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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. cot
1/ cos t
the longest axis of an ellipse 2a
y= +-(b/a) (x-h) + k
cos t/ sin t

2. Asymptote of hyperbola that opens left and right.
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
y= +-(b/a) (x-h) + k
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
(side adjacent to given angle) sin (given angle) - h = b(sina)

3. Probabilty
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
c^2 = a^2 + b^2
No triangle

4. sin2 t + cos2 t =
(x-h)^2 + (y-k)^2 = r^2
sin2 t + cos2 t =
1
order Doesn't Matter

5. Adding Matrices
ad - bc
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
y= +-(a/b) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

6. sec t
1/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
(x-h)^2 + (y-k)^2 = r^2
sinA/a=sinB/b=sinC/c

7. Equations of Hyperbola
= 1 + tan2 t
2 events that can't be done together.
1/ sin 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

8. Solving Triangle if angle is obtuse
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
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

9. Inclusion Exclusion Principle
2p
n(A u B0 = n(A) + n(B) - n(A n B)
one triangle
nCrx^n-ry^r

10. distance between focus and directrix
2p
length from one covertex to the other 2b
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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

11. Combinations

12. Permutations
m X N - rows by columns
nCrx^n-ry^r
2b²/a
Order Matters

13. Focal Width of Ellipses
(x-h)^2 + (y-k)^2 = r^2
nCrx^n-ry^r
2b²/a
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

14. Addition Principle
Two Triangles
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
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

15. If A is obtuse a> b
one triangle
No triangle
nPr= (n!)/(n-r)!
1/ sin t

16. tan t
length from one covertex to the other 2b
sin2 t + cos2 t =
sin t/ cos t
(side adjacent to given angle) sin (given angle) - h = b(sina)

17. Combination Formula
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nCr= (n!)/((n-r)! r!)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
the shortest axis of an ellipse 2b

18. Binomial Theorem
y= +-(a/b) (x-h) + k
nCrx^n-ry^r
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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.

19. If A is acute a = h
2b²/a
order Doesn't Matter
one triangle
length from one covertex to the other 2b

20. Permutation Formula
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.
nPr= (n!)/(n-r)!
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
(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

21. Asymptote of hyperbola that opens up and down
center - p
y= +-(a/b) (x-h) + k
2b²/a
Two Triangles

22. Major Axis
ad - bc
2b²/a
the longest axis of an ellipse 2a
_ _ 1/detA * | d -b | |-c a | - -

23. Ellipses Conic Section
4p
one triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle

24. Law of Cosines
c²=a²+b²-2abcosC
Order Matters
Two Triangles
Given an m x n matrix A - its transpose is the n x m

25. Multiply Matrices
nCrx^n-ry^r
Multiply Row By Column - Columns of first must be equal to rows of second
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

26. matrices order
m X N - rows by columns
sin t/ cos t
sin2 t + cos2 t =
c^2 = a^2 - b^2

27. 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.
1/ cos t
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.

28. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)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
sin t/ cos t
1/ sin t

29. If A is obtuse a=< b
Order Matters
center - p
No triangle
y= +-(b/a) (x-h) + k

30. csc t
one 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.
1/ sin t
2 events that can't be done together.

31. If A is acute a > h
center - p
order Doesn't Matter
one triangle
Order Matters

32. Focal Width
Multiply Row By Column - Columns of first must be equal to rows of second
2 events that can't be done together.
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
4p

33. sec2 t
the shortest axis of an ellipse 2b
one triangle
= 1 + tan2 t
nCr= (n!)/((n-r)! r!)

34. Heron's Formula
nCr= (n!)/((n-r)! r!)
order Doesn't Matter
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
sinA/a=sinB/b=sinC/c

35. h =
(side adjacent to given angle) sin (given angle) - h = b(sina)
n(A u B0 = n(A) + n(B) - n(A n B)
Order Matters
nCrx^n-ry^r

36. Law of Sines
sinA/a=sinB/b=sinC/c
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Given an m x n matrix A - its transpose is the n x m
(x-h)^2 + (y-k)^2 = r^2

37. Complement Principle
sinA/a=sinB/b=sinC/c
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
c^2 = a^2 + b^2
one triangle

38. Determinant
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
m X N - rows by columns
ad - bc

39. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Length of one vertex to the other 2a
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
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.

40. Mutually Exclusive

41. Conjugate Axis
length from one covertex to the other 2b
sinA/a=sinB/b=sinC/c
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

42. Area Of a Triangle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
2b²/a
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

43. Focus of ellipses
2p
one triangle
c^2 = a^2 - b^2
Two Triangles

44. Focus of Parabola
nCrx^n-ry^r
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Center + P
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

45. Inverse of 2X2 matrix
y= +-(b/a) (x-h) + k
the shortest axis of an ellipse 2b
ratio
_ _ 1/detA * | d -b | |-c a | - -

46. 1=
Center + P
c²=a²+b²-2abcosC
ad - bc
sin2 t + cos2 t =

47. If A is acute a<h
No 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.
(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

48. Minor Axis
one triangle
2b²/a
= 1 + tan2 t
the shortest axis of an ellipse 2b

49. odds:
the longest axis of an ellipse 2a
sin2 t + cos2 t =
ratio
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.

50. 1 + tan2 t =
m X N - rows by columns
Given an m x n matrix A - its transpose is the n x m
sec2 t
sinA/a=sinB/b=sinC/c