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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. Binomial Theorem
Multiply Row By Column - Columns of first must be equal to rows of second
Two Triangles
No triangle
nCrx^n-ry^r

2. Law of Sines
_ _ 1/detA * | d -b | |-c a | - -
Center + P
sinA/a=sinB/b=sinC/c
Given an m x n matrix A - its transpose is the n x m

3. Solving Triangle if angle is obtuse
Center + P
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
y= +-(b/a) (x-h) + k

4. Adding Matrices
c^2 = a^2 + b^2
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
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter

5. 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
c^2 = a^2 - b^2
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nPr= (n!)/(n-r)!

6. Asymptote of hyperbola that opens up and down
sin2 t + cos2 t =
2p
y= +-(a/b) (x-h) + k
y= +-(b/a) (x-h) + k

7. Focal Width
1
y= +-(a/b) (x-h) + k
4p
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

8. Addition Principle
n(A u B0 = n(A) + n(B) - n(A n B)
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.
No triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

9. If A is acute a<h
the longest axis of an ellipse 2a
No triangle
y= +-(a/b) (x-h) + k
sec2 t

10. Inverse of 2X2 matrix
nPr= (n!)/(n-r)!
1/ sin t
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
_ _ 1/detA * | d -b | |-c a | - -

11. 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
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
_ _ 1/detA * | d -b | |-c a | - -

12. Major Axis
c^2 = a^2 + b^2
(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
the longest axis of an ellipse 2a
one triangle

13. Permutations
_ _ 1/detA * | d -b | |-c a | - -
Order Matters
one triangle
sec2 t

14. 1 + tan2 t =
(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
one triangle
nCrx^n-ry^r

15. Focus of Hyperbola
c^2 = a^2 + b^2
one triangle
1
one triangle

16. Cramer's rule
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
sec2 t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

17. Focal Width of Ellipses
Order Matters
sin t/ cos t
2b²/a
sin2 t + cos2 t =

18. Permutation Formula
nPr= (n!)/(n-r)!
1/ sin t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2 events that can't be done together.

19. matrices order
y= +-(b/a) (x-h) + k
c^2 = a^2 + b^2
m X N - rows by columns
nCr= (n!)/((n-r)! r!)

20. cot
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
y= +-(b/a) (x-h) + k
cos t/ sin t
one triangle

21. Multiply Matrices
one triangle
No triangle
Multiply Row By Column - Columns of first must be equal to rows of second
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

22. Transverse Axis
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
one triangle
Length of one vertex to the other 2a
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.

23. If A is obtuse a=< b
No triangle
Multiply Row By Column - Columns of first must be equal to rows of second
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)

24. Combination Formula
one triangle
nCr= (n!)/((n-r)! r!)
c²=a²+b²-2abcosC
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

25. csc t
Given an m x n matrix A - its transpose is the n x m
Order Matters
1/ sin t
ad - bc

26. Conjugate Axis
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
Order Matters
length from one covertex to the other 2b
nCr= (n!)/((n-r)! r!)

27. Combinations

28. If A is acute a > h
Length of one vertex to the other 2a
sin t/ cos t
one triangle
nCr= (n!)/((n-r)! r!)

29. 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)
1/ sin t
y= +-(b/a) (x-h) + k

30. 1=
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Order Matters
= 1 + tan2 t
sin2 t + cos2 t =

31. 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.
length from one covertex to the other 2b
= 1 + tan2 t
No triangle

32. Focus of Parabola
Multiply Row By Column - Columns of first must be equal to rows of second
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
Center + P

33. distance between focus and directrix
2p
Given an m x n matrix A - its transpose is the n x m
2 events that can't be done together.
= 1 + tan2 t

34. Circle Conic Section
cos t/ sin t
nCr= (n!)/((n-r)! r!)
(x-h)^2 + (y-k)^2 = r^2
ad - bc

35. Transpose Matrices
nPr= (n!)/(n-r)!
_ _ 1/detA * | d -b | |-c a | - -
Order Matters
Given an m x n matrix A - its transpose is the n x m

36. Directrix
Two Triangles
= 1 + tan2 t
center - p
nPr= (n!)/(n-r)!

37. Ellipses Conic Section
1
2 events that can't be done together.
ad - bc
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

38. tan t
Order Matters
sec2 t
y= +-(a/b) (x-h) + k
sin t/ cos t

39. Minor Axis
No triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
the shortest axis of an ellipse 2b
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

40. Complement Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
one triangle
y= +-(b/a) (x-h) + k
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

41. h =
nCrx^n-ry^r
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
(side adjacent to given angle) sin (given angle) - h = b(sina)

42. Mutually Exclusive

43. Heron's Formula
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.
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
Two Triangles

44. If A is acute h<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
nPr= (n!)/(n-r)!
Two Triangles
sinA/a=sinB/b=sinC/c

45. If A is obtuse a> b
one triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nCr= (n!)/((n-r)! r!)
center - p

46. Determinant
center - p
Center + P
ad - bc
_ _ 1/detA * | d -b | |-c a | - -

47. sin2 t + cos2 t =
one triangle
nPr= (n!)/(n-r)!
1
4p

48. The Multiplication Principle
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
one triangle
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.
n(A u B0 = n(A) + n(B) - n(A n B)

49. If A is acute a = h
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
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.
_ _ 1/detA * | d -b | |-c a | - -
one triangle

50. Asymptote of hyperbola that opens left and right.
the shortest axis of an ellipse 2b
No triangle
y= +-(b/a) (x-h) + k
Order Matters