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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
m X N - rows by columns
1/ sin t
= 1 + tan2 t
one triangle

2. If A is acute a = h
one triangle
1
2 events that can't be done together.
Order Matters

3. h =
(side adjacent to given angle) sin (given angle) - h = b(sina)
c²=a²+b²-2abcosC
one triangle
cos t/ sin t

4. 1=
sin2 t + cos2 t =
Order Matters
length from one covertex to the other 2b
No triangle

5. 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
nCrx^n-ry^r
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.
(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

6. Transpose Matrices
order Doesn't Matter
Given an m x n matrix A - its transpose is the n x m
(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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

7. Directrix
nCr= (n!)/((n-r)! r!)
2 events that can't be done together.
center - p
(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

8. Major Axis
nCr= (n!)/((n-r)! r!)
= 1 + tan2 t
the longest axis of an ellipse 2a
(side adjacent to given angle) sin (given angle) - h = b(sina)

9. 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.
No triangle
sin2 t + cos2 t =
c^2 = a^2 + b^2

10. Multiply Matrices
the longest axis of an ellipse 2a
Multiply Row By Column - Columns of first must be equal to rows of second
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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.

11. If A is acute a<h
Order Matters
sin2 t + cos2 t =
one triangle
No triangle

12. Determinant
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
No triangle
ad - bc
= 1 + tan2 t

13. sec t
2 events that can't be done together.
1/ cos t
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
c²=a²+b²-2abcosC

14. Area Of a Triangle
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.
sin t/ cos t
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.

15. 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
n(A u B0 = n(A) + n(B) - n(A n B)
Center + P
(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

16. Transverse Axis
_ _ 1/detA * | d -b | |-c a | - -
Center + P
2 events that can't be done together.
Length of one vertex to the other 2a

17. Solving Triangle if angle is obtuse
1/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
4p

18. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Length of one vertex to the other 2a
1/ cos t
No triangle

19. distance between focus and directrix
one triangle
center - p
2p
4p

20. Focal Width
4p
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
(x-h)^2 + (y-k)^2 = r^2
2b²/a

21. Permutation Formula
order Doesn't Matter
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nPr= (n!)/(n-r)!
one triangle

22. If A is acute h<a<b
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Length of one vertex to the other 2a
Two Triangles
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

23. Probabilty
one triangle
2p
sinA/a=sinB/b=sinC/c
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

24. Law of Sines
sinA/a=sinB/b=sinC/c
nPr= (n!)/(n-r)!
y= +-(a/b) (x-h) + k
Center + P

25. Focus of Parabola
Center + P
Order Matters
(side adjacent to given angle) sin (given angle) - h = b(sina)
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

26. Law of Cosines
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
c^2 = a^2 + b^2
Order Matters
c²=a²+b²-2abcosC

27. Asymptote of hyperbola that opens up and down
sin2 t + cos2 t =
y= +-(a/b) (x-h) + k
one triangle
c^2 = a^2 - b^2

28. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
order Doesn't Matter
the longest axis of an ellipse 2a
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

29. Circle Conic Section
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
length from one covertex to the other 2b
(x-h)^2 + (y-k)^2 = r^2
one triangle

30. Permutations
c^2 = a^2 - b^2
nCrx^n-ry^r
Order Matters
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

31. 1 + tan2 t =
the shortest axis of an ellipse 2b
sec2 t
Multiply Row By Column - Columns of first must be equal to rows of second
(x-h)^2 + (y-k)^2 = r^2

32. Focus of ellipses
sinA/a=sinB/b=sinC/c
c^2 = a^2 - b^2
m X N - rows by columns
nCr= (n!)/((n-r)! r!)

33. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1/ sin t
y= +-(a/b) (x-h) + k
(side adjacent to given angle) sin (given angle) - h = b(sina)

34. sec2 t
= 1 + tan2 t
ratio
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
(x-h)^2 + (y-k)^2 = r^2

35. Mutually Exclusive

36. Minor Axis
Center + P
the shortest axis of an ellipse 2b
(side adjacent to given angle) sin (given angle) - h = b(sina)
nCr= (n!)/((n-r)! r!)

37. Focus of Hyperbola
Two Triangles
y= +-(b/a) (x-h) + k
4p
c^2 = a^2 + b^2

38. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
y= +-(a/b) (x-h) + k
nCr= (n!)/((n-r)! r!)
m X N - rows by columns

39. If A is obtuse a=< b
No triangle
nCrx^n-ry^r
2p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

40. sin2 t + cos2 t =
2p
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1
Order Matters

41. Asymptote of hyperbola that opens left and right.
the shortest axis of an ellipse 2b
y= +-(b/a) (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.
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

42. Cramer's rule
1/ sin t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
2b²/a
ratio

43. If A is acute a > h
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Two Triangles
one triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

44. odds:
cos t/ sin t
Center + P
ratio
ad - bc

45. Combination Formula
one triangle
nCr= (n!)/((n-r)! r!)
length from one covertex to the other 2b
Order Matters

46. Binomial Theorem
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.
nCrx^n-ry^r
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.
= 1 + tan2 t

47. Complement Principle
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
sinA/a=sinB/b=sinC/c
the shortest axis of an ellipse 2b

48. Conjugate Axis
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the shortest axis of an ellipse 2b
length from one covertex to the other 2b
nCrx^n-ry^r

49. Inclusion Exclusion Principle
sinA/a=sinB/b=sinC/c
sin2 t + cos2 t =
n(A u B0 = n(A) + n(B) - n(A n B)
2 events that can't be done together.

50. tan t
No triangle
sec2 t
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sin t/ cos t