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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. The Multiplication Principle
= 1 + tan2 t
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.
sinA/a=sinB/b=sinC/c
sin2 t + cos2 t =

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

3. Focal Width
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
No triangle
4p
1

4. odds:
ratio
y= +-(a/b) (x-h) + k
2b²/a
1/ cos t

5. Major Axis
the longest axis of an ellipse 2a
m X N - rows by columns
2 events that can't be done together.
_ _ 1/detA * | d -b | |-c a | - -

6. sec t
the longest axis of an ellipse 2a
1/ cos t
c^2 = a^2 + b^2
1/ sin t

7. If A is acute a = h
one triangle
nCr= (n!)/((n-r)! r!)
1/ sin t
cos t/ sin t

8. Permutation Formula
c^2 = a^2 - b^2
nPr= (n!)/(n-r)!
cos t/ sin t
No triangle

9. 1 + tan2 t =
c^2 = a^2 - b^2
sec2 t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sinA/a=sinB/b=sinC/c

10. cot
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sinA/a=sinB/b=sinC/c
cos t/ sin t
No triangle

11. Asymptote of hyperbola that opens left and right.
y= +-(a/b) (x-h) + k
Order Matters
y= +-(b/a) (x-h) + k
center - p

12. Multiply Matrices
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c^2 = a^2 + b^2
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Multiply Row By Column - Columns of first must be equal to rows of second

13. Mutually Exclusive

14. sin2 t + cos2 t =
sinA/a=sinB/b=sinC/c
1
sec2 t
1/ cos t

15. sec2 t
_ _ 1/detA * | d -b | |-c a | - -
one triangle
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

16. distance between focus and directrix
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)!
2p
ratio

17. If A is acute h<a<b
1/ sin t
nCrx^n-ry^r
Two Triangles
length from one covertex to the other 2b

18. Law of Sines
cos t/ sin t
one triangle
sin t/ cos t
sinA/a=sinB/b=sinC/c

19. If A is acute a > h
one triangle
the longest axis of an ellipse 2a
Center + P
c²=a²+b²-2abcosC

20. Equation of Parabola
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)
4p
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

21. Combinations

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

23. 1=
the shortest axis of an ellipse 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
sin2 t + cos2 t =
Length of one vertex to the other 2a

24. Conjugate Axis
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.
2p
length from one covertex to the other 2b
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

25. Focus of Hyperbola
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.
sin2 t + cos2 t =
y= +-(a/b) (x-h) + k
c^2 = a^2 + b^2

26. Cramer's rule
the shortest axis of an ellipse 2b
the longest axis of an ellipse 2a
c^2 = a^2 - b^2
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

27. Determinant
ad - bc
sin2 t + cos2 t =
sinA/a=sinB/b=sinC/c
y= +-(b/a) (x-h) + k

28. Combination Formula
nCrx^n-ry^r
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
nCr= (n!)/((n-r)! r!)

29. If A is obtuse a=< b
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
1
the longest axis of an ellipse 2a
No triangle

30. Addition Principle
1
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
center - p

31. Focus of ellipses
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
ad - bc
2b²/a
c^2 = a^2 - b^2

32. Focal Width of Ellipses
2b²/a
one triangle
(side adjacent to given angle) sin (given angle) - h = b(sina)
c^2 = a^2 + b^2

33. Adding Matrices
one triangle
(x-h)^2 + (y-k)^2 = r^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
the shortest axis of an ellipse 2b

34. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
one triangle
No triangle

35. Inverse of 2X2 matrix
Two Triangles
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 | - -

36. Solving Triangle if angle is obtuse
n(A u B0 = n(A) + n(B) - n(A n B)
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
Center + P

37. Permutations
Given an m x n matrix A - its transpose is the n x m
nCrx^n-ry^r
nPr= (n!)/(n-r)!
Order Matters

38. h =
Order Matters
(side adjacent to given angle) sin (given angle) - h = b(sina)
1
c^2 = a^2 - b^2

39. Focus of Parabola
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
m X N - rows by columns
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

40. Transpose 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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
length from one covertex to the other 2b
Given an m x n matrix A - its transpose is the n x m

41. Area Of a Triangle
center - p
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.
Given an m x n matrix A - its transpose is the n x m

42. matrices order
c²=a²+b²-2abcosC
m X N - rows by columns
one triangle
1

43. Asymptote of hyperbola that opens up and down
ad - bc
y= +-(a/b) (x-h) + k
the longest axis of an ellipse 2a
length from one covertex to the other 2b

44. Heron's Formula
nCrx^n-ry^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
y= +-(a/b) (x-h) + k
Multiply Row By Column - Columns of first must be equal to rows of second

45. If A is acute a<h
2b²/a
No triangle
nPr= (n!)/(n-r)!
4p

46. 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
(side adjacent to given angle) sin (given angle) - h = b(sina)
nCrx^n-ry^r
c^2 = a^2 - b^2

47. Ellipses Conic Section
order Doesn't Matter
(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
No triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

48. Complement Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
No triangle
length from one covertex to the other 2b
c^2 = a^2 - b^2

49. Law of Cosines
one triangle
nPr= (n!)/(n-r)!
c²=a²+b²-2abcosC
center - p

50. Binomial Theorem
nCrx^n-ry^r
one triangle
Order Matters
center - p