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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. 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
Two Triangles
sinA/a=sinB/b=sinC/c

2. 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
(x-h)^2 + (y-k)^2 = r^2
Multiply Row By Column - Columns of first must be equal to rows of second
Two Triangles

3. Conjugate Axis
(x-h)^2 + (y-k)^2 = r^2
nCrx^n-ry^r
Multiply Row By Column - Columns of first must be equal to rows of second
length from one covertex to the other 2b

4. Cramer's rule
2p
the shortest axis of an ellipse 2b
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
_ _ 1/detA * | d -b | |-c a | - -

5. Area Of a Triangle
nCr= (n!)/((n-r)! r!)
order Doesn't Matter
Length of one vertex to the other 2a
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

6. Focus of Hyperbola
c²=a²+b²-2abcosC
Length of one vertex to the other 2a
c^2 = a^2 - b^2
c^2 = a^2 + b^2

7. Focus of Parabola
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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
Multiply Row By Column - Columns of first must be equal to rows of second
Center + P

8. Transverse Axis
Length of one vertex to the other 2a
ad - bc
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Center + P

9. If A is obtuse a=< b
No triangle
2 events that can't be done together.
Center + P
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.

10. Combinations

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11. Focal Width
order Doesn't Matter
_ _ 1/detA * | d -b | |-c a | - -
2 events that can't be done together.
4p

12. sec2 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
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
2p
= 1 + tan2 t

13. Law of Sines
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
the shortest axis of an ellipse 2b
sinA/a=sinB/b=sinC/c

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)
one triangle
y= +-(b/a) (x-h) + k
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

15. If A is acute a > h
one triangle
= 1 + tan2 t
2 events that can't be done together.
nCrx^n-ry^r

16. h =
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
No triangle
(side adjacent to given angle) sin (given angle) - h = b(sina)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

17. matrices order
n(A u B0 = n(A) + n(B) - n(A n B)
y= +-(b/a) (x-h) + k
m X N - rows by columns
ad - bc

18. Addition Principle
2b²/a
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/detA * | d -b | |-c a | - -
c²=a²+b²-2abcosC

19. If A is obtuse a> b
the shortest axis of an ellipse 2b
n(A u B0 = n(A) + n(B) - n(A n B)
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle

20. Determinant
ad - bc
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
ratio
1/ cos t

21. Minor Axis
one triangle
4p
the shortest axis of an ellipse 2b
c^2 = a^2 - b^2

22. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
center - p

23. Binomial Theorem
one triangle
nCrx^n-ry^r
Multiply Row By Column - Columns of first must be equal to rows of second
c^2 = a^2 + b^2

24. 1 + tan2 t =
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sec2 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
Center + P

25. odds:
Two Triangles
one triangle
ratio
c^2 = a^2 + b^2

26. Inclusion Exclusion Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
n(A u B0 = n(A) + n(B) - n(A n B)
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.

27. Law of Cosines
ratio
c²=a²+b²-2abcosC
one triangle
1

28. Complement Principle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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

29. Transpose Matrices
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
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.

30. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
length from one covertex to the other 2b
Order Matters
(x-h)^2 + (y-k)^2 = r^2

31. Asymptote of hyperbola that opens left and right.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1/ sin t
y= +-(b/a) (x-h) + k
sin2 t + cos2 t =

32. Focus of ellipses
ratio
c^2 = a^2 - b^2
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
2p

33. Equation of Parabola
2b²/a
ad - bc
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
sinA/a=sinB/b=sinC/c

34. If A is acute a<h
cos t/ sin t
one triangle
No triangle
order Doesn't Matter

35. Solving Triangle if angle is obtuse
nCr= (n!)/((n-r)! r!)
Multiply Row By Column - Columns of first must be equal to rows of second
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
No triangle

36. tan t
2 events that can't be done together.
No triangle
sin t/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

37. Inverse of 2X2 matrix
2 events that can't be done together.
_ _ 1/detA * | d -b | |-c a | - -
sec2 t
ratio

38. sin2 t + cos2 t =
4p
center - p
1
nCr= (n!)/((n-r)! r!)

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

40. sec t
(side adjacent to given angle) sin (given angle) - h = b(sina)
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
1/ cos t

41. Directrix
nCrx^n-ry^r
1
center - p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

42. Permutations
Length of one vertex to the other 2a
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
one triangle

43. csc t
Given an m x n matrix A - its transpose is the n x m
c²=a²+b²-2abcosC
nCrx^n-ry^r
1/ sin t

44. Major Axis
the longest axis of an ellipse 2a
No triangle
one triangle
Two Triangles

45. Multiply Matrices
y= +-(a/b) (x-h) + k
center - p
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.
Multiply Row By Column - Columns of first must be equal to rows of second

46. Adding Matrices
y= +-(a/b) (x-h) + k
the longest axis of an ellipse 2a
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

47. Ellipses Conic Section
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.
Two Triangles
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nPr= (n!)/(n-r)!

48. 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
1/ cos t
c²=a²+b²-2abcosC
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.

49. If A is acute h<a<b
sin2 t + cos2 t =
Two Triangles
order Doesn't Matter
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

50. 1=
sin2 t + cos2 t =
c²=a²+b²-2abcosC
center - p
Multiply Row By Column - Columns of first must be equal to rows of second