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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 + tan2 t =
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
y= +-(a/b) (x-h) + k
sec2 t
nPr= (n!)/(n-r)!

2. distance between focus and directrix
2p
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
n(A u B0 = n(A) + n(B) - n(A n B)
y= +-(b/a) (x-h) + k

3. If A is acute a > h
c^2 = a^2 + b^2
Two Triangles
4p
one triangle

4. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sec2 t
nCrx^n-ry^r

5. Equation of Parabola
one triangle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
y= +-(a/b) (x-h) + k

6. sin2 t + cos2 t =
1
nCrx^n-ry^r
Center + P
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

7. cot
cos t/ sin t
Center + P
Multiply Row By Column - Columns of first must be equal to rows of second
ad - bc

8. Combination Formula
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
nCrx^n-ry^r
y= +-(a/b) (x-h) + k

9. odds:
nCrx^n-ry^r
Center + P
ratio
the longest axis of an ellipse 2a

10. Directrix
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)
the shortest axis of an ellipse 2b
center - p

11. Focus of Parabola
y= +-(a/b) (x-h) + k
Center + P
ratio
(side adjacent to given angle) sin (given angle) - h = b(sina)

12. Permutation Formula
= 1 + tan2 t
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nPr= (n!)/(n-r)!

13. 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/ cos t
2 events that can't be done together.
(side adjacent to given angle) sin (given angle) - h = b(sina)

14. 1=
sin2 t + cos2 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
sin t/ cos t
cos t/ sin t

15. Solving Triangle if angle is obtuse
sin2 t + cos2 t =
length from one covertex to the other 2b
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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

16. Focal Width
No triangle
4p
one triangle
the shortest axis of an ellipse 2b

17. Cramer's rule
2b²/a
one triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
m X N - rows by columns

18. 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.
No triangle
length from one covertex to the other 2b
the shortest axis of an ellipse 2b

19. Inclusion Exclusion Principle
1/ cos t
c²=a²+b²-2abcosC
sec2 t
n(A u B0 = n(A) + n(B) - n(A n B)

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

21. sec2 t
= 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.
nPr= (n!)/(n-r)!
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

22. Combinations

23. Law of Sines
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
y= +-(a/b) (x-h) + k
Multiply Row By Column - Columns of first must be equal to rows of second

24. Mutually Exclusive

25. Complement Principle
= 1 + tan2 t
c^2 = a^2 - b^2
(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)

26. Focus of Hyperbola
c^2 = a^2 + b^2
Order Matters
m X N - rows by columns
2 events that can't be done together.

27. If A is obtuse a> b
c^2 = a^2 - b^2
one triangle
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
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.

28. Asymptote of hyperbola that opens left and right.
ratio
the longest axis of an ellipse 2a
Two Triangles
y= +-(b/a) (x-h) + k

29. If A is obtuse a=< b
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
No triangle
(side adjacent to given angle) sin (given angle) - h = b(sina)
cos t/ sin t

30. Transpose Matrices
sinA/a=sinB/b=sinC/c
y= +-(a/b) (x-h) + k
Given an m x n matrix A - its transpose is the n x m
n(A u B0 = n(A) + n(B) - n(A n B)

31. The Multiplication Principle
1
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.
c²=a²+b²-2abcosC

32. csc t
1/ sin t
No triangle
c^2 = a^2 - b^2
2b²/a

33. matrices order
sin t/ cos t
y= +-(a/b) (x-h) + k
m X N - rows by columns
sinA/a=sinB/b=sinC/c

34. Addition Principle
c^2 = a^2 + b^2
(side adjacent to given angle) sin (given angle) - h = b(sina)
one triangle
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. Conjugate Axis
No triangle
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 longest axis of an ellipse 2a
length from one covertex to the other 2b

36. Adding Matrices
(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
Length of one vertex to the other 2a
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
No triangle

37. Focal Width of Ellipses
2b²/a
Center + P
= 1 + tan2 t
nCrx^n-ry^r

38. Binomial Theorem
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
nCrx^n-ry^r
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
ratio

39. Multiply Matrices
Multiply Row By Column - Columns of first must be equal to rows of second
1
cos t/ sin t
c^2 = a^2 + b^2

40. Ellipses Conic Section
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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
1/ sin t

41. If A is acute h<a<b
ratio
Two Triangles
_ _ 1/detA * | d -b | |-c a | - -
the longest axis of an ellipse 2a

42. Minor Axis
the shortest axis of an ellipse 2b
1
Given an m x n matrix A - its transpose is the n x m
sin2 t + cos2 t =

43. Transverse Axis
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Two Triangles
Length of one vertex to the other 2a
one triangle

44. Major Axis
No triangle
_ _ 1/detA * | d -b | |-c a | - -
nCr= (n!)/((n-r)! r!)
the longest axis of an ellipse 2a

45. Law of Cosines
c²=a²+b²-2abcosC
sin2 t + cos2 t =
1/ sin t
nPr= (n!)/(n-r)!

46. Heron's Formula
No triangle
c²=a²+b²-2abcosC
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
Two Triangles

47. tan t
Multiply Row By Column - Columns of first must be equal to rows of second
sin t/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Length of one vertex to the other 2a

48. If A is acute a = h
(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)
sec2 t
one triangle

49. h =
2 events that can't be done together.
(side adjacent to given angle) sin (given angle) - h = b(sina)
length from one covertex to the other 2b
2b²/a

50. Determinant
2 events that can't be done together.
c²=a²+b²-2abcosC
ad - bc
cos t/ sin t