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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. tan t
sin t/ cos t
(side adjacent to given angle) sin (given angle) - h = b(sina)
the shortest axis of an ellipse 2b
ad - bc

2. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
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.
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

3. Minor Axis
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
the shortest axis of an ellipse 2b
m X N - rows by columns
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

4. If A is acute a > h
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
one triangle
sinA/a=sinB/b=sinC/c
nCr= (n!)/((n-r)! r!)

5. Focus of ellipses
c^2 = a^2 - b^2
1
(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

6. sec t
sin t/ cos t
1/ cos t
2 events that can't be done together.
one triangle

7. Binomial Theorem
nCrx^n-ry^r
2 events that can't be done together.
2b²/a
sec2 t

8. sin2 t + cos2 t =
_ _ 1/detA * | d -b | |-c a | - -
1
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
sin t/ cos t

9. If A is acute a = h
2b²/a
one triangle
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.

10. Heron's Formula
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
sin t/ 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

11. csc t
2 events that can't be done together.
1/ sin t
1
c²=a²+b²-2abcosC

12. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
c^2 = a^2 + b^2
2 events that can't be done together.
c^2 = a^2 - b^2

13. odds:
ratio
one triangle
the shortest axis of an ellipse 2b
2b²/a

14. Law of Cosines
Multiply Row By Column - Columns of first must be equal to rows of second
c²=a²+b²-2abcosC
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1/ sin t

15. h =
Multiply Row By Column - Columns of first must be equal to rows of second
(side adjacent to given angle) sin (given angle) - h = b(sina)
order Doesn't Matter
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

16. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
y= +-(b/a) (x-h) + k

17. 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
Given an m x n matrix A - its transpose is the n x m
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
Center + P

18. Focal Width of Ellipses
one triangle
c^2 = a^2 - b^2
the longest axis of an ellipse 2a
2b²/a

19. Asymptote of hyperbola that opens up and down
n(A u B0 = n(A) + n(B) - n(A n B)
y= +-(a/b) (x-h) + k
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.
= 1 + tan2 t

20. The Multiplication Principle
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
sin t/ cos 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.
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. Major Axis
Length of one vertex to the other 2a
sinA/a=sinB/b=sinC/c
the longest axis of an ellipse 2a
length from one covertex to the other 2b

22. 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.
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
1

23. Inclusion Exclusion Principle
1/ cos t
n(A u B0 = n(A) + n(B) - n(A n B)
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
4p

24. Combination Formula
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
c²=a²+b²-2abcosC
1/ sin t
nCr= (n!)/((n-r)! r!)

25. cot
c^2 = a^2 + b^2
cos t/ sin t
nCrx^n-ry^r
1

26. Focus of Hyperbola
c^2 = a^2 + b^2
No triangle
ad - bc
_ _ 1/detA * | d -b | |-c a | - -

27. Directrix
c²=a²+b²-2abcosC
center - p
4p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

28. Addition Principle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ratio
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)

29. Asymptote of hyperbola that opens left and right.
(x-h)^2 + (y-k)^2 = r^2
y= +-(b/a) (x-h) + k
(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
Center + P

30. 1 + tan2 t =
sec2 t
2b²/a
Center + P
y= +-(a/b) (x-h) + k

31. Complement Principle
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
= 1 + tan2 t
Order Matters
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

32. Determinant
length from one covertex to the other 2b
sin t/ cos t
(side adjacent to given angle) sin (given angle) - h = b(sina)
ad - bc

33. sec2 t
= 1 + tan2 t
center - p
Two Triangles
2b²/a

34. Law of Sines
2 events that can't be done together.
2p
sinA/a=sinB/b=sinC/c
Multiply Row By Column - Columns of first must be equal to rows of second

35. distance between focus and directrix
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2b²/a
Multiply Row By Column - Columns of first must be equal to rows of second
2p

36. Focal Width
4p
sin t/ cos t
nCrx^n-ry^r
c^2 = a^2 + b^2

37. Focus of Parabola
nCrx^n-ry^r
Center + P
4p
Multiply Row By Column - Columns of first must be equal to rows of second

38. Inverse of 2X2 matrix
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
_ _ 1/detA * | d -b | |-c a | - -
2 events that can't be done together.

39. Mutually Exclusive

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40. Combinations

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41. Circle Conic Section
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
1
(x-h)^2 + (y-k)^2 = r^2

42. Permutation Formula
sin2 t + cos2 t =
nPr= (n!)/(n-r)!
sin t/ cos t
2p

43. If A is obtuse a> b
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!)
one triangle
1

44. Transpose Matrices
1/ cos t
Two Triangles
No triangle
Given an m x n matrix A - its transpose is the n x m

45. Solving Triangle if angle is obtuse
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
(side adjacent to given angle) sin (given angle) - h = b(sina)
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

46. If A is obtuse a=< b
cos t/ sin t
sinA/a=sinB/b=sinC/c
No triangle
order Doesn't Matter

47. 1=
length from one covertex to the other 2b
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle
sin2 t + cos2 t =

48. Conjugate Axis
one triangle
length from one covertex to the other 2b
1/ sin t
= 1 + tan2 t

49. matrices order
Given an m x n matrix A - its transpose is the n x m
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
m X N - rows by columns
nCr= (n!)/((n-r)! r!)

50. If A is acute a<h
No triangle
nCrx^n-ry^r
= 1 + tan2 t
c^2 = a^2 - b^2