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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. h =
y= +-(b/a) (x-h) + k
(side adjacent to given angle) sin (given angle) - h = b(sina)
_ _ 1/detA * | d -b | |-c a | - -
n(A u B0 = n(A) + n(B) - n(A n B)

2. Transverse Axis
No triangle
m X N - rows by columns
2b²/a
Length of one vertex to the other 2a

3. Focal Width
Given an m x n matrix A - its transpose is the n x m
1
4p
No triangle

4. Focal Width of Ellipses
_ _ 1/detA * | d -b | |-c a | - -
cos t/ sin t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
2b²/a

5. Directrix
(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)
1/ cos t
center - p

6. Major Axis
c²=a²+b²-2abcosC
the longest axis of an ellipse 2a
one triangle
sinA/a=sinB/b=sinC/c

7. matrices order
m X N - rows by columns
length from one covertex to the other 2b
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
sec2 t

8. Cramer's rule
sec2 t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
one triangle
ad - bc

9. Mutually Exclusive

10. Transpose 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
Given an m x n matrix A - its transpose is the n x m
the longest axis of an ellipse 2a
one triangle

11. 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.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sin t/ cos t

12. Focus of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
2p
1/ sin t
Center + P

13. Inverse of 2X2 matrix
c^2 = a^2 + b^2
4p
_ _ 1/detA * | d -b | |-c a | - -
No triangle

14. Complement Principle
y= +-(a/b) (x-h) + k
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2 events that can't be done together.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

15. Law of Sines
sin t/ cos t
ratio
No triangle
sinA/a=sinB/b=sinC/c

16. Determinant
length from one covertex to the other 2b
1/ sin t
= 1 + tan2 t
ad - bc

17. sec t
ad - bc
n(A u B0 = n(A) + n(B) - n(A n B)
1/ cos t
sec2 t

18. Asymptote of hyperbola that opens left and right.
No triangle
y= +-(b/a) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

19. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
No triangle
1
4p

20. 1 + tan2 t =
one triangle
= 1 + tan2 t
sec2 t
Given an m x n matrix A - its transpose is the n x m

21. Binomial Theorem
nCrx^n-ry^r
c²=a²+b²-2abcosC
sin2 t + cos2 t =
sin t/ cos t

22. Law of Cosines
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
y= +-(a/b) (x-h) + k
c²=a²+b²-2abcosC

23. Combination Formula
nCr= (n!)/((n-r)! r!)
Length of one vertex to the other 2a
c^2 = a^2 - b^2
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

24. If A is acute h<a<b
Order Matters
2 events that can't be done together.
length from one covertex to the other 2b
Two Triangles

25. Heron's Formula
one triangle
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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.
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

26. If A is acute a<h
sec2 t
y= +-(a/b) (x-h) + k
No triangle
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

27. If A is acute a = h
m X N - rows by columns
center - p
nCrx^n-ry^r
one triangle

28. 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
2b²/a
ad - bc
sin2 t + cos2 t =

29. Addition Principle
sin t/ cos 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.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
(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

30. Permutation Formula
c^2 = a^2 - b^2
y= +-(a/b) (x-h) + k
nPr= (n!)/(n-r)!
1/ cos t

31. 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.
2b²/a
the shortest axis of an ellipse 2b
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

32. odds:
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.
ratio
length from one covertex to the other 2b
y= +-(a/b) (x-h) + k

33. Focus of Hyperbola
c^2 = a^2 + b^2
the shortest axis of an ellipse 2b
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Order Matters

34. Probabilty
one triangle
center - p
sin2 t + cos2 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

35. If A is obtuse a> b
one triangle
the longest axis of an ellipse 2a
No triangle
nCrx^n-ry^r

36. Focus of ellipses
the longest axis of an ellipse 2a
sinA/a=sinB/b=sinC/c
1
c^2 = a^2 - b^2

37. Minor Axis
(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
the shortest axis of an ellipse 2b
_ _ 1/detA * | d -b | |-c a | - -
2b²/a

38. Solving Triangle if angle is obtuse
ad - bc
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
(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
(side adjacent to given angle) sin (given angle) - h = b(sina)

39. Permutations
center - p
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Order Matters
Given an m x n matrix A - its transpose is the n x m

40. Combinations

41. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter
cos t/ sin t
No triangle

42. sin2 t + cos2 t =
Given an m x n matrix A - its transpose is the n x m
1
n(A u B0 = n(A) + n(B) - n(A n B)
= 1 + tan2 t

43. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
order Doesn't Matter
sinA/a=sinB/b=sinC/c
center - p

44. Equations of Hyperbola
y= +-(a/b) (x-h) + k
nPr= (n!)/(n-r)!
(x-h)^2 + (y-k)^2 = r^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

45. 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.
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.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
nCrx^n-ry^r

46. distance between focus and directrix
2p
y= +-(b/a) (x-h) + k
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.

47. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
ad - bc
Given an m x n matrix A - its transpose is the n x m
1

48. Conjugate Axis
ad - bc
length from one covertex to the other 2b
sinA/a=sinB/b=sinC/c
sec2 t

49. cot
cos t/ sin t
(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)
c²=a²+b²-2abcosC

50. csc t
sin2 t + cos2 t =
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
1/ sin t
1/ cos t