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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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
1/ cos t
c²=a²+b²-2abcosC
sinA/a=sinB/b=sinC/c

2. If A is obtuse a=< b
2 events that can't be done together.
No triangle
Order Matters
Center + P

3. Inclusion Exclusion Principle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
_ _ 1/detA * | d -b | |-c a | - -
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)

4. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
y= +-(a/b) (x-h) + k
4p
1/ sin t

5. cot
c^2 = a^2 - b^2
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
cos t/ sin t
Given an m x n matrix A - its transpose is the n x m

6. Solving Triangle if angle is obtuse
(x-h)^2 + (y-k)^2 = r^2
1/ sin t
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
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

7. Focus of ellipses
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c^2 = a^2 - b^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
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.

8. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
2 events that can't be done together.
(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
cos t/ sin t

9. If A is acute h<a<b
y= +-(b/a) (x-h) + k
c^2 = a^2 + b^2
one triangle
Two Triangles

10. Transverse Axis
Length of one vertex to the other 2a
1/ sin 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.
Order Matters

11. Circle Conic Section
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
one triangle
1
(x-h)^2 + (y-k)^2 = r^2

12. Addition Principle
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.
c^2 = a^2 - b^2
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

13. The Multiplication Principle
Given an m x n matrix A - its transpose is the n x m
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
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
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.

14. tan t
y= +-(a/b) (x-h) + k
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
sin t/ cos t
nCr= (n!)/((n-r)! r!)

15. Combination Formula
Center + P
c^2 = a^2 + b^2
nCr= (n!)/((n-r)! r!)
c²=a²+b²-2abcosC

16. Transpose Matrices
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.
ratio
Given an m x n matrix A - its transpose is the n x m

17. If A is obtuse a> b
order Doesn't Matter
y= +-(a/b) (x-h) + k
one triangle
sin t/ cos t

18. odds:
2 events that can't be done together.
ratio
sinA/a=sinB/b=sinC/c
sin t/ cos t

19. Equations of Hyperbola
Given an m x n matrix A - its transpose is the n x m
4p
(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
Multiply Row By Column - Columns of first must be equal to rows of second

20. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
1
(x-h)^2 + (y-k)^2 = r^2
Order Matters

21. Law of Cosines
one triangle
1/ cos t
c²=a²+b²-2abcosC
c^2 = a^2 + b^2

22. 1=
one triangle
sin2 t + cos2 t =
Multiply Row By Column - Columns of first must be equal to rows of second
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

23. Major Axis
Two Triangles
= 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
the longest axis of an ellipse 2a

24. 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
Center + P
Two Triangles

25. Binomial Theorem
nCrx^n-ry^r
c²=a²+b²-2abcosC
2b²/a
Multiply Row By Column - Columns of first must be equal to rows of second

26. Probabilty
ratio
No triangle
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

27. Combinations

28. If A is acute a > h
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
sin t/ cos t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle

29. Minor Axis
length from one covertex to the other 2b
the shortest axis of an ellipse 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
one triangle

30. Equation of Parabola
y= +-(a/b) (x-h) + k
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
order Doesn't Matter
the longest axis of an ellipse 2a

31. Directrix
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
center - p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
the longest axis of an ellipse 2a

32. Complement Principle
2p
(side adjacent to given angle) sin (given angle) - h = b(sina)
= 1 + tan2 t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

33. Law of Sines
nCr= (n!)/((n-r)! r!)
sinA/a=sinB/b=sinC/c
2p
cos t/ sin t

34. Heron's Formula
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
ratio
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
1

35. matrices order
= 1 + tan2 t
m X N - rows by columns
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

36. Focus of Hyperbola
c^2 = a^2 + b^2
Center + P
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 a is always bigger term

37. Permutations
Multiply Row By Column - Columns of first must be equal to rows of second
y= +-(b/a) (x-h) + k
center - p
Order Matters

38. Focus of Parabola
center - p
Center + P
y= +-(b/a) (x-h) + k
1/ sin t

39. sec2 t
one triangle
1
c²=a²+b²-2abcosC
= 1 + tan2 t

40. csc t
1/ sin t
sinA/a=sinB/b=sinC/c
Two Triangles
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

41. Asymptote of hyperbola that opens up and down
sin t/ cos 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
ad - bc

42. Asymptote of hyperbola that opens left and right.
one triangle
y= +-(b/a) (x-h) + k
Order Matters
nPr= (n!)/(n-r)!

43. distance between focus and directrix
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
(x-h)^2 + (y-k)^2 = r^2
2p
1/ cos t

44. Determinant
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Two Triangles
ad - bc
m X N - rows by columns

45. Conjugate Axis
2 events that can't be done together.
length from one covertex to the other 2b
Center + P
m X N - rows by columns

46. Mutually Exclusive

47. h =
(side adjacent to given angle) sin (given angle) - h = b(sina)
c²=a²+b²-2abcosC
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.
(x-h)^2 + (y-k)^2 = r^2

48. Multiply Matrices
y= +-(b/a) (x-h) + k
the longest axis of an ellipse 2a
nCrx^n-ry^r
Multiply Row By Column - Columns of first must be equal to rows of second

49. Permutation Formula
2 events that can't be done together.
y= +-(b/a) (x-h) + k
sec2 t
nPr= (n!)/(n-r)!

50. If A is acute a = h
1
Given an m x n matrix A - its transpose is the n x m
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
one triangle