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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. sec t
one triangle
sin2 t + cos2 t =
1/ cos t
sin t/ cos t

2. Directrix
center - p
n(A u B0 = n(A) + n(B) - n(A n B)
Order Matters
(x-h)^2 + (y-k)^2 = r^2

3. Inverse of 2X2 matrix
(x-h)^2 + (y-k)^2 = r^2
ratio
_ _ 1/detA * | d -b | |-c a | - -
(side adjacent to given angle) sin (given angle) - h = b(sina)

4. Complement Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
1/ sin t
cos t/ 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

5. Focus of Hyperbola
1/ sin t
Order Matters
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

6. cot
No triangle
cos t/ sin t
c²=a²+b²-2abcosC
1

7. Solving Triangle if angle is obtuse
1
Order Matters
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
y= +-(b/a) (x-h) + k

8. Asymptote of hyperbola that opens up and down
y= +-(a/b) (x-h) + k
4p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
n(A u B0 = n(A) + n(B) - n(A n B)

9. Transverse Axis
Length of one vertex to the other 2a
2p
sin2 t + cos2 t =
sinA/a=sinB/b=sinC/c

10. Minor Axis
Order Matters
c²=a²+b²-2abcosC
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
the shortest axis of an ellipse 2b

11. h =
one triangle
Order Matters
(side adjacent to given angle) sin (given angle) - h = b(sina)
the longest axis of an ellipse 2a

12. If A is obtuse a=< b
y= +-(a/b) (x-h) + k
No triangle
c^2 = a^2 + b^2
_ _ 1/detA * | d -b | |-c a | - -

13. Focal Width
cos t/ sin t
4p
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
center - p

14. Probabilty
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
No triangle
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
the shortest axis of an ellipse 2b

15. If A is acute h<a<b
nCrx^n-ry^r
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Two Triangles
sin2 t + cos2 t =

16. Focus of ellipses
c^2 = a^2 - b^2
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
center - p
c^2 = a^2 + b^2

17. 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.
2p
No triangle

18. sin2 t + cos2 t =
c^2 = a^2 + b^2
No triangle
(x-h)^2 + (y-k)^2 = r^2
1

19. Focus of Parabola
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.
nPr= (n!)/(n-r)!
Center + P

20. Transpose Matrices
Given an m x n matrix A - its transpose is the n x m
sec2 t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
sinA/a=sinB/b=sinC/c

21. Equations of Hyperbola
ratio
order Doesn't Matter
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
(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

22. If A is acute a = h
2 events that can't be done together.
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
(side adjacent to given angle) sin (given angle) - h = b(sina)

23. If A is acute a<h
one triangle
No triangle
Center + P
Two Triangles

24. 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
(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
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

25. odds:
order Doesn't Matter
the longest axis of an ellipse 2a
ratio
ad - bc

26. matrices order
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
m X N - rows by columns
nCrx^n-ry^r

27. If A is obtuse a> b
sin2 t + cos2 t =
Center + P
(side adjacent to given angle) sin (given angle) - h = b(sina)
one triangle

28. Permutation Formula
nPr= (n!)/(n-r)!
sec2 t
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 - (y-k)^2 - (x-h)^2/a^2 b^2 = 1 - a is always positive term

29. Combinations

30. Conjugate Axis
length from one covertex to the other 2b
Given an m x n matrix A - its transpose is the n x m
No triangle
nPr= (n!)/(n-r)!

31. Law of Sines
1/ cos t
No triangle
sinA/a=sinB/b=sinC/c
length from one covertex to the other 2b

32. Adding Matrices
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nCrx^n-ry^r
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.

33. Asymptote of hyperbola that opens left and right.
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
2b²/a
y= +-(b/a) (x-h) + k

34. Equation of Parabola
2p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
sin2 t + cos2 t =
one triangle

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

36. Binomial Theorem
nCrx^n-ry^r
one triangle
one triangle
No triangle

37. Permutations
_ _ 1/detA * | d -b | |-c a | - -
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
the longest axis of an ellipse 2a

38. Determinant
Multiply Row By Column - Columns of first must be equal to rows of second
1/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
ad - bc

39. 1=
1/ sin t
sin2 t + cos2 t =
center - p
nPr= (n!)/(n-r)!

40. Major Axis
Order Matters
2b²/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.
the longest axis of an ellipse 2a

41. Mutually Exclusive

42. 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
2b²/a
order Doesn't Matter

43. sec2 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
= 1 + tan2 t
1/ cos t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

44. The Multiplication Principle
n(A u B0 = n(A) + n(B) - n(A n B)
Multiply Row By Column - Columns of first must be equal to rows of second
y= +-(a/b) (x-h) + k
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.

45. Combination Formula
nCr= (n!)/((n-r)! r!)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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

46. Multiply Matrices
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Multiply Row By Column - Columns of first must be equal to rows of second
Length of one vertex to the other 2a
4p

47. csc t
sinA/a=sinB/b=sinC/c
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2 events that can't be done together.
1/ sin t

48. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Order Matters
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
order Doesn't Matter

49. tan t
the shortest axis of an ellipse 2b
one triangle
sin t/ cos t
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

50. Focal Width of Ellipses
2b²/a
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
one triangle
y= +-(b/a) (x-h) + k