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

2. Inverse of 2X2 matrix
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle
sin t/ cos t
_ _ 1/detA * | d -b | |-c a | - -

3. csc t
1/ sin t
No triangle
2p
Order Matters

4. If A is acute h<a<b
y= +-(b/a) (x-h) + k
(side adjacent to given angle) sin (given angle) - h = b(sina)
No triangle
Two Triangles

5. Binomial Theorem
_ _ 1/detA * | d -b | |-c a | - -
nCrx^n-ry^r
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)

6. Directrix
No triangle
No 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
center - p

7. Transpose Matrices
sin2 t + cos2 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
Given an m x n matrix A - its transpose is the n x m
Length of one vertex to the other 2a

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

9. Combinations

10. Heron's Formula
order Doesn't Matter
1/ cos t
1/ sin 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

11. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter
Length of one vertex to the other 2a
Given an m x n matrix A - its transpose is the n x m

12. Complement Principle
cos t/ sin t
length from one covertex to the other 2b
the shortest axis of an ellipse 2b
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

13. If A is acute a > h
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
sin2 t + cos2 t =
y= +-(a/b) (x-h) + k

14. sin2 t + cos2 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
1
one triangle

15. cot
cos t/ sin t
1/ sin t
(side adjacent to given angle) sin (given angle) - h = b(sina)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

16. sec2 t
order Doesn't Matter
Length of one vertex to the other 2a
= 1 + tan2 t
sin t/ cos t

17. If A is obtuse a> b
m X N - rows by columns
order Doesn't Matter
No triangle
one triangle

18. Focus of Hyperbola
order Doesn't Matter
c^2 = a^2 + b^2
= 1 + tan2 t
(side adjacent to given angle) sin (given angle) - h = b(sina)

19. Determinant
y= +-(b/a) (x-h) + k
1/ sin t
ad - bc
1

20. Equations of Hyperbola
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
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
(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)!

21. h =
one triangle
Center + P
n(A u B0 = n(A) + n(B) - n(A n B)
(side adjacent to given angle) sin (given angle) - h = b(sina)

22. 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
ratio
(side adjacent to given angle) sin (given angle) - h = b(sina)
center - p

23. Asymptote of hyperbola that opens left and right.
ad - bc
y= +-(b/a) (x-h) + k
1/ cos t
one triangle

24. 1=
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
sin2 t + cos2 t =
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
1/ sin t

25. Mutually Exclusive

26. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
1
one triangle
c^2 = a^2 + b^2

27. Major Axis
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
the longest axis of an ellipse 2a
m X N - rows by columns
Given an m x n matrix A - its transpose is the n x m

28. Area Of a Triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sec2 t
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.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

29. The Multiplication Principle
order Doesn't Matter
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.
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

30. Cramer's rule
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nCrx^n-ry^r
m X N - rows by columns

31. distance between focus and directrix
4p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
2p
the longest axis of an ellipse 2a

32. odds:
sin t/ cos t
sin2 t + cos2 t =
Given an m x n matrix A - its transpose is the n x m
ratio

33. Permutations
the longest axis of an ellipse 2a
sec2 t
(side adjacent to given angle) sin (given angle) - h = b(sina)
Order Matters

34. Combination Formula
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
nCr= (n!)/((n-r)! r!)
one triangle

35. Solving Triangle if angle is obtuse
the shortest axis of an ellipse 2b
Multiply Row By Column - Columns of first must be equal to rows of second
sinA/a=sinB/b=sinC/c
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

36. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
ratio
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

37. Focal Width of Ellipses
one triangle
2b²/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
nCrx^n-ry^r

38. Focus of ellipses
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.
2 events that can't be done together.
2p
c^2 = a^2 - b^2

39. Focal Width
Multiply Row By Column - Columns of first must be equal to rows of second
4p
No triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

40. Transverse Axis
Length of one vertex to the other 2a
1/ sin t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
= 1 + tan2 t

41. matrices order
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
m X N - rows by columns
sinA/a=sinB/b=sinC/c

42. If A is acute a<h
c^2 = a^2 - b^2
No triangle
= 1 + tan2 t
2 events that can't be done together.

43. Law of Sines
sinA/a=sinB/b=sinC/c
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sin2 t + cos2 t =
n(A u B0 = n(A) + n(B) - n(A n B)

44. Law of Cosines
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
one triangle
No triangle
c²=a²+b²-2abcosC

45. Conjugate Axis
Multiply Row By Column - Columns of first must be equal to rows of second
length from one covertex to the other 2b
n(A u B0 = n(A) + n(B) - n(A n B)
the longest axis of an ellipse 2a

46. Focus of Parabola
No triangle
Two Triangles
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Center + P

47. If A is obtuse a=< b
_ _ 1/detA * | d -b | |-c a | - -
nCr= (n!)/((n-r)! r!)
m X N - rows by columns
No triangle

48. If A is acute a = h
center - p
one triangle
sinA/a=sinB/b=sinC/c
nCr= (n!)/((n-r)! r!)

49. Multiply Matrices
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
1/ sin t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

50. 1 + tan2 t =
c^2 = a^2 + b^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.
ad - bc
sec2 t