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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
sin2 t + cos2 t =
1/ cos t
ad - bc
one triangle

2. If A is acute a = h
the longest axis of an ellipse 2a
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
No triangle
one triangle

3. Inclusion Exclusion Principle
Two Triangles
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nPr= (n!)/(n-r)!
n(A u B0 = n(A) + n(B) - n(A n B)

4. Complement Principle
Order Matters
Length of one vertex to the other 2a
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Center + P

5. Combination Formula
sin2 t + cos2 t =
nCr= (n!)/((n-r)! r!)
ad - bc
No triangle

6. Equations of Hyperbola
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
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
(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

7. 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.
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
one triangle

8. Major Axis
the longest axis of an ellipse 2a
ad - bc
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
nPr= (n!)/(n-r)!

9. csc t
1/ sin t
Two Triangles
y= +-(a/b) (x-h) + k
2b²/a

10. Equation of Parabola
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
one triangle
No triangle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

11. h =
4p
c^2 = a^2 - b^2
the longest axis of an ellipse 2a
(side adjacent to given angle) sin (given angle) - h = b(sina)

12. Combinations

13. 1=
sin2 t + cos2 t =
Length of one vertex to the other 2a
No triangle
cos t/ sin t

14. Adding Matrices
m X N - rows by columns
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

15. Asymptote of hyperbola that opens up and down
(side adjacent to given angle) sin (given angle) - h = b(sina)
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 shortest axis of an ellipse 2b
y= +-(a/b) (x-h) + k

16. Ellipses Conic Section
Two Triangles
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1/ cos t
one triangle

17. Transverse Axis
1/ cos t
Length of one vertex to the other 2a
1/ sin t
4p

18. Solving Triangle if angle is obtuse
Given an m x n matrix A - its transpose is the n x m
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nPr= (n!)/(n-r)!

19. Permutation Formula
nPr= (n!)/(n-r)!
= 1 + tan2 t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
length from one covertex to the other 2b

20. Mutually Exclusive

21. If A is acute a > h
Multiply Row By Column - Columns of first must be equal to rows of second
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
one triangle

22. Focal Width
length from one covertex to the other 2b
4p
2 events that can't be done together.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

23. sin2 t + cos2 t =
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nCrx^n-ry^r
1
4p

24. 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
the longest axis of an ellipse 2a
cos t/ sin t
one triangle

25. odds:
ratio
nPr= (n!)/(n-r)!
2p
sin t/ cos t

26. Law of Cosines
2p
c²=a²+b²-2abcosC
Order Matters
(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

27. Permutations
_ _ 1/detA * | d -b | |-c a | - -
one triangle
Order Matters
the longest axis of an ellipse 2a

28. Addition Principle
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 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!)
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.

29. Focal Width of Ellipses
cos t/ sin t
sin t/ cos t
one triangle
2b²/a

30. Binomial Theorem
Two Triangles
sinA/a=sinB/b=sinC/c
nCrx^n-ry^r
length from one covertex to the other 2b

31. If A is acute a<h
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
No triangle
y= +-(a/b) (x-h) + k
c²=a²+b²-2abcosC

32. Conjugate Axis
(side adjacent to given angle) sin (given angle) - h = b(sina)
(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
Two Triangles
length from one covertex to the other 2b

33. cot
1/ cos 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.
m X N - rows by columns
cos t/ sin t

34. Asymptote of hyperbola that opens left and right.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
2p

35. 1 + tan2 t =
Given an m x n matrix A - its transpose is the n x m
cos t/ sin t
sec2 t
sin2 t + cos2 t =

36. matrices order
m X N - rows by columns
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
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
No triangle

37. Circle Conic Section
cos t/ sin t
one triangle
sin t/ cos t
(x-h)^2 + (y-k)^2 = r^2

38. Determinant
ad - bc
Center + P
sec2 t
nCrx^n-ry^r

39. If A is obtuse a> b
y= +-(a/b) (x-h) + k
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
one triangle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

40. The Multiplication Principle
nCrx^n-ry^r
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.
center - p
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

41. tan t
sin t/ cos t
center - p
1
y= +-(a/b) (x-h) + k

42. Cramer's rule
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
No triangle

43. If A is acute h<a<b
sin2 t + cos2 t =
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
m X N - rows by columns

44. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
2 events that can't be done together.
sinA/a=sinB/b=sinC/c
the longest axis of an ellipse 2a

45. Focus of ellipses
No triangle
1
c^2 = a^2 - b^2
one triangle

46. If A is obtuse a=< b
y= +-(a/b) (x-h) + k
No triangle
sinA/a=sinB/b=sinC/c
Multiply Row By Column - Columns of first must be equal to rows of second

47. Minor Axis
length from one covertex to the other 2b
1/ cos t
nPr= (n!)/(n-r)!
the shortest axis of an ellipse 2b

48. sec2 t
Multiply Row By Column - Columns of first must be equal to rows of second
nCrx^n-ry^r
= 1 + tan2 t
_ _ 1/detA * | d -b | |-c a | - -

49. 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
y= +-(b/a) (x-h) + k
No triangle
(x-h)^2 + (y-k)^2 = r^2

50. Focus of Parabola
Center + P
y= +-(b/a) (x-h) + k
c^2 = a^2 - b^2
No triangle