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CLEP Pre - Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
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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. Directrix
Given an m x n matrix A - its transpose is the n x m
y= +-(b/a) (x-h) + k
center - p
Order Matters

2. sec2 t
= 1 + tan2 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
order Doesn't Matter
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

3. If A is obtuse a=< b
No triangle
one triangle
y= +-(b/a) (x-h) + k
Center + P

4. 1 + tan2 t =
c^2 = a^2 + b^2
the shortest axis of an ellipse 2b
_ _ 1/detA * | d -b | |-c a | - -
sec2 t

5. Conjugate Axis
= 1 + tan2 t
y= +-(a/b) (x-h) + k
length from one covertex to the other 2b
ad - bc

6. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Given an m x n matrix A - its transpose is the n x m
c^2 = a^2 + b^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

7. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Order Matters
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
4p

8. Focal Width of Ellipses
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
2b²/a
(side adjacent to given angle) sin (given angle) - h = b(sina)
the longest axis of an ellipse 2a

9. Major Axis
sec2 t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
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)

10. Circle Conic Section
(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.
_ _ 1/detA * | d -b | |-c a | - -
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

11. matrices order
the shortest axis of an ellipse 2b
1/ cos t
m X N - rows by columns
(x-h)^2 + (y-k)^2 = r^2

12. tan t
one triangle
sin t/ cos t
c^2 = a^2 + b^2
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

13. sec 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/ cos t
No triangle
the shortest axis of an ellipse 2b

14. csc t
(side adjacent to given angle) sin (given angle) - h = b(sina)
nCr= (n!)/((n-r)! r!)
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.

15. If A is acute a = h
No triangle
one triangle
2 events that can't be done together.
4p

16. h =
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 a is always bigger term
(side adjacent to given angle) sin (given angle) - h = b(sina)
y= +-(b/a) (x-h) + k

17. 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
Given an m x n matrix A - its transpose is the n x m
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
1/ cos t

18. Minor Axis
ad - bc
the shortest axis of an ellipse 2b
Length of one vertex to the other 2a
4p

19. Asymptote of hyperbola that opens up and down
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
the shortest axis of an ellipse 2b
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
y= +-(a/b) (x-h) + k

20. Multiply Matrices
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
Given an m x n matrix A - its transpose is the n x m
1/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second

21. cot
the shortest axis of an ellipse 2b
Two Triangles
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
cos t/ sin t

22. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
= 1 + tan2 t
y= +-(b/a) (x-h) + k
one triangle

23. Transverse Axis
2p
= 1 + tan2 t
Length of one vertex to the other 2a
1/ cos t

24. Focus of Hyperbola
c^2 = a^2 + b^2
c^2 = a^2 - b^2
the shortest axis of an ellipse 2b
nPr= (n!)/(n-r)!

25. Permutations
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
(x-h)^2 + (y-k)^2 = r^2
Order Matters

26. Focus of ellipses
= 1 + tan2 t
(x-h)^2 + (y-k)^2 = r^2
c^2 = a^2 - b^2
Length of one vertex to the other 2a

27. Mutually Exclusive

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28. sin2 t + cos2 t =
1
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sinA/a=sinB/b=sinC/c
4p

29. If A is acute h<a<b
one triangle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
nPr= (n!)/(n-r)!
Two Triangles

30. If A is acute a > h
the longest axis of an ellipse 2a
n(A u B0 = n(A) + n(B) - n(A n B)
ad - bc
one triangle

31. Binomial Theorem
nCrx^n-ry^r
n(A u B0 = n(A) + n(B) - n(A n B)
y= +-(a/b) (x-h) + k
one triangle

32. Law of Sines
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
sin2 t + cos2 t =
sinA/a=sinB/b=sinC/c
Order Matters

33. Asymptote of hyperbola that opens left and right.
y= +-(b/a) (x-h) + k
Order Matters
(x-h)^2 + (y-k)^2 = r^2
center - p

34. Ellipses Conic Section
c^2 = a^2 - b^2
2b²/a
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
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

35. Complement Principle
y= +-(b/a) (x-h) + k
(side adjacent to given angle) sin (given angle) - h = b(sina)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
n(A u B0 = n(A) + n(B) - n(A n B)

36. The Multiplication Principle
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
2b²/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.

37. Equations of Hyperbola
4p
(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
2p
sinA/a=sinB/b=sinC/c

38. Area Of a Triangle
y= +-(a/b) (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.
sin t/ cos t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

39. Determinant
_ _ 1/detA * | d -b | |-c a | - -
Center + P
ratio
ad - bc

40. Combinations

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41. Addition 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.
y= +-(a/b) (x-h) + k
= 1 + tan2 t
4p

42. If A is obtuse a> b
one triangle
1/ cos t
4p
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.

43. 1=
m X N - rows by columns
sin2 t + cos2 t =
Two Triangles
cos t/ sin t

44. Focus of Parabola
c^2 = a^2 - b^2
nCrx^n-ry^r
nCr= (n!)/((n-r)! r!)
Center + P

45. Transpose Matrices
4p
ratio
nPr= (n!)/(n-r)!
Given an m x n matrix A - its transpose is the n x m

46. Permutation Formula
(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
nCr= (n!)/((n-r)! r!)
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nPr= (n!)/(n-r)!

47. Focal Width
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.
the shortest axis of an ellipse 2b
4p

48. Inverse of 2X2 matrix
sec2 t
y= +-(a/b) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
Multiply Row By Column - Columns of first must be equal to rows of second

49. odds:
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
ratio
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
center - p

50. If A is acute a<h
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.
the longest axis of an ellipse 2a
No triangle
1

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CLEP Pre - Calculus 2

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