4p
Multiply Row By Column - Columns of first must be equal to rows of second
_ _ 1/detA * | d -b | |-c a | - -

18. Adding Matrices
Center + P
No triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

19. Binomial Theorem
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2p
ratio
nCrx^n-ry^r

20. csc t
the shortest axis of an ellipse 2b
1/ sin t
m X N - rows by columns
Center + P

21. Asymptote of hyperbola that opens left and right.
y= +-(b/a) (x-h) + k
nPr= (n!)/(n-r)!
(x-h)^2 - (y-k)^2/a^2 b^2 = 1 - (y-k)^2 - (x-h)^2/a^2 b^2 = 1 - a is always positive term
_ _ 1/detA * | d -b | |-c a | - -

22. Inclusion Exclusion Principle
the shortest axis of an ellipse 2b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
n(A u B0 = n(A) + n(B) - n(A n B)
No triangle

23. Addition Principle
(x-h)^2 + (y-k)^2 = r^2
If two actions are mutually exclusive and the first can be done in n1 ways and the second in n2 ways- then one action OR the other can be done in n1 + n2 ways.
No triangle
2b²/a

24. 1 + tan2 t =
sec2 t
Two Triangles
If two actions are mutually exclusive and the first can be done in n1 ways and the second in n2 ways- then one action OR the other can be done in n1 + n2 ways.
nCr= (n!)/((n-r)! r!)

25. cot
nCr= (n!)/((n-r)! r!)
c^2 = a^2 - b^2
cos t/ sin t
_ _ 1/detA * | d -b | |-c a | - -

26. Complement Principle
one triangle
c^2 = a^2 - b^2
Center + P
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

27. sin2 t + cos2 t =
1
n(A u B0 = n(A) + n(B) - n(A n B)
Center + P
nPr= (n!)/(n-r)!

28. Solving Triangle if angle is obtuse
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
length from one covertex to the other 2b
m X N - rows by columns
Length of one vertex to the other 2a

29. If A is acute a = h
Order Matters
c^2 = a^2 + b^2
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
one triangle

30. Mutually Exclusive

31. Minor Axis
1/ sin t
one triangle
the shortest axis of an ellipse 2b
_ _ 1/detA * | d -b | |-c a | - -

32. tan t
cos t/ sin t
If an action can be performed in n1 ways - and for each of these ways another action can be performed in n2 ways - then the two actions can be performed together in n1n2 ways.
ratio
sin t/ cos t

33. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
center - p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
(x-h)^2 + (y-k)^2 = r^2

34. Permutation Formula
No triangle
c²=a²+b²-2abcosC
center - p
nPr= (n!)/(n-r)!

35. Combination Formula
nCr= (n!)/((n-r)! r!)
nCrx^n-ry^r
ad - bc
Order Matters

36. sec2 t
sec2 t
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
ratio
= 1 + tan2 t

37. h =
1/ cos t
the longest axis of an ellipse 2a
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
(side adjacent to given angle) sin (given angle) - h = b(sina)

38. Asymptote of hyperbola that opens up and down
nPr= (n!)/(n-r)!
one triangle
y= +-(a/b) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

39. Transpose Matrices
ratio
Order Matters
Given an m x n matrix A - its transpose is the n x m
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

40. Circle Conic Section
2 events that can't be done together.
2b²/a
(x-h)^2 + (y-k)^2 = r^2
If an action can be performed in n1 ways - and for each of these ways another action can be performed in n2 ways - then the two actions can be performed together in n1n2 ways.

41. If A is acute a > h
one triangle
(x-h)^2 - (y-k)^2/a^2 b^2 = 1 - (y-k)^2 - (x-h)^2/a^2 b^2 = 1 - a is always positive term
_ _ 1/detA * | d -b | |-c a | - -
2p

42. Equations of Hyperbola
cos t/ sin t
order Doesn't Matter
(x-h)^2 - (y-k)^2/a^2 b^2 = 1 - (y-k)^2 - (x-h)^2/a^2 b^2 = 1 - a is always positive term
sin t/ cos t

43. sec t
y= +-(b/a) (x-h) + k
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
order Doesn't Matter
1/ cos t

44. odds:
nCr= (n!)/((n-r)! r!)
2p
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
ratio

45. Focal Width
If two actions are mutually exclusive and the first can be done in n1 ways and the second in n2 ways- then one action OR the other can be done in n1 + n2 ways.
one triangle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
4p

46. Heron's Formula
nCrx^n-ry^r
Given three sides of a triangle you can use Herons formula to find the area of the triangle A = v(s(s-a)(s-b)(s-c)) - S = (a + b + c)/2
1
the longest axis of an ellipse 2a

47. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Two Triangles
the shortest axis of an ellipse 2b
4p

48. Combinations

49. Determinant
ad - bc
center - p
2 events that can't be done together.
ratio

50. Permutations
order Doesn't Matter
Order Matters
m X N - rows by columns
center - p