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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. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
the longest axis of an ellipse 2a
nCr= (n!)/((n-r)! r!)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

2. Asymptote of hyperbola that opens left and right.
y= +-(b/a) (x-h) + k
nCrx^n-ry^r
Center + P
(side adjacent to given angle) sin (given angle) - h = b(sina)

3. If A is acute h<a<b
nPr= (n!)/(n-r)!
= 1 + tan2 t
Two Triangles
the shortest axis of an ellipse 2b

4. Complement Principle
nCr= (n!)/((n-r)! r!)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
1/ sin t
order Doesn't Matter

5. Area Of a Triangle
Given an m x n matrix A - its transpose is the n x m
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
No triangle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

6. Equations of Hyperbola
Multiply Row By Column - Columns of first must be equal to rows of second
sinA/a=sinB/b=sinC/c
nCr= (n!)/((n-r)! 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

7. Adding Matrices
y= +-(a/b) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
c²=a²+b²-2abcosC
m X N - rows by columns

8. Permutations
Order Matters
y= +-(b/a) (x-h) + k
= 1 + tan2 t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

9. Binomial Theorem
nCrx^n-ry^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.
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
nCr= (n!)/((n-r)! r!)

10. If A is acute a > h
Multiply Row By Column - Columns of first must be equal to rows of second
sec2 t
2p
one triangle

11. Focal Width of Ellipses
= 1 + tan2 t
one triangle
cos t/ sin t
2b²/a

12. sin2 t + cos2 t =
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
1
the longest axis of an ellipse 2a

13. Addition Principle
(side adjacent to given angle) sin (given angle) - h = b(sina)
= 1 + tan2 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.
one triangle

14. Major Axis
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
nPr= (n!)/(n-r)!
the longest axis of an ellipse 2a

15. Focus of Parabola
sec2 t
Center + P
c^2 = a^2 + b^2
No triangle

16. Solving Triangle if angle is obtuse
nPr= (n!)/(n-r)!
Center + P
Order Matters
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

17. Transverse Axis
4p
Length of one vertex to the other 2a
sinA/a=sinB/b=sinC/c
1

18. Equation of Parabola
Multiply Row By Column - Columns of first must be equal to rows of second
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Center + P
center - p

19. Focus of ellipses
nCr= (n!)/((n-r)! r!)
c^2 = a^2 - b^2
c^2 = a^2 + b^2
Order Matters

20. csc 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
1
nCr= (n!)/((n-r)! r!)
1/ sin t

21. Combinations

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22. Conjugate Axis
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
length from one covertex to the other 2b
sec2 t
= 1 + tan2 t

23. 1=
y= +-(b/a) (x-h) + k
sin2 t + cos2 t =
Multiply Row By Column - Columns of first must be equal to rows of second
Two Triangles

24. Inclusion Exclusion Principle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Center + P
= 1 + tan2 t
n(A u B0 = n(A) + n(B) - n(A n B)

25. sec2 t
Center + P
= 1 + tan2 t
sec2 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

26. Directrix
sinA/a=sinB/b=sinC/c
1/ cos t
ratio
center - p

27. matrices order
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ratio
Given an m x n matrix A - its transpose is the n x m
m X N - rows by columns

28. tan t
No triangle
= 1 + tan2 t
sec2 t
sin t/ cos t

29. The Multiplication Principle
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.
nCr= (n!)/((n-r)! r!)
sin2 t + cos2 t =
m X N - rows by columns

30. Transpose Matrices
nCr= (n!)/((n-r)! r!)
Given an m x n matrix A - its transpose is the n x m
Length of one vertex to the other 2a
ratio

31. Law of Cosines
y= +-(a/b) (x-h) + k
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
c²=a²+b²-2abcosC
one triangle

32. Determinant
Multiply Row By Column - Columns of first must be equal to rows of second
c^2 = a^2 - b^2
2p
ad - bc

33. Focal Width
Given an m x n matrix A - its transpose is the n x m
4p
c^2 = a^2 - b^2
2 events that can't be done together.

34. distance between focus and directrix
m X N - rows by columns
y= +-(a/b) (x-h) + k
2p
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.

35. odds:
ratio
sin t/ cos t
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
2p

36. If A is acute a = h
one triangle
Two Triangles
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

37. Circle Conic Section
m X N - rows by columns
(x-h)^2 + (y-k)^2 = r^2
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
cos t/ sin t

38. cot
Order Matters
cos t/ sin t
2p
1/ cos t

39. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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/detA * | d -b | |-c a | - -

40. If A is acute a<h
No triangle
sin t/ cos t
order Doesn't Matter
1

41. Combination Formula
sinA/a=sinB/b=sinC/c
the shortest axis of an ellipse 2b
nCr= (n!)/((n-r)! r!)
No triangle

42. Mutually Exclusive

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43. Probabilty
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
= 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

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

45. Permutation Formula
= 1 + tan2 t
nPr= (n!)/(n-r)!
length from one covertex to the other 2b
Length of one vertex to the other 2a

46. If A is obtuse a=< b
1/ cos t
No triangle
nCrx^n-ry^r
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

47. h =
Multiply Row By Column - Columns of first must be equal to rows of second
(side adjacent to given angle) sin (given angle) - h = b(sina)
(x-h)^2 + (y-k)^2 = r^2
c^2 = a^2 + b^2

48. Minor Axis
the shortest axis of an ellipse 2b
one triangle
1/ 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

49. Cramer's rule
the shortest axis of an ellipse 2b
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
m X N - rows by columns
c^2 = a^2 - b^2

50. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Given an m x n matrix A - its transpose is the n x m
Order Matters
(side adjacent to given angle) sin (given angle) - h = b(sina)