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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. If A is acute h<a<b
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.
Two Triangles
y= +-(b/a) (x-h) + k
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

2. Transverse Axis
ratio
Length of one vertex to the other 2a
sin t/ cos t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

3. Directrix
nPr= (n!)/(n-r)!
center - p
2 events that can't be done together.
cos t/ sin t

4. tan t
n(A u B0 = n(A) + n(B) - n(A n B)
cos t/ sin t
Center + P
sin t/ cos t

5. Minor Axis
the shortest axis of an ellipse 2b
No triangle
y= +-(a/b) (x-h) + k
one triangle

6. Inverse of 2X2 matrix
2b²/a
1/ 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.
_ _ 1/detA * | d -b | |-c a | - -

7. Focus of Parabola
nCr= (n!)/((n-r)! r!)
c²=a²+b²-2abcosC
Center + P
No triangle

8. If A is obtuse a=< b
nCr= (n!)/((n-r)! r!)
No triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sin t/ cos t

9. Permutation Formula
the longest axis of an ellipse 2a
c^2 = a^2 + b^2
nPr= (n!)/(n-r)!
m X N - rows by columns

10. Addition Principle
No triangle
Length of one vertex to the other 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.

11. Permutations
c^2 = a^2 + b^2
2p
Order Matters
c²=a²+b²-2abcosC

12. Asymptote of hyperbola that opens left and right.
No triangle
y= +-(b/a) (x-h) + k
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
the longest axis of an ellipse 2a

13. Equation of Parabola
sin2 t + cos2 t =
2b²/a
Order Matters
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

14. Binomial Theorem
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
nCrx^n-ry^r
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
order Doesn't Matter

15. Conjugate Axis
length from one covertex to the other 2b
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
sec2 t

16. sec2 t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
= 1 + tan2 t
ratio

17. distance between focus and directrix
sinA/a=sinB/b=sinC/c
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
2p
1/ cos t

18. If A is acute a = h
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nPr= (n!)/(n-r)!
sinA/a=sinB/b=sinC/c
one triangle

19. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
1/ sin t
4p
= 1 + tan2 t

20. Combinations

21. Inclusion Exclusion Principle
sin2 t + cos2 t =
2p
length from one covertex to the other 2b
n(A u B0 = n(A) + n(B) - n(A n B)

22. 1=
sin2 t + cos2 t =
(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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)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.

23. cot
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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.
_ _ 1/detA * | d -b | |-c a | - -

24. Law of Cosines
(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
Order Matters
(side adjacent to given angle) sin (given angle) - h = b(sina)
c²=a²+b²-2abcosC

25. Probabilty
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
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
n(A u B0 = n(A) + n(B) - n(A n B)
the shortest axis of an ellipse 2b

26. Major Axis
the longest axis of an ellipse 2a
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 + tan2 t
(x-h)^2 + (y-k)^2 = r^2

27. Adding Matrices
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1/ sin t
n(A u B0 = n(A) + n(B) - n(A n B)

28. csc t
1/ cos t
1/ sin t
one triangle
the longest axis of an ellipse 2a

29. If A is obtuse a> b
(x-h)^2 + (y-k)^2 = r^2
2 events that can't be done together.
one triangle
nCr= (n!)/((n-r)! r!)

30. Law of Sines
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Multiply Row By Column - Columns of first must be equal to rows of second
sinA/a=sinB/b=sinC/c
1/ sin t

31. sin2 t + cos2 t =
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
1/ sin t
1
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.

32. Mutually Exclusive

33. Equations of Hyperbola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Order Matters
(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
one triangle

34. h =
No triangle
2p
(side adjacent to given angle) sin (given angle) - h = b(sina)
the longest axis of an ellipse 2a

35. The Multiplication Principle
sinA/a=sinB/b=sinC/c
length from one covertex to the other 2b
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.
sec2 t

36. Area Of a Triangle
= 1 + tan2 t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Given an m x n matrix A - its transpose is the n x m
(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

37. Combination Formula
sin2 t + cos2 t =
nCr= (n!)/((n-r)! r!)
1/ cos t
y= +-(a/b) (x-h) + k

38. If A is acute a<h
No triangle
sin2 t + cos2 t =
Given an m x n matrix A - its transpose is the n x m
4p

39. Complement Principle
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.
4p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

40. odds:
one triangle
ratio
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.
m X N - rows by columns

41. Focus of ellipses
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.
Center + P
c^2 = a^2 - b^2
the longest axis of an ellipse 2a

42. Focal Width of Ellipses
= 1 + tan2 t
2b²/a
one triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

43. Focus of Hyperbola
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.
c^2 = a^2 + b^2
sec2 t
Length of one vertex to the other 2a

44. Focal Width
cos t/ sin t
4p
c^2 = a^2 - b^2
sin t/ cos t

45. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
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
Center + P
y= +-(a/b) (x-h) + k

46. Solving Triangle if angle is obtuse
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
1/ sin t
Order Matters

47. Multiply Matrices
sec2 t
one triangle
Multiply Row By Column - Columns of first must be equal to rows of second
No triangle

48. Transpose Matrices
(side adjacent to given angle) sin (given angle) - h = b(sina)
ad - bc
2b²/a
Given an m x n matrix A - its transpose is the n x m

49. Circle Conic Section
sin t/ cos t
the shortest axis of an ellipse 2b
(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.

50. 1 + tan2 t =
nPr= (n!)/(n-r)!
center - p
Center + P
sec2 t