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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. Major Axis
nPr= (n!)/(n-r)!
one triangle
the longest axis of an ellipse 2a
one triangle

2. tan t
c^2 = a^2 - b^2
ad - bc
one triangle
sin t/ cos t

3. Inverse of 2X2 matrix
center - p
_ _ 1/detA * | d -b | |-c a | - -
ratio
cos t/ sin t

4. If A is acute a<h
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
nPr= (n!)/(n-r)!
No triangle
Length of one vertex to the other 2a

5. cot
n(A u B0 = n(A) + n(B) - n(A n B)
ratio
m X N - rows by columns
cos t/ sin t

6. 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.
nCr= (n!)/((n-r)! r!)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ad - bc

7. Permutations
(x-h)^2 + (y-k)^2 = r^2
nPr= (n!)/(n-r)!
Order Matters
sec2 t

8. Mutually Exclusive

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9. 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
one triangle
length from one covertex to the other 2b
ad - bc

10. Focus of Parabola
Center + P
1
cos t/ sin t
sinA/a=sinB/b=sinC/c

11. Heron's Formula
Order Matters
No triangle
one triangle
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

12. Equation of Parabola
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.
sinA/a=sinB/b=sinC/c
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Two Triangles

13. Asymptote of hyperbola that opens up and down
the shortest axis of an ellipse 2b
y= +-(a/b) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Order Matters

14. Directrix
_ _ 1/detA * | d -b | |-c a | - -
center - p
nCrx^n-ry^r
sec2 t

15. If A is obtuse a> b
(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
nCr= (n!)/((n-r)! r!)
Order Matters

16. Conjugate Axis
length from one covertex to the other 2b
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
y= +-(b/a) (x-h) + k
Given an m x n matrix A - its transpose is the n x m

17. If A is acute a > h
(x-h)^2 + (y-k)^2 = r^2
one triangle
the longest axis of an ellipse 2a
sin t/ cos t

18. Minor Axis
c^2 = a^2 + b^2
(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)
the shortest axis of an ellipse 2b

19. Circle Conic Section
y= +-(a/b) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
Center + P
(x-h)^2 + (y-k)^2 = r^2

20. 1=
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sin2 t + cos2 t =
sin t/ cos t
one triangle

21. matrices order
n(A u B0 = n(A) + n(B) - n(A n B)
Center + P
m X N - rows by columns
4p

22. distance between focus and directrix
Length of one vertex to the other 2a
No triangle
2p
c^2 = a^2 + b^2

23. Combination Formula
c^2 = a^2 + b^2
nCr= (n!)/((n-r)! r!)
Length of one vertex to the other 2a
Order Matters

24. Transverse Axis
y= +-(a/b) (x-h) + k
Length of one vertex to the other 2a
2p
the longest axis of an ellipse 2a

25. sec t
1/ cos t
m X N - rows by columns
2p
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

26. h =
Multiply Row By Column - Columns of first must be equal to rows of second
order Doesn't Matter
(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

27. Law of Cosines
1/ cos t
1
the shortest axis of an ellipse 2b
c²=a²+b²-2abcosC

28. Focus of ellipses
c^2 = a^2 - b^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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.

29. Focal Width of Ellipses
4p
2b²/a
Two Triangles
length from one covertex to the other 2b

30. Focus of Hyperbola
the longest axis of an ellipse 2a
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
No triangle
c^2 = a^2 + b^2

31. Law of Sines
m X N - rows by columns
2p
sinA/a=sinB/b=sinC/c
Multiply Row By Column - Columns of first must be equal to rows of second

32. Probabilty
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
length from one covertex to the other 2b
sin t/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second

33. odds:
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
ad - bc
nCr= (n!)/((n-r)! r!)
ratio

34. Asymptote of hyperbola that opens left and right.
y= +-(a/b) (x-h) + k
nCrx^n-ry^r
y= +-(b/a) (x-h) + k
No triangle

35. Determinant
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
ad - bc
c^2 = a^2 + b^2
ratio

36. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the shortest axis of an ellipse 2b
Length of one vertex to the other 2a
(side adjacent to given angle) sin (given angle) - h = b(sina)

37. Focal Width
Center + P
4p
ratio
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

38. Transpose Matrices
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
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.

39. Cramer's rule
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
ad - bc
Multiply Row By Column - Columns of first must be equal to rows of second

40. csc t
c^2 = a^2 - b^2
1/ sin t
ad - bc
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

41. Binomial Theorem
nPr= (n!)/(n-r)!
nCrx^n-ry^r
Length of one vertex to the other 2a
4p

42. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
one triangle
sinA/a=sinB/b=sinC/c
= 1 + tan2 t

43. If A is acute h<a<b
c^2 = a^2 + b^2
Two Triangles
2 events that can't be done together.
1

44. Area Of a Triangle
= 1 + tan2 t
No triangle
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
2p

45. Combinations

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46. sin2 t + cos2 t =
1
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Order Matters
No triangle

47. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
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
Two Triangles

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.
2 events that can't be done together.
length from one covertex to the other 2b
1

49. If A is acute a = h
c^2 = a^2 + b^2
Order Matters
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

50. Complement Principle
ratio
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2p
1