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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. Combinations

2. Complement Principle
c^2 = a^2 - b^2
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Multiply Row By Column - Columns of first must be equal to rows of second
1/ cos t

3. 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
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
1/ cos t

4. If A is acute a > h
1/ sin 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
one triangle
(side adjacent to given angle) sin (given angle) - h = b(sina)

5. Combination Formula
sin t/ cos t
nCr= (n!)/((n-r)! r!)
2 events that can't be done together.
(x-h)^2 + (y-k)^2 = r^2

6. sin2 t + cos2 t =
2b²/a
length from one covertex to the other 2b
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

7. Minor Axis
the shortest axis of an ellipse 2b
sinA/a=sinB/b=sinC/c
sec2 t
sin t/ cos t

8. Focus of ellipses
c^2 = a^2 - b^2
Multiply Row By Column - Columns of first must be equal to rows of second
one triangle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

9. tan t
sin t/ cos t
one triangle
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

10. The Multiplication Principle
nCr= (n!)/((n-r)! r!)
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
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.
(side adjacent to given angle) sin (given angle) - h = b(sina)

11. Major Axis
the longest axis of an ellipse 2a
(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
nCr= (n!)/((n-r)! r!)
sinA/a=sinB/b=sinC/c

12. cot
c^2 = a^2 - b^2
Two Triangles
cos t/ sin t
1/ cos t

13. If A is acute h<a<b
Two Triangles
= 1 + tan2 t
_ _ 1/detA * | d -b | |-c a | - -
c²=a²+b²-2abcosC

14. Heron's Formula
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
(x-h)^2 + (y-k)^2 = r^2
one triangle

15. Focal Width
4p
ratio
Given an m x n matrix A - its transpose is the n x m
n(A u B0 = n(A) + n(B) - n(A n B)

16. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
cos t/ sin t
4p
one triangle

17. Focal Width 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
y= +-(a/b) (x-h) + k
2b²/a
Multiply Row By Column - Columns of first must be equal to rows of second

18. Focus of Hyperbola
= 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.
2b²/a
c^2 = a^2 + b^2

19. Cramer's rule
c²=a²+b²-2abcosC
cos t/ sin t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
(x-h)^2 + (y-k)^2 = r^2

20. Area Of a Triangle
ad - bc
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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

21. If A is acute a<h
Order Matters
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
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
No triangle

22. h =
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
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
(side adjacent to given angle) sin (given angle) - h = b(sina)

23. Inclusion Exclusion Principle
nCr= (n!)/((n-r)! r!)
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
n(A u B0 = n(A) + n(B) - n(A n B)
m X N - rows by columns

24. odds:
sin t/ cos t
ratio
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
one triangle

25. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
= 1 + tan2 t
No triangle
2p

26. Directrix
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
center - p
1/ cos t

27. If A is acute a = h
one triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
m X N - rows by columns
c²=a²+b²-2abcosC

28. Permutations
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Length of one vertex to the other 2a
Order Matters
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

29. sec t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
2b²/a
(x-h)^2 + (y-k)^2 = r^2
1/ cos t

30. matrices order
m X N - rows by columns
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
y= +-(b/a) (x-h) + k
cos t/ sin t

31. Inverse of 2X2 matrix
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/detA * | d -b | |-c a | - -
2p
ratio

32. Mutually Exclusive

33. Addition Principle
c^2 = a^2 - b^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
nCr= (n!)/((n-r)! 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.

34. 1=
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
sin2 t + cos2 t =
length from one covertex to the other 2b
one triangle

35. Solving Triangle if angle is obtuse
_ _ 1/detA * | d -b | |-c a | - -
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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
the longest axis of an ellipse 2a

36. If A is obtuse a=< b
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.
m X N - rows by columns
No triangle
center - p

37. Law of Sines
Given an m x n matrix A - its transpose is the n x m
length from one covertex to the other 2b
sinA/a=sinB/b=sinC/c
1

38. Circle Conic Section
nPr= (n!)/(n-r)!
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
(x-h)^2 + (y-k)^2 = r^2

39. Transverse Axis
Center + P
the shortest axis of an ellipse 2b
Length of one vertex to the other 2a
c²=a²+b²-2abcosC

40. Transpose Matrices
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
Given an m x n matrix A - its transpose is the n x m
nCr= (n!)/((n-r)! r!)
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

41. Multiply Matrices
sin t/ cos t
No triangle
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

42. Asymptote of hyperbola that opens left and right.
2b²/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
y= +-(b/a) (x-h) + k
c^2 = a^2 - b^2

43. 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
one triangle
Order Matters
2p

44. 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.
order Doesn't Matter
sec2 t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

45. Permutation Formula
nPr= (n!)/(n-r)!
nCrx^n-ry^r
sin2 t + cos2 t =
ad - bc

46. Law of Cosines
Given an m x n matrix A - its transpose is the n x m
c²=a²+b²-2abcosC
(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/detA * | d -b | |-c a | - -

47. Ellipses Conic Section
ratio
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
order Doesn't Matter
2b²/a

48. If A is obtuse a> b
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
(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
m X N - rows by columns
one triangle

49. Focus of Parabola
Center + P
m X N - rows by columns
c²=a²+b²-2abcosC
c^2 = a^2 - b^2

50. Probabilty
2 events that can't be done together.
the shortest axis of an ellipse 2b
center - p
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