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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. csc t
= 1 + tan2 t
ratio
y= +-(b/a) (x-h) + k
1/ sin t

2. 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
sin t/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Two Triangles

3. Permutation Formula
one triangle
(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
nPr= (n!)/(n-r)!

4. The Multiplication Principle
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
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.

5. Determinant
y= +-(b/a) (x-h) + k
ad - bc
(x-h)^2 + (y-k)^2 = r^2
nCrx^n-ry^r

6. Circle Conic Section
nCrx^n-ry^r
Center + P
(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.

7. If A is acute a = h
1/ sin t
Multiply Row By Column - Columns of first must be equal to rows of second
one triangle
length from one covertex to the other 2b

8. distance between focus and directrix
2p
= 1 + tan2 t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
sec2 t

9. Equation of Parabola
(x-h)^2 + (y-k)^2 = r^2
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
ad - bc
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

10. sec t
1/ cos t
y= +-(b/a) (x-h) + k
4p
Two Triangles

11. Conjugate Axis
length from one covertex to the other 2b
one triangle
sin t/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

12. Focus of Parabola
c²=a²+b²-2abcosC
Center + P
2p
Multiply Row By Column - Columns of first must be equal to rows of second

13. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Order Matters
y= +-(a/b) (x-h) + k
one triangle

14. Asymptote of hyperbola that opens left and right.
Center + P
c²=a²+b²-2abcosC
y= +-(b/a) (x-h) + k
c^2 = a^2 + b^2

15. Transverse Axis
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.
nCr= (n!)/((n-r)! r!)
nPr= (n!)/(n-r)!

16. Focus of Hyperbola
c^2 = a^2 + b^2
nCr= (n!)/((n-r)! r!)
1/ cos t
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

17. tan t
_ _ 1/detA * | d -b | |-c a | - -
one triangle
center - p
sin t/ cos t

18. Multiply Matrices
Center + P
order Doesn't Matter
Multiply Row By Column - Columns of first must be equal to rows of second
the longest axis of an ellipse 2a

19. Addition Principle
m X N - rows by columns
2p
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.
the longest axis of an ellipse 2a

20. 1 + tan2 t =
ratio
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.
sec2 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.

21. Complement Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
= 1 + tan2 t
sin t/ 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

22. If A is acute a<h
sec2 t
No triangle
Order Matters
center - p

23. Permutations
nCrx^n-ry^r
Order Matters
m X N - rows by columns
one triangle

24. Law of Sines
1
length from one covertex to the other 2b
sinA/a=sinB/b=sinC/c
nCrx^n-ry^r

25. Focal Width
m X N - rows by columns
(x-h)^2 + (y-k)^2 = r^2
4p
Multiply Row By Column - Columns of first must be equal to rows of second

26. Minor Axis
the shortest axis of an ellipse 2b
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
y= +-(a/b) (x-h) + k
sinA/a=sinB/b=sinC/c

27. matrices order
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
_ _ 1/detA * | d -b | |-c a | - -
sec2 t
m X N - rows by columns

28. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
Order Matters
sec2 t
the longest axis of an ellipse 2a

29. Equations of Hyperbola
sin t/ cos t
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
the longest axis of an ellipse 2a

30. Mutually Exclusive

31. Probabilty
(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
_ _ 1/detA * | d -b | |-c 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.

32. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
y= +-(b/a) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
(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

33. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
ratio
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

34. 1=
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
sin2 t + cos2 t =
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

35. If A is acute h<a<b
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
y= +-(a/b) (x-h) + k
(x-h)^2 + (y-k)^2 = r^2

36. Focus of ellipses
4p
y= +-(b/a) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
c^2 = a^2 - b^2

37. Combination Formula
_ _ 1/detA * | d -b | |-c 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
nCr= (n!)/((n-r)! r!)
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

38. If A is acute a > h
one triangle
nCr= (n!)/((n-r)! r!)
m X N - rows by columns
ratio

39. sin2 t + cos2 t =
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
one triangle
No triangle
1

40. Directrix
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.
one triangle
center - p
No triangle

41. odds:
the longest axis of an ellipse 2a
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
ratio
ad - bc

42. cot
1/ cos t
(side adjacent to given angle) sin (given angle) - h = b(sina)
cos t/ sin t
Multiply Row By Column - Columns of first must be equal to rows of second

43. Focal Width of Ellipses
2b²/a
No triangle
one triangle
center - p

44. Inclusion Exclusion Principle
Order Matters
sin t/ cos t
n(A u B0 = n(A) + n(B) - n(A n B)
2b²/a

45. h =
1
(side adjacent to given angle) sin (given angle) - h = b(sina)
length from one covertex to the other 2b
c²=a²+b²-2abcosC

46. 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.
nCrx^n-ry^r
sec2 t
the longest axis of an ellipse 2a

47. Law of Cosines
Two Triangles
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
c²=a²+b²-2abcosC

48. sec2 t
order Doesn't Matter
= 1 + tan2 t
No triangle
nPr= (n!)/(n-r)!

49. Combinations

50. Major Axis
ad - bc
the longest axis of an ellipse 2a
1/ sin t
Center + P