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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. Major Axis
nCr= (n!)/((n-r)! r!)
the longest axis of an ellipse 2a
length from one covertex to the other 2b
ad - bc

2. 1 + tan2 t =
one triangle
sec2 t
1/ sin t
2b²/a

3. Ellipses Conic Section
nCrx^n-ry^r
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
one triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

4. Minor Axis
(side adjacent to given angle) sin (given angle) - h = b(sina)
the shortest axis of an ellipse 2b
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

5. tan t
n(A u B0 = n(A) + n(B) - n(A n B)
sin t/ cos t
nPr= (n!)/(n-r)!
_ _ 1/detA * | d -b | |-c a | - -

6. Determinant
cos t/ sin t
c^2 = a^2 - b^2
one triangle
ad - bc

7. matrices order
m X N - rows by columns
_ _ 1/detA * | d -b | |-c a | - -
c^2 = a^2 + b^2
cos t/ sin t

8. Permutations
Length of one vertex to the other 2a
c²=a²+b²-2abcosC
Order Matters
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.

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.
ratio
nPr= (n!)/(n-r)!
c²=a²+b²-2abcosC

10. Focus of ellipses
(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
c^2 = a^2 - b^2
n(A u B0 = n(A) + n(B) - n(A n B)
2b²/a

11. Focus of Parabola
sin2 t + cos2 t =
1
Center + P
c^2 = a^2 + b^2

12. If A is acute h<a<b
c^2 = a^2 - b^2
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
c²=a²+b²-2abcosC

13. Binomial Theorem
nCrx^n-ry^r
(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
one triangle
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

14. 1=
1/ cos t
sin2 t + cos2 t =
No triangle
n(A u B0 = n(A) + n(B) - n(A n B)

15. Focal Width
1/ sin t
c²=a²+b²-2abcosC
Center + P
4p

16. If A is obtuse a=< b
No triangle
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.
Given an m x n matrix A - its transpose is the n x m
sec2 t

17. Conjugate Axis
length from one covertex to the other 2b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
No triangle
y= +-(a/b) (x-h) + k

18. distance between focus and directrix
4p
one triangle
sin2 t + cos2 t =
2p

19. Permutation Formula
sec2 t
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
Multiply Row By Column - Columns of first must be equal to rows of second
nPr= (n!)/(n-r)!

20. Inverse of 2X2 matrix
y= +-(b/a) (x-h) + k
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
_ _ 1/detA * | d -b | |-c a | - -
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

21. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
c^2 = a^2 - b^2
nCrx^n-ry^r
center - p

22. cot
4p
2 events that can't be done together.
cos t/ sin t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

23. sec t
sec2 t
one triangle
1/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

24. Combinations

25. Mutually Exclusive

26. Directrix
order Doesn't Matter
center - p
2 events that can't be done together.
Multiply Row By Column - Columns of first must be equal to rows of second

27. sec2 t
Center + P
2 events that can't be done together.
= 1 + tan2 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.

28. Circle Conic Section
ratio
Length of one vertex to the other 2a
Given an m x n matrix A - its transpose is the n x m
(x-h)^2 + (y-k)^2 = r^2

29. 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.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
center - p
No triangle

30. Combination Formula
2 events that can't be done together.
nCr= (n!)/((n-r)! r!)
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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

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

32. Asymptote of hyperbola that opens up and down
sec2 t
y= +-(a/b) (x-h) + k
nPr= (n!)/(n-r)!
c^2 = a^2 - b^2

33. Equations of Hyperbola
sinA/a=sinB/b=sinC/c
2p
(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
2b²/a

34. Transverse Axis
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 from one covertex to the other 2b
Length of one vertex to the other 2a
center - p

35. h =
c²=a²+b²-2abcosC
(side adjacent to given angle) sin (given angle) - h = b(sina)
No triangle
_ _ 1/detA * | d -b | |-c a | - -

36. Asymptote of hyperbola that opens left and right.
center - p
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
length from one covertex to the other 2b

37. Focal Width of Ellipses
sec2 t
2b²/a
the longest axis of an ellipse 2a
Two Triangles

38. Law of Sines
(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
sinA/a=sinB/b=sinC/c
Given an m x n matrix A - its transpose is the n x m
1/ sin t

39. Adding Matrices
2p
(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
No triangle

40. If A is acute a > h
c^2 = a^2 - b^2
c²=a²+b²-2abcosC
sec2 t
one triangle

41. sin2 t + cos2 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
y= +-(a/b) (x-h) + k
1
Multiply Row By Column - Columns of first must be equal to rows of second

42. Solving Triangle if angle is obtuse
1/ sin t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
n(A u B0 = n(A) + n(B) - n(A n B)
the shortest axis of an ellipse 2b

43. csc t
Two Triangles
sec2 t
1/ sin t
ad - bc

44. If A is obtuse a> b
sec2 t
one triangle
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
c²=a²+b²-2abcosC

45. Multiply Matrices
c²=a²+b²-2abcosC
Given an m x n matrix A - its transpose is the n x m
Multiply Row By Column - Columns of first must be equal to rows of second
order Doesn't Matter

46. Addition Principle
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.
length from one covertex to the other 2b
ratio

47. Heron's Formula
Given an m x n matrix A - its transpose is the n x m
one triangle
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
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. Area Of a Triangle
No triangle
Given an m x n matrix A - its transpose is the n x m
c^2 = a^2 - b^2
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

49. Equation of Parabola
4p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)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.
Two Triangles

50. Probabilty
order Doesn't Matter
_ _ 1/detA * | d -b | |-c a | - -
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
Length of one vertex to the other 2a