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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. Asymptote of hyperbola that opens left and right.
sin t/ cos t
y= +-(b/a) (x-h) + k
(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 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

2. Mutually Exclusive

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3. Law of Sines
nPr= (n!)/(n-r)!
sinA/a=sinB/b=sinC/c
1/ sin t
c^2 = a^2 + b^2

4. sin2 t + cos2 t =
c^2 = a^2 - b^2
2p
Length of one vertex to the other 2a
1

5. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
nPr= (n!)/(n-r)!
one triangle
cos t/ sin t

6. Inverse of 2X2 matrix
2b²/a
_ _ 1/detA * | d -b | |-c a | - -
center - p
nPr= (n!)/(n-r)!

7. Circle Conic Section
sin t/ cos t
(x-h)^2 + (y-k)^2 = r^2
n(A u B0 = n(A) + n(B) - n(A n B)
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

8. Ellipses Conic Section
1/ cos t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1
the shortest axis of an ellipse 2b

9. Cramer's rule
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.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

10. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
Given an m x n matrix A - its transpose is the n x m
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
ratio

11. tan t
Given an m x n matrix A - its transpose is the n x m
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.
sin t/ cos t
Length of one vertex to the other 2a

12. Probabilty
length from one covertex to the other 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
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 an m x n matrix A - its transpose is the n x m

13. Directrix
Order Matters
c²=a²+b²-2abcosC
center - p
ratio

14. Focal Width
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.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
4p
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

15. The Multiplication Principle
sinA/a=sinB/b=sinC/c
sin t/ cos 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.
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

16. odds:
Two Triangles
c²=a²+b²-2abcosC
c^2 = a^2 - b^2
ratio

17. If A is obtuse a=< b
No triangle
_ _ 1/detA * | d -b | |-c a | - -
sin2 t + cos2 t =
ad - bc

18. Major Axis
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Center + P
the longest axis of an ellipse 2a
the shortest axis of an ellipse 2b

19. Law of Cosines
y= +-(b/a) (x-h) + k
nCrx^n-ry^r
c²=a²+b²-2abcosC
Multiply Row By Column - Columns of first must be equal to rows of second

20. sec2 t
c²=a²+b²-2abcosC
= 1 + tan2 t
1
center - p

21. Multiply Matrices
Multiply Row By Column - Columns of first must be equal to rows of second
nPr= (n!)/(n-r)!
c^2 = a^2 - b^2
Two Triangles

22. Combination Formula
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.
nCr= (n!)/((n-r)! r!)
ad - bc
Given an m x n matrix A - its transpose is the n x m

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

24. Adding Matrices
y= +-(a/b) (x-h) + k
order Doesn't Matter
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
c²=a²+b²-2abcosC

25. Inclusion Exclusion Principle
the shortest axis of an ellipse 2b
2p
n(A u B0 = n(A) + n(B) - n(A n B)
sin2 t + cos2 t =

26. Conjugate Axis
m X N - rows by columns
length from one covertex to the other 2b
center - p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

27. If A is obtuse a> b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sinA/a=sinB/b=sinC/c
one triangle
1/ sin t

28. Transpose Matrices
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
center - p
Given an m x n matrix A - its transpose is the n x m
No triangle

29. If A is acute a > h
one triangle
ad - bc
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
m X N - rows by columns

30. distance between focus and directrix
2p
order Doesn't Matter
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

31. matrices order
m X N - rows by columns
Length of one vertex to the other 2a
Given an m x n matrix A - its transpose is the n x m
ratio

32. If A is acute h<a<b
one triangle
Two Triangles
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter

33. Equations of Hyperbola
c^2 = a^2 - b^2
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
(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

34. Area Of a Triangle
_ _ 1/detA * | d -b | |-c a | - -
y= +-(a/b) (x-h) + k
Center + P
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

35. 1 + tan2 t =
length from one covertex to the other 2b
Two Triangles
sin2 t + cos2 t =
sec2 t

36. Focal Width of Ellipses
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
2b²/a
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Order Matters

37. Binomial Theorem
the longest axis of an ellipse 2a
nCrx^n-ry^r
sin2 t + cos2 t =
No triangle

38. If A is acute a = h
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
one triangle
Multiply Row By Column - Columns of first must be equal to rows of second
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.

39. 1=
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sin2 t + cos2 t =
_ _ 1/detA * | d -b | |-c a | - -
No triangle

40. csc t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
1/ sin t
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

41. Addition Principle
1/ sin 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
one 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.

42. Permutations
one 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.
(x-h)^2 + (y-k)^2 = r^2
Order Matters

43. Permutation Formula
nPr= (n!)/(n-r)!
nCrx^n-ry^r
c^2 = a^2 - b^2
one triangle

44. h =
the longest axis of an ellipse 2a
(side adjacent to given angle) sin (given angle) - h = b(sina)
2 events that can't be done together.
nCrx^n-ry^r

45. Transverse Axis
ad - bc
order Doesn't Matter
c^2 = a^2 + b^2
Length of one vertex to the other 2a

46. Combinations

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47. sec t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
1/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second
_ _ 1/detA * | d -b | |-c a | - -

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

49. Focus of Parabola
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
one triangle
Center + P
n(A u B0 = n(A) + n(B) - n(A n B)

50. Focus of ellipses
No triangle
sec2 t
_ _ 1/detA * | d -b | |-c a | - -
c^2 = a^2 - b^2