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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. sec2 t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
center - p
= 1 + tan2 t
n(A u B0 = n(A) + n(B) - n(A n B)

2. Combinations

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3. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
4p
center - p

4. csc t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
ad - bc
1/ sin t
the longest axis of an ellipse 2a

5. Directrix
sinA/a=sinB/b=sinC/c
center - p
c²=a²+b²-2abcosC
c^2 = a^2 - b^2

6. Focal Width of Ellipses
2p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
y= +-(b/a) (x-h) + k
2b²/a

7. Transverse Axis
one triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2 events that can't be done together.
Length of one vertex to the other 2a

8. cot
_ _ 1/detA * | d -b | |-c a | - -
Two Triangles
cos t/ sin t
c^2 = a^2 - b^2

9. Area Of a Triangle
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
2p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
one triangle

10. Mutually Exclusive

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11. Complement Principle
Order Matters
2p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
one triangle

12. If A is acute a = h
m X N - rows by columns
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

13. Focus of Parabola
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.
Center + P
m X N - rows by columns
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

14. If A is acute a > h
y= +-(a/b) (x-h) + k
cos t/ sin t
1/ cos t
one triangle

15. sec t
y= +-(a/b) (x-h) + k
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/ cos t
c^2 = a^2 - b^2

16. Law of Cosines
c²=a²+b²-2abcosC
y= +-(b/a) (x-h) + k
2p
c^2 = a^2 + b^2

17. Adding Matrices
= 1 + tan2 t
nCr= (n!)/((n-r)! r!)
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
the longest axis of an ellipse 2a

18. If A is obtuse a=< b
the shortest axis of an ellipse 2b
sin t/ cos t
Given an m x n matrix A - its transpose is the n x m
No triangle

19. Equations of Hyperbola
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
ad - bc
ratio

20. If A is acute a<h
2p
_ _ 1/detA * | d -b | |-c a | - -
No triangle
Two Triangles

21. Permutation Formula
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nPr= (n!)/(n-r)!
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.

22. Focus of Hyperbola
the longest axis of an ellipse 2a
c^2 = a^2 + b^2
2 events that can't be done together.
4p

23. Transpose Matrices
one triangle
c²=a²+b²-2abcosC
Given an m x n matrix A - its transpose is the n x m
(side adjacent to given angle) sin (given angle) - h = b(sina)

24. Probabilty
2b²/a
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
Center + P
Order Matters

25. Law of Sines
ad - bc
sinA/a=sinB/b=sinC/c
= 1 + tan2 t
4p

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

27. Equation of Parabola
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.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1/ cos t

28. matrices order
m X N - rows by columns
length from one covertex to the other 2b
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
Multiply Row By Column - Columns of first must be equal to rows of second

29. Binomial Theorem
y= +-(a/b) (x-h) + k
nCrx^n-ry^r
Multiply Row By Column - Columns of first must be equal to rows of second
center - p

30. 1 + tan2 t =
one triangle
(x-h)^2 + (y-k)^2 = r^2
sec2 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

31. Inclusion Exclusion Principle
1/ cos t
c^2 = a^2 + b^2
n(A u B0 = n(A) + n(B) - n(A n B)
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

32. 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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
cos t/ sin t
Order Matters

33. tan t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
sin t/ cos t
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
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

34. Permutations
Given an m x n matrix A - its transpose is the n x m
Order Matters
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sinA/a=sinB/b=sinC/c

35. odds:
c²=a²+b²-2abcosC
m X N - rows by columns
ratio
No triangle

36. Asymptote of hyperbola that opens up and down
ratio
(x-h)^2 + (y-k)^2 = r^2
y= +-(a/b) (x-h) + k
sin t/ cos t

37. Addition Principle
ratio
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.
Multiply Row By Column - Columns of first must be equal to rows of second
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

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

39. The Multiplication Principle
(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
Center + P
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.
2p

40. If A is acute h<a<b
Two Triangles
Order Matters
nCrx^n-ry^r
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

41. Focal Width
4p
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
1/ sin t

42. h =
(side adjacent to given angle) sin (given angle) - h = b(sina)
(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
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
sinA/a=sinB/b=sinC/c

43. sin2 t + cos2 t =
nCr= (n!)/((n-r)! r!)
one triangle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
1

44. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
y= +-(b/a) (x-h) + k
= 1 + tan2 t
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

45. If A is obtuse a> b
= 1 + tan2 t
one triangle
1/ sin t
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.

46. Focus of ellipses
_ _ 1/detA * | d -b | |-c a | - -
c^2 = a^2 - b^2
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
the longest axis of an ellipse 2a

47. 1=
sin2 t + cos2 t =
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c^2 = a^2 + b^2
sec2 t

48. Heron's Formula
4p
order Doesn't Matter
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
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

49. Multiply Matrices
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
Order Matters
y= +-(a/b) (x-h) + k
Multiply Row By Column - Columns of first must be equal to rows of second

50. Combination Formula
y= +-(b/a) (x-h) + k
c^2 = a^2 + b^2
nCr= (n!)/((n-r)! r!)
_ _ 1/detA * | d -b | |-c a | - -