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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. Transpose Matrices
Given an m x n matrix A - its transpose is the n x m
ad - bc
2 events that can't be done together.
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

2. Minor Axis
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2 events that can't be done together.
= 1 + tan2 t
the shortest axis of an ellipse 2b

3. Focal Width
4p
c²=a²+b²-2abcosC
2b²/a
ratio

4. Law of Cosines
sin2 t + cos2 t =
c²=a²+b²-2abcosC
(side adjacent to given angle) sin (given angle) - h = b(sina)
Order Matters

5. Combination Formula
1/ sin t
order Doesn't Matter
ratio
nCr= (n!)/((n-r)! r!)

6. Complement Principle
(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
Center + P
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

7. Major Axis
2p
the longest axis of an ellipse 2a
Multiply Row By Column - Columns of first must be equal to rows of second
Two Triangles

8. sec t
nPr= (n!)/(n-r)!
Multiply Row By Column - Columns of first must be equal to rows of second
1/ cos t
Two Triangles

9. Determinant
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
ad - bc
Two Triangles
1

10. Probabilty
4p
one triangle
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

11. If A is obtuse a> b
nPr= (n!)/(n-r)!
c^2 = a^2 + b^2
_ _ 1/detA * | d -b | |-c a | - -
one triangle

12. Multiply Matrices
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Multiply Row By Column - Columns of first must be equal to rows of second
1/ sin t
nPr= (n!)/(n-r)!

13. If A is acute a = h
cos t/ sin t
one triangle
length from one covertex to the other 2b
nCrx^n-ry^r

14. If A is acute a > h
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2p
ad - bc
one triangle

15. Heron's Formula
m X N - rows by columns
Two Triangles
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/ cos t

16. Inverse of 2X2 matrix
Length of one vertex to the other 2a
nCr= (n!)/((n-r)! r!)
cos t/ sin t
_ _ 1/detA * | d -b | |-c a | - -

17. matrices order
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2 events that can't be done together.
m X N - rows by columns

18. Transverse Axis
length from one covertex to the other 2b
Length of one vertex to the other 2a
(x-h)^2 + (y-k)^2 = r^2
the shortest axis of an ellipse 2b

19. Directrix
center - p
one triangle
nCr= (n!)/((n-r)! r!)
No triangle

20. Asymptote of hyperbola that opens left and right.
Order Matters
m X N - rows by columns
y= +-(b/a) (x-h) + k
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

21. Area Of a Triangle
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.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
ratio
1/ sin t

22. Combinations

23. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle
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

24. If A is acute h<a<b
nCrx^n-ry^r
Two Triangles
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2b²/a

25. Cramer's rule
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nPr= (n!)/(n-r)!
one triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

26. Solving Triangle if angle is obtuse
c^2 = a^2 - b^2
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.
one triangle
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

27. Permutations
nPr= (n!)/(n-r)!
Order Matters
n(A u B0 = n(A) + n(B) - n(A n B)
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

28. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
nCrx^n-ry^r
(side adjacent to given angle) sin (given angle) - h = b(sina)
_ _ 1/detA * | d -b | |-c a | - -

29. 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.
Order Matters
4p
sin t/ cos t

30. Law of Sines
sinA/a=sinB/b=sinC/c
2b²/a
nPr= (n!)/(n-r)!
length from one covertex to the other 2b

31. Binomial Theorem
cos t/ sin t
sinA/a=sinB/b=sinC/c
nCrx^n-ry^r
(x-h)^2 + (y-k)^2 = r^2

32. csc t
1/ sin t
(x-h)^2 + (y-k)^2 = r^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1

33. 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.
ratio
Order Matters
_ _ 1/detA * | d -b | |-c a | - -

34. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
No triangle
y= +-(a/b) (x-h) + k
nCrx^n-ry^r

35. sin2 t + cos2 t =
1/ cos t
one triangle
4p
1

36. Conjugate Axis
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 + tan2 t
length from one covertex to the other 2b

37. Focus of ellipses
c^2 = a^2 - b^2
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
cos t/ sin t
c^2 = a^2 + b^2

38. odds:
ratio
cos t/ sin t
(x-h)^2 + (y-k)^2 = r^2
sinA/a=sinB/b=sinC/c

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

40. 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 =
(x-h)^2 + (y-k)^2 = r^2
sec2 t

41. Circle Conic Section
sin2 t + cos2 t =
m X N - rows by columns
(x-h)^2 + (y-k)^2 = r^2
cos t/ sin t

42. Focal Width of Ellipses
sinA/a=sinB/b=sinC/c
Two Triangles
2b²/a
nCr= (n!)/((n-r)! r!)

43. Equation of Parabola
ratio
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
sin2 t + cos2 t =
sin t/ cos t

44. Equations of Hyperbola
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
(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
sec2 t

45. sec2 t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
one triangle
= 1 + tan2 t
2 events that can't be done together.

46. h =
1/ cos t
(side adjacent to given angle) sin (given angle) - h = b(sina)
(x-h)^2 + (y-k)^2 = r^2
1

47. 1 + tan2 t =
c^2 = a^2 - b^2
2p
sec2 t
ratio

48. Permutation Formula
nPr= (n!)/(n-r)!
cos t/ sin t
2p
the longest axis of an ellipse 2a

49. tan t
2p
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.
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

50. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
Two Triangles
c²=a²+b²-2abcosC
ad - bc