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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. Permutation Formula
Two Triangles
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
sec2 t

2. sec t
n(A u B0 = n(A) + n(B) - n(A n B)
Order Matters
1/ cos t
ratio

3. 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
c^2 = a^2 - b^2
the longest axis of an ellipse 2a
Order Matters

4. sin2 t + cos2 t =
1
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
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. Combination Formula
1/ sin t
nCr= (n!)/((n-r)! r!)
1/ cos t
Length of one vertex to the other 2a

6. Focus of Parabola
length from one covertex to the other 2b
Center + P
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

7. The Multiplication Principle
(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.
y= +-(a/b) (x-h) + k
nCr= (n!)/((n-r)! r!)

8. Heron's Formula
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
Length of one vertex to the other 2a
Order Matters

9. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
one triangle
order Doesn't Matter
2b²/a

10. Inclusion Exclusion Principle
c^2 = a^2 + b^2
Length of one vertex to the other 2a
n(A u B0 = n(A) + n(B) - n(A n B)
ratio

11. Asymptote of hyperbola that opens left and right.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
c²=a²+b²-2abcosC
m X N - rows by columns
y= +-(b/a) (x-h) + k

12. Focal Width
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
4p
nPr= (n!)/(n-r)!
Multiply Row By Column - Columns of first must be equal to rows of second

13. sec2 t
one triangle
nPr= (n!)/(n-r)!
= 1 + tan2 t
center - p

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

15. Focus of ellipses
No triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c^2 = a^2 - b^2
y= +-(a/b) (x-h) + k

16. Conjugate Axis
1
length from one covertex to the other 2b
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

17. Equations of Hyperbola
nPr= (n!)/(n-r)!
length from one covertex to the other 2b
(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
2 events that can't be done together.

18. Law of Sines
Order Matters
y= +-(b/a) (x-h) + k
Two Triangles
sinA/a=sinB/b=sinC/c

19. Complement Principle
n(A u B0 = n(A) + n(B) - n(A n B)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
No triangle
1

20. cot
center - p
m X N - rows by columns
cos t/ sin t
Order Matters

21. Binomial Theorem
one triangle
Length of one vertex to the other 2a
n(A u B0 = n(A) + n(B) - n(A n B)
nCrx^n-ry^r

22. If A is obtuse a=< b
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
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.
No triangle

23. If A is acute a = h
sin2 t + cos2 t =
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
one triangle
sec2 t

24. Focal Width of Ellipses
No triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
2b²/a
= 1 + tan2 t

25. Mutually Exclusive

26. Focus of Hyperbola
Center + P
2b²/a
the longest axis of an ellipse 2a
c^2 = a^2 + b^2

27. Determinant
(side adjacent to given angle) sin (given angle) - h = b(sina)
4p
ad - bc
1/ sin t

28. 1=
one triangle
_ _ 1/detA * | d -b | |-c a | - -
nCrx^n-ry^r
sin2 t + cos2 t =

29. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
one triangle
No triangle
y= +-(a/b) (x-h) + k

30. matrices order
1/ sin t
m X N - rows by columns
nPr= (n!)/(n-r)!
cos t/ sin t

31. h =
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.
center - p
1
(side adjacent to given angle) sin (given angle) - h = b(sina)

32. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
= 1 + tan2 t
cos t/ sin t

33. If A is obtuse a> b
y= +-(a/b) (x-h) + k
one triangle
(side adjacent to given angle) sin (given angle) - h = b(sina)
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

34. 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
sin t/ cos t
_ _ 1/detA * | d -b | |-c a | - -
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

35. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
m X N - rows by columns
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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

36. Multiply Matrices
y= +-(b/a) (x-h) + k
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
4p

37. If A is acute a > h
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
sec2 t
one triangle

38. Permutations
c²=a²+b²-2abcosC
y= +-(b/a) (x-h) + k
Order Matters
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

39. Asymptote of hyperbola that opens up and down
1
c^2 = a^2 - b^2
y= +-(a/b) (x-h) + k
2p

40. Transverse Axis
center - p
c^2 = a^2 + b^2
Length of one vertex to the other 2a
n(A u B0 = n(A) + n(B) - n(A n B)

41. Minor Axis
y= +-(a/b) (x-h) + k
the shortest axis of an ellipse 2b
one triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

42. Transpose Matrices
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Order Matters
1/ sin t
Given an m x n matrix A - its transpose is the n x m

43. 1 + tan2 t =
nPr= (n!)/(n-r)!
1/ sin t
(side adjacent to given angle) sin (given angle) - h = b(sina)
sec2 t

44. Major Axis
Multiply Row By Column - Columns of first must be equal to rows of second
the longest axis of an ellipse 2a
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
sin2 t + cos2 t =

45. tan t
sin t/ cos t
one triangle
_ _ 1/detA * | d -b | |-c a | - -
2b²/a

46. Directrix
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2p
center - p
nCr= (n!)/((n-r)! r!)

47. Area Of a Triangle
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.
nCrx^n-ry^r
c²=a²+b²-2abcosC

48. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
y= +-(b/a) (x-h) + k
nCr= (n!)/((n-r)! r!)
1

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

50. If A is acute a<h
No triangle
sinA/a=sinB/b=sinC/c
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
one triangle