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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. Complement Principle
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
2 events that can't be done together.
(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)

2. Equations of Hyperbola
length from one covertex to the other 2b
(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
order Doesn't Matter

3. 1 + tan2 t =
sec2 t
No triangle
Center + P
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

4. Multiply Matrices
Multiply Row By Column - Columns of first must be equal to rows of second
Given an m x n matrix A - its transpose is the n x m
one triangle
2p

5. odds:
sinA/a=sinB/b=sinC/c
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
ratio
sin t/ cos t

6. If A is acute a = h
No triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Two Triangles
one triangle

7. Major Axis
cos t/ sin t
the longest axis of an ellipse 2a
sin t/ cos t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

8. sin2 t + cos2 t =
1
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sec2 t
y= +-(b/a) (x-h) + k

9. 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.
(x-h)^2 + (y-k)^2 = r^2
1
_ _ 1/detA * | d -b | |-c a | - -

10. Solving Triangle if angle is obtuse
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
No triangle

11. Cramer's rule
one triangle
Two Triangles
Multiply Row By Column - Columns of first must be equal to rows of second
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

12. Focal Width
sinA/a=sinB/b=sinC/c
1/ cos t
center - p
4p

13. Transverse Axis
No triangle
(x-h)^2 + (y-k)^2 = r^2
Length of one vertex to the other 2a
1/ cos t

14. Mutually Exclusive

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15. Focus of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
c²=a²+b²-2abcosC
ratio
Center + P

16. sec t
one triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1/ cos t
Given an m x n matrix A - its transpose is the n x m

17. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
one triangle
Multiply Row By Column - Columns of first must be equal to rows of second
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.

18. Permutations
Center + P
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Order Matters
y= +-(b/a) (x-h) + k

19. If A is obtuse a> b
nPr= (n!)/(n-r)!
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
one triangle
sinA/a=sinB/b=sinC/c

20. Adding Matrices
1
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
c^2 = a^2 - b^2
4p

21. Binomial Theorem
Center + P
y= +-(a/b) (x-h) + k
the longest axis of an ellipse 2a
nCrx^n-ry^r

22. Heron's 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
one triangle
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
4p

23. Inclusion Exclusion Principle
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
m X N - rows by columns
No triangle

24. csc t
1/ sin t
No triangle
m X N - rows by columns
the shortest axis of an ellipse 2b

25. tan t
sin t/ cos t
(x-h)^2 + (y-k)^2 = r^2
c²=a²+b²-2abcosC
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.

26. Law of Sines
sinA/a=sinB/b=sinC/c
one triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
y= +-(b/a) (x-h) + k

27. Transpose 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
4p
Given an m x n matrix A - its transpose is the n x m
c^2 = a^2 - b^2

28. Permutation Formula
cos t/ sin t
2b²/a
nPr= (n!)/(n-r)!
m X N - rows by columns

29. Asymptote of hyperbola that opens left and right.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
the longest axis of an ellipse 2a
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2 = r^2

30. Equation of Parabola
c²=a²+b²-2abcosC
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ratio
the longest axis of an ellipse 2a

31. If A is acute a > h
No triangle
2 events that can't be done together.
one triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

32. Focus of ellipses
c^2 = a^2 - b^2
No triangle
order Doesn't Matter
Length of one vertex to the other 2a

33. Combinations

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34. Asymptote of hyperbola that opens up and down
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
y= +-(a/b) (x-h) + k
No triangle

35. Combination Formula
y= +-(a/b) (x-h) + k
Order Matters
nCr= (n!)/((n-r)! r!)
nCrx^n-ry^r

36. Focus of Hyperbola
(x-h)^2 + (y-k)^2 = r^2
Multiply Row By Column - Columns of first must be equal to rows of second
c^2 = a^2 + b^2
center - p

37. Probabilty
nCr= (n!)/((n-r)! r!)
1/ sin t
center - p
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

38. If A is obtuse a=< b
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.
No triangle
n(A u B0 = n(A) + n(B) - n(A n B)

39. Conjugate Axis
sinA/a=sinB/b=sinC/c
m X N - rows by columns
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
length from one covertex to the other 2b

40. matrices order
(x-h)^2 + (y-k)^2 = r^2
Center + P
order Doesn't Matter
m X N - rows by columns

41. cot
n(A u B0 = n(A) + n(B) - n(A n B)
cos t/ sin t
(x-h)^2 + (y-k)^2 = r^2
center - p

42. If A is acute a<h
one triangle
Two Triangles
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
No triangle

43. Addition Principle
4p
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.
2p
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

44. If A is acute h<a<b
_ _ 1/detA * | d -b | |-c a | - -
one triangle
Multiply Row By Column - Columns of first must be equal to rows of second
Two Triangles

45. Minor Axis
= 1 + tan2 t
sin2 t + cos2 t =
n(A u B0 = n(A) + n(B) - n(A n B)
the shortest axis of an ellipse 2b

46. Determinant
1/ cos t
one triangle
1/ sin t
ad - bc

47. Law of Cosines
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ad - bc
c²=a²+b²-2abcosC
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

48. Focal Width of Ellipses
m X N - rows by columns
y= +-(b/a) (x-h) + k
2b²/a
Given an m x n matrix A - its transpose is the n x m

49. 1=
length from one covertex to the other 2b
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sin2 t + cos2 t =
4p

50. 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.
sinA/a=sinB/b=sinC/c
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.
Multiply Row By Column - Columns of first must be equal to rows of second