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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. Combinations

2. If A is obtuse a=< b
Given an m x n matrix A - its transpose is the n x m
center - p
c^2 = a^2 + b^2
No triangle

3. Complement Principle
_ _ 1/detA * | d -b | |-c a | - -
1/ cos t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
one triangle

4. Equations of Hyperbola
y= +-(a/b) (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
No triangle
Center + P

5. csc t
2 events that can't be done together.
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/ sin t
4p

6. Major Axis
the longest axis of an ellipse 2a
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
1/ sin t
y= +-(a/b) (x-h) + k

7. If A is acute h<a<b
(side adjacent to given angle) sin (given angle) - h = b(sina)
cos t/ sin t
nCrx^n-ry^r
Two Triangles

8. 1=
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sin2 t + cos2 t =
Center + P
n(A u B0 = n(A) + n(B) - n(A n B)

9. If A is acute a = h
y= +-(b/a) (x-h) + k
Order Matters
one triangle
c²=a²+b²-2abcosC

10. Transpose Matrices
Given an m x n matrix A - its transpose is the n x m
= 1 + tan2 t
cos t/ sin t
ad - bc

11. Asymptote of hyperbola that opens left and right.
the shortest axis of an ellipse 2b
center - p
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

12. Combination Formula
nCr= (n!)/((n-r)! r!)
ad - bc
c^2 = a^2 - b^2
c²=a²+b²-2abcosC

13. Permutations
(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
Order Matters
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
sec2 t

14. 1 + tan2 t =
sec2 t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Center + P
c^2 = a^2 - b^2

15. Area Of a Triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
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
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

16. Ellipses Conic Section
sec2 t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Two Triangles
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

17. 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.
(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
center - p
one triangle

18. h =
1/ cos t
2p
c^2 = a^2 + b^2
(side adjacent to given angle) sin (given angle) - h = b(sina)

19. Transverse Axis
Length of one vertex to the other 2a
1/ sin t
1/ cos t
cos t/ sin t

20. Law of Sines
sinA/a=sinB/b=sinC/c
y= +-(b/a) (x-h) + k
Given an m x n matrix A - its transpose is the n x m
length from one covertex to the other 2b

21. Heron's Formula
_ _ 1/detA * | d -b | |-c a | - -
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
Order Matters

22. If A is acute a<h
length from one covertex to the other 2b
1
one triangle
No triangle

23. Focus of Parabola
c^2 = a^2 + b^2
sinA/a=sinB/b=sinC/c
Center + P
(side adjacent to given angle) sin (given angle) - h = b(sina)

24. Cramer's rule
sin t/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
n(A u B0 = n(A) + n(B) - n(A n B)
sinA/a=sinB/b=sinC/c

25. Adding Matrices
Length of one vertex to the other 2a
Center + P
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

26. Equation of Parabola
c²=a²+b²-2abcosC
1
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

27. Minor Axis
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the shortest axis of an ellipse 2b
(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.

28. Inverse of 2X2 matrix
c^2 = a^2 - b^2
n(A u B0 = n(A) + n(B) - n(A n B)
one triangle
_ _ 1/detA * | d -b | |-c a | - -

29. Permutation Formula
cos t/ sin t
nPr= (n!)/(n-r)!
nCr= (n!)/((n-r)! r!)
(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. 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)
one triangle

31. Focus of Hyperbola
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
Order Matters
2p

32. If A is acute a > h
y= +-(a/b) (x-h) + k
one triangle
= 1 + tan2 t
c^2 = a^2 + b^2

33. sec2 t
= 1 + tan2 t
Multiply Row By Column - Columns of first must be equal to rows of second
(x-h)^2 + (y-k)^2 = r^2
the longest axis of an ellipse 2a

34. 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
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Two Triangles
2 events that can't be done together.

35. Directrix
center - p
Order Matters
1/ sin t
Given an m x n matrix A - its transpose is the n x m

36. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
4p
_ _ 1/detA * | d -b | |-c a | - -
nCr= (n!)/((n-r)! r!)

37. cot
c²=a²+b²-2abcosC
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
cos t/ sin t
n(A u B0 = n(A) + n(B) - n(A n B)

38. Focal Width of Ellipses
2b²/a
center - p
Center + P
ad - bc

39. tan t
c²=a²+b²-2abcosC
sin t/ cos t
c^2 = a^2 + b^2
2p

40. Multiply Matrices
order Doesn't Matter
Multiply Row By Column - Columns of first must be equal to rows of second
center - p
nPr= (n!)/(n-r)!

41. sin2 t + cos2 t =
Order Matters
sin2 t + cos2 t =
n(A u B0 = n(A) + n(B) - n(A n B)
1

42. Binomial Theorem
4p
n(A u B0 = n(A) + n(B) - n(A n B)
nCrx^n-ry^r
No triangle

43. Focal Width
c^2 = a^2 + b^2
2p
Multiply Row By Column - Columns of first must be equal to rows of second
4p

44. odds:
ratio
length from one covertex to the other 2b
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Order Matters

45. distance between focus and directrix
Order Matters
2p
ad - bc
= 1 + tan2 t

46. Determinant
ad - bc
nCr= (n!)/((n-r)! r!)
Length of one vertex to the other 2a
Center + P

47. matrices order
(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
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
m X N - rows by columns

48. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
No triangle
one triangle

49. Solving Triangle if angle is obtuse
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
1/ cos t
nPr= (n!)/(n-r)!
one triangle

50. Conjugate Axis
one triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nPr= (n!)/(n-r)!
length from one covertex to the other 2b