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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=
ratio
sin2 t + cos2 t =
one triangle
c^2 = a^2 - b^2

2. h =
cos t/ sin t
1/ sin t
(side adjacent to given angle) sin (given angle) - h = b(sina)
ratio

3. Directrix
1
2 events that can't be done together.
center - p
one triangle

4. Transverse Axis
Length of one vertex to the other 2a
Given an m x n matrix A - its transpose is the n x m
c²=a²+b²-2abcosC
length from one covertex to the other 2b

5. 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
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
Two Triangles

6. If A is acute a<h
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
y= +-(a/b) (x-h) + k
No triangle

7. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
_ _ 1/detA * | d -b | |-c a | - -
order Doesn't Matter
Multiply Row By Column - Columns of first must be equal to rows of second

8. sin2 t + cos2 t =
length from one covertex to the other 2b
one triangle
1
nCr= (n!)/((n-r)! r!)

9. Ellipses Conic Section
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.
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the shortest axis of an ellipse 2b
2 events that can't be done together.

10. Combinations

11. Major Axis
the longest axis of an ellipse 2a
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
1
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

12. If A is acute h<a<b
sec2 t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Two Triangles
(side adjacent to given angle) sin (given angle) - h = b(sina)

13. Law of Sines
nCr= (n!)/((n-r)! r!)
No triangle
sinA/a=sinB/b=sinC/c
one triangle

14. tan t
sin t/ cos t
Given an m x n matrix A - its transpose is the n x m
ratio
order Doesn't Matter

15. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
order Doesn't Matter
sinA/a=sinB/b=sinC/c
one triangle

16. cot
Multiply Row By Column - Columns of first must be equal to rows of second
1/ sin t
cos t/ sin t
ratio

17. Mutually Exclusive

18. matrices order
m X N - rows by columns
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
sin2 t + cos2 t =
ad - bc

19. Asymptote of hyperbola that opens up and down
nCr= (n!)/((n-r)! r!)
y= +-(a/b) (x-h) + k
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

20. 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
nCrx^n-ry^r
y= +-(a/b) (x-h) + k
Center + P

21. Multiply Matrices
y= +-(b/a) (x-h) + k
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
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

22. Conjugate Axis
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
length from one covertex to the other 2b
n(A u B0 = n(A) + n(B) - n(A n B)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

23. Permutation Formula
1/ sin t
nPr= (n!)/(n-r)!
ad - bc
No triangle

24. Binomial Theorem
(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 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.
nCrx^n-ry^r
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

25. Focus of Parabola
n(A u B0 = n(A) + n(B) - n(A n B)
Center + P
1/ sin 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.

26. If A is acute a > h
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
the shortest axis of an ellipse 2b
Two Triangles

27. Complement Principle
= 1 + tan2 t
one triangle
order Doesn't Matter
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

28. Cramer's rule
(side adjacent to given angle) sin (given angle) - h = b(sina)
length from one covertex to the other 2b
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= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

29. Focus of ellipses
(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
Order Matters
(x-h)^2 + (y-k)^2 = r^2
c^2 = a^2 - b^2

30. Combination Formula
y= +-(b/a) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2p
nCr= (n!)/((n-r)! r!)

31. Circle Conic Section
one triangle
(x-h)^2 + (y-k)^2 = r^2
No triangle
n(A u B0 = n(A) + n(B) - n(A n B)

32. Focus of Hyperbola
one triangle
the longest axis of an ellipse 2a
c^2 = a^2 + b^2
ratio

33. Permutations
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2p
1
Order Matters

34. sec2 t
= 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
Length of one vertex to the other 2a

35. odds:
order Doesn't Matter
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
nCr= (n!)/((n-r)! r!)
ratio

36. distance between focus and directrix
c^2 = a^2 + b^2
2p
Multiply Row By Column - Columns of first must be equal to rows of second
(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

37. Asymptote of hyperbola that opens left and right.
= 1 + tan2 t
c²=a²+b²-2abcosC
y= +-(b/a) (x-h) + k
sinA/a=sinB/b=sinC/c

38. Solving Triangle if angle is obtuse
1/ sin t
(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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

39. Probabilty
length from one covertex to the other 2b
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
c²=a²+b²-2abcosC
Order Matters

40. Law of Cosines
ad - bc
2b²/a
c²=a²+b²-2abcosC
= 1 + tan2 t

41. Adding Matrices
ad - bc
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

42. Minor Axis
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
ad - bc
the shortest axis of an ellipse 2b
Order Matters

43. Area Of a Triangle
1
2b²/a
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.

44. Heron's Formula
1/ cos 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
Two Triangles
sin2 t + cos2 t =

45. If A is obtuse a=< b
1/ sin t
No triangle
cos t/ sin t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

46. Equation of Parabola
Two Triangles
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
order Doesn't Matter
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

47. If A is acute a = h
m X N - rows by columns
ratio
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.

48. 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.
the longest axis of an ellipse 2a
one triangle
order Doesn't Matter

49. sec t
order Doesn't Matter
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
1/ cos t
c²=a²+b²-2abcosC

50. Focal Width of Ellipses
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sec2 t
c^2 = a^2 - b^2
2b²/a