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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. 1=
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
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
c²=a²+b²-2abcosC
sin2 t + cos2 t =

2. tan t
sin t/ cos t
c²=a²+b²-2abcosC
= 1 + tan2 t
Center + P

3. Minor Axis
m X N - rows by columns
y= +-(a/b) (x-h) + k
the shortest axis of an ellipse 2b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

4. Probabilty
c²=a²+b²-2abcosC
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
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

5. Focal Width
4p
1
y= +-(a/b) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -

6. distance between focus and directrix
1/ cos t
Length of one vertex to the other 2a
2p
ratio

7. h =
(side adjacent to given angle) sin (given angle) - h = b(sina)
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
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

8. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
one triangle
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
c^2 = a^2 - b^2

9. Heron's Formula
2p
(side adjacent to given angle) sin (given angle) - h = b(sina)
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
sinA/a=sinB/b=sinC/c

10. csc t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
y= +-(a/b) (x-h) + k
sin2 t + cos2 t =
1/ sin t

11. Complement Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
ad - bc
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

12. Focus of Hyperbola
n(A u B0 = n(A) + n(B) - n(A n B)
Multiply Row By Column - Columns of first must be equal to rows of second
sinA/a=sinB/b=sinC/c
c^2 = a^2 + b^2

13. matrices order
nCr= (n!)/((n-r)! r!)
order Doesn't Matter
m X N - rows by columns
Multiply Row By Column - Columns of first must be equal to rows of second

14. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
1/ sin t
one triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

15. If A is acute a > h
c²=a²+b²-2abcosC
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle
Center + P

16. Solving Triangle if angle is obtuse
Given an m x n matrix A - its transpose is the n x m
c^2 = a^2 + b^2
(x-h)^2 + (y-k)^2 = r^2
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

17. sin2 t + cos2 t =
1
the longest axis of an ellipse 2a
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.
c²=a²+b²-2abcosC

18. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
Given an m x n matrix A - its transpose is the n x m
cos t/ 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.

19. Major Axis
length from one covertex to the other 2b
the longest axis of an ellipse 2a
= 1 + tan2 t
Multiply Row By Column - Columns of first must be equal to rows of second

20. Law of Sines
1/ sin t
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
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

21. cot
cos t/ sin t
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

22. Multiply Matrices
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
c²=a²+b²-2abcosC
= 1 + tan2 t
Multiply Row By Column - Columns of first must be equal to rows of second

23. If A is acute a<h
Center + P
one triangle
No triangle
n(A u B0 = n(A) + n(B) - n(A n B)

24. Equation of Parabola
No triangle
2b²/a
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ad - bc

25. Combinations

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26. Focus of ellipses
ad - bc
c^2 = a^2 - b^2
the shortest axis of an ellipse 2b
2 events that can't be done together.

27. sec2 t
= 1 + tan2 t
sin2 t + cos2 t =
Multiply Row By Column - Columns of first must be equal to rows of second
the shortest axis of an ellipse 2b

28. odds:
ratio
(x-h)^2 + (y-k)^2 = r^2
c²=a²+b²-2abcosC
1/ cos t

29. Determinant
No triangle
c^2 = a^2 + b^2
ad - bc
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

30. sec t
1/ cos t
4p
sin2 t + cos2 t =
No triangle

31. Transpose Matrices
Given an m x n matrix A - its transpose is the n x m
Order Matters
length from one covertex to the other 2b
sin2 t + cos2 t =

32. If A is obtuse a=< b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2b²/a
sin2 t + cos2 t =
No triangle

33. Inclusion Exclusion Principle
nCr= (n!)/((n-r)! r!)
c²=a²+b²-2abcosC
n(A u B0 = n(A) + n(B) - n(A n B)
Given an m x n matrix A - its transpose is the n x m

34. Addition Principle
(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
c^2 = a^2 + b^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.

35. If A is obtuse a> b
cos t/ sin t
Center + P
1
one triangle

36. Focus of Parabola
one triangle
Center + P
sin t/ cos t
order Doesn't Matter

37. Focal Width of Ellipses
sin t/ cos t
2b²/a
c^2 = a^2 - b^2
ratio

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

39. Asymptote of hyperbola that opens left and right.
nCrx^n-ry^r
m X N - rows by columns
y= +-(b/a) (x-h) + k
sin t/ cos t

40. The Multiplication Principle
Length of one vertex to the other 2a
one triangle
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

41. 1 + tan2 t =
nCrx^n-ry^r
2 events that can't be done together.
c^2 = a^2 + b^2
sec2 t

42. If A is acute h<a<b
sin t/ cos t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Two Triangles
Length of one vertex to the other 2a

43. Conjugate Axis
= 1 + tan2 t
Multiply Row By Column - Columns of first must be equal to rows of second
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
length from one covertex to the other 2b

44. Transverse Axis
(side adjacent to given angle) sin (given angle) - h = b(sina)
Given an m x n matrix A - its transpose is the n x m
Length of one vertex to the other 2a
1/ cos t

45. Adding Matrices
2 events that can't be done together.
nPr= (n!)/(n-r)!
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter

46. Mutually Exclusive

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47. Directrix
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
center - p
one triangle
nPr= (n!)/(n-r)!

48. Area Of a Triangle
nCrx^n-ry^r
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.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

49. Combination Formula
ad - bc
1
Order Matters
nCr= (n!)/((n-r)! r!)

50. Equations of Hyperbola
(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
= 1 + tan2 t
Length of one vertex to the other 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