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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. tan t
one triangle
2 events that can't be done together.
y= +-(a/b) (x-h) + k
sin t/ cos t

2. Asymptote of hyperbola that opens left and right.
center - p
y= +-(b/a) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
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

3. Transverse Axis
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
Two Triangles
Length of one vertex to the other 2a

4. Inverse of 2X2 matrix
Given an m x n matrix A - its transpose is the n x m
1/ sin t
= 1 + tan2 t
_ _ 1/detA * | d -b | |-c a | - -

5. Law of Sines
c^2 = a^2 + b^2
2b²/a
nCr= (n!)/((n-r)! r!)
sinA/a=sinB/b=sinC/c

6. If A is acute a > h
= 1 + tan2 t
cos t/ sin t
one triangle
y= +-(a/b) (x-h) + k

7. If A is obtuse a=< b
y= +-(a/b) (x-h) + k
No triangle
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
2p

8. 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
n(A u B0 = n(A) + n(B) - n(A n B)
the shortest axis of an ellipse 2b
y= +-(b/a) (x-h) + k

9. Permutation Formula
nPr= (n!)/(n-r)!
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
sinA/a=sinB/b=sinC/c
2p

10. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
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
ratio

11. Mutually Exclusive

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12. Focal Width
1
c^2 = a^2 - b^2
4p
1/ cos t

13. Law of Cosines
c²=a²+b²-2abcosC
order Doesn't Matter
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
Multiply Row By Column - Columns of first must be equal to rows of second

14. If A is obtuse a> b
m X N - rows by columns
_ _ 1/detA * | d -b | |-c a | - -
one triangle
sec2 t

15. Asymptote of hyperbola that opens up and down
No triangle
y= +-(a/b) (x-h) + k
sec2 t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

16. Focal Width of Ellipses
2p
= 1 + tan2 t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2b²/a

17. csc t
nCrx^n-ry^r
2 events that can't be done together.
1/ sin t
order Doesn't Matter

18. Complement Principle
one triangle
1
sin2 t + cos2 t =
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

19. Combinations

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20. Multiply Matrices
Given an m x n matrix A - its transpose is the n x m
Multiply Row By Column - Columns of first must be equal to rows of second
c²=a²+b²-2abcosC
ad - bc

21. Ellipses Conic Section
_ _ 1/detA * | d -b | |-c a | - -
1
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
c²=a²+b²-2abcosC

22. Major Axis
(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
4p
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the longest axis of an ellipse 2a

23. Binomial Theorem
(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
ad - bc
c^2 = a^2 - b^2
nCrx^n-ry^r

24. distance between focus and directrix
nPr= (n!)/(n-r)!
No triangle
2p
c^2 = a^2 - b^2

25. If A is acute a<h
(side adjacent to given angle) sin (given angle) - h = b(sina)
sin t/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second
No triangle

26. Cramer's rule
m X N - rows by columns
No triangle
y= +-(a/b) (x-h) + k
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

27. 1 + tan2 t =
sec2 t
Given an m x n matrix A - its transpose is the n x m
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 Matters

28. The Multiplication Principle
sin2 t + cos2 t =
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.
length from one covertex to the other 2b

29. Equations of Hyperbola
ratio
c²=a²+b²-2abcosC
sec2 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

30. 1=
sin2 t + cos2 t =
1
2p
Order Matters

31. If A is acute h<a<b
nCr= (n!)/((n-r)! r!)
Two Triangles
one triangle
sec2 t

32. Solving Triangle if angle is obtuse
2b²/a
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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

33. sin2 t + cos2 t =
Order Matters
c²=a²+b²-2abcosC
No triangle
1

34. Directrix
Two Triangles
nCr= (n!)/((n-r)! r!)
center - p
one triangle

35. Conjugate Axis
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
length from one covertex to the other 2b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
= 1 + tan2 t

36. Area Of a Triangle
sin2 t + cos2 t =
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
ad - bc
sin t/ cos t

37. Adding Matrices
c²=a²+b²-2abcosC
one triangle
Order Matters
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

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

39. Focus of Hyperbola
nCrx^n-ry^r
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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

40. Heron's Formula
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
(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)!

41. matrices order
m X N - rows by columns
c^2 = a^2 + b^2
1/ cos t
order Doesn't Matter

42. Transpose Matrices
Given an m x n matrix A - its transpose is the n x m
nCr= (n!)/((n-r)! r!)
the shortest axis of an ellipse 2b
_ _ 1/detA * | d -b | |-c a | - -

43. Combination Formula
the longest axis of an ellipse 2a
nCr= (n!)/((n-r)! r!)
one triangle
1/ cos t

44. h =
c^2 = a^2 - b^2
sinA/a=sinB/b=sinC/c
Multiply Row By Column - Columns of first must be equal to rows of second
(side adjacent to given angle) sin (given angle) - h = b(sina)

45. sec2 t
= 1 + tan2 t
(side adjacent to given angle) sin (given angle) - h = b(sina)
1
one triangle

46. Minor Axis
No triangle
Two Triangles
the shortest axis of an ellipse 2b
n(A u B0 = n(A) + n(B) - n(A n B)

47. cot
the shortest axis of an ellipse 2b
cos t/ sin t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
nPr= (n!)/(n-r)!

48. Inclusion Exclusion Principle
order Doesn't Matter
1
n(A u B0 = n(A) + n(B) - n(A n B)
one triangle

49. Permutations
one triangle
sin t/ cos t
2 events that can't be done together.
Order Matters

50. Focus of Parabola
Order Matters
_ _ 1/detA * | d -b | |-c a | - -
Center + P
sin t/ cos t