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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. If A is acute a = h
_ _ 1/detA * | d -b | |-c a | - -
one triangle
y= +-(b/a) (x-h) + k
No triangle

2. sec t
1/ cos t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
nCr= (n!)/((n-r)! r!)
one triangle

3. Ellipses Conic Section
nCr= (n!)/((n-r)! r!)
cos t/ sin t
sec2 t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

4. Circle Conic Section
n(A u B0 = n(A) + n(B) - n(A n B)
the shortest axis of an ellipse 2b
(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
(x-h)^2 + (y-k)^2 = r^2

5. Asymptote of hyperbola that opens left and right.
length from one covertex to the other 2b
Given an m x n matrix A - its transpose is the n x m
y= +-(b/a) (x-h) + k
Order Matters

6. Permutations
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Two Triangles
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
Order Matters

7. Combination Formula
nCr= (n!)/((n-r)! r!)
y= +-(b/a) (x-h) + k
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.

8. Binomial Theorem
center - p
nCrx^n-ry^r
m X N - rows by columns
1/ sin t

9. Focal Width
cos t/ sin t
4p
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1/ cos t

10. Transpose Matrices
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
m X N - rows by columns
Given an m x n matrix A - its transpose is the n x m

11. sec2 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
= 1 + tan2 t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

12. matrices order
cos t/ sin t
c^2 = a^2 + b^2
the shortest axis of an ellipse 2b
m X N - rows by columns

13. Multiply Matrices
the longest axis of an ellipse 2a
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Center + P
Multiply Row By Column - Columns of first must be equal to rows of second

14. Focus of Hyperbola
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
m X N - rows by columns
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
c^2 = a^2 + b^2

15. 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)
sin t/ cos t
sinA/a=sinB/b=sinC/c

16. Determinant
ad - bc
1/ cos t
= 1 + tan2 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.

17. csc t
1/ sin t
one triangle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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

18. Inclusion Exclusion Principle
center - p
ad - bc
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.
n(A u B0 = n(A) + n(B) - n(A n B)

19. Solving Triangle if angle is obtuse
one triangle
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
the longest axis of an ellipse 2a

20. If A is acute a<h
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
No triangle
Two Triangles
nCrx^n-ry^r

21. Focal Width of Ellipses
c^2 = a^2 - b^2
nCrx^n-ry^r
(x-h)^2 + (y-k)^2 = r^2
2b²/a

22. Adding Matrices
order Doesn't Matter
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
(side adjacent to given angle) sin (given angle) - h = b(sina)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

23. Law of Cosines
ratio
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
Center + P

24. Area Of a Triangle
nCrx^n-ry^r
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
= 1 + tan2 t
m X N - rows by columns

25. Probabilty
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Center + P
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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

26. 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
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

27. If A is acute a > h
sin t/ cos t
= 1 + tan2 t
nCrx^n-ry^r
one triangle

28. Conjugate Axis
length from one covertex to the other 2b
sinA/a=sinB/b=sinC/c
Length of one vertex to the other 2a
cos t/ sin t

29. The Multiplication Principle
Length of one vertex to the other 2a
sinA/a=sinB/b=sinC/c
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.
the shortest axis of an ellipse 2b

30. Law of Sines
one triangle
sec2 t
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sinA/a=sinB/b=sinC/c

31. Permutation Formula
Two Triangles
= 1 + tan2 t
nPr= (n!)/(n-r)!
one triangle

32. Combinations

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33. Asymptote of hyperbola that opens up and down
ad - bc
one triangle
(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
y= +-(a/b) (x-h) + k

34. odds:
ratio
2p
No triangle
cos t/ sin t

35. If A is obtuse a> b
(side adjacent to given angle) sin (given angle) - h = b(sina)
one triangle
2p
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

36. Heron's Formula
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
cos t/ sin t
c²=a²+b²-2abcosC
one triangle

37. Transverse Axis
Length of one vertex to the other 2a
nCr= (n!)/((n-r)! r!)
nCrx^n-ry^r
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.

38. h =
sin2 t + cos2 t =
n(A u B0 = n(A) + n(B) - n(A n B)
nCr= (n!)/((n-r)! r!)
(side adjacent to given angle) sin (given angle) - h = b(sina)

39. Focus of Parabola
length from one covertex to the other 2b
Center + P
cos t/ sin t
4p

40. distance between focus and directrix
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Center + P
nCr= (n!)/((n-r)! r!)
2p

41. Addition Principle
center - p
y= +-(b/a) (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.
Length of one vertex to the other 2a

42. 1 + tan2 t =
2b²/a
No triangle
c²=a²+b²-2abcosC
sec2 t

43. Minor Axis
sinA/a=sinB/b=sinC/c
nCrx^n-ry^r
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the shortest axis of an ellipse 2b

44. Inverse of 2X2 matrix
= 1 + tan2 t
_ _ 1/detA * | d -b | |-c a | - -
one triangle
(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. Cramer's rule
c^2 = a^2 + b^2
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.
Center + P
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

46. sin2 t + cos2 t =
= 1 + tan2 t
2 events that can't be done together.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
1

47. tan t
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 a is always bigger term
No triangle
sin t/ cos t

48. Directrix
nCr= (n!)/((n-r)! r!)
No triangle
center - p
= 1 + tan2 t

49. If A is obtuse a=< b
No triangle
length from one covertex to the other 2b
nPr= (n!)/(n-r)!
_ _ 1/detA * | d -b | |-c a | - -

50. Equation of Parabola
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.
sin t/ cos t
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