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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. sec2 t
2 events that can't be done together.
sec2 t
_ _ 1/detA * | d -b | |-c a | - -
= 1 + tan2 t

2. tan t
sinA/a=sinB/b=sinC/c
Given an m x n matrix A - its transpose is the n x m
n(A u B0 = n(A) + n(B) - n(A n B)
sin t/ cos t

3. csc t
c^2 = a^2 + b^2
1/ sin t
2p
(side adjacent to given angle) sin (given angle) - h = b(sina)

4. Determinant
ad - bc
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c²=a²+b²-2abcosC
c^2 = a^2 + b^2

5. Conjugate Axis
nPr= (n!)/(n-r)!
y= +-(b/a) (x-h) + k
4p
length from one covertex to the other 2b

6. Focus of ellipses
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
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

7. Multiply Matrices
sin2 t + cos2 t =
Multiply Row By Column - Columns of first must be equal to rows of second
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

8. Permutation Formula
1
nPr= (n!)/(n-r)!
1/ cos t
length from one covertex to the other 2b

9. Asymptote of hyperbola that opens up and down
_ _ 1/detA * | d -b | |-c a | - -
nCrx^n-ry^r
y= +-(a/b) (x-h) + k
Two Triangles

10. Mutually Exclusive

11. Combination Formula
ratio
the shortest axis of an ellipse 2b
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nCr= (n!)/((n-r)! r!)

12. Transpose Matrices
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
one triangle
Two Triangles

13. Combinations

14. 1=
sin2 t + cos2 t =
Center + P
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

15. Probabilty
nCrx^n-ry^r
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
Center + P

16. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
2 events that can't be done together.
ad - bc
(side adjacent to given angle) sin (given angle) - h = b(sina)

17. Focal Width of Ellipses
2b²/a
one triangle
nPr= (n!)/(n-r)!
Multiply Row By Column - Columns of first must be equal to rows of second

18. 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.
(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
Order Matters
2p

19. If A is acute a > h
No triangle
one triangle
c^2 = a^2 + b^2
Two Triangles

20. Asymptote of hyperbola that opens left and right.
(side adjacent to given angle) sin (given angle) - h = b(sina)
c²=a²+b²-2abcosC
1/ sin t
y= +-(b/a) (x-h) + k

21. 1 + tan2 t =
sec2 t
c^2 = a^2 + b^2
nPr= (n!)/(n-r)!
nCr= (n!)/((n-r)! r!)

22. Minor Axis
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c²=a²+b²-2abcosC
the shortest axis of an ellipse 2b
sec2 t

23. Binomial Theorem
sin t/ cos t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
one triangle
nCrx^n-ry^r

24. Adding Matrices
c^2 = a^2 + b^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
ratio
c²=a²+b²-2abcosC

25. h =
2 events that can't be done together.
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 of one vertex to the other 2a
(side adjacent to given angle) sin (given angle) - h = b(sina)

26. Inclusion Exclusion Principle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Order Matters
n(A u B0 = n(A) + n(B) - n(A n B)
(x-h)^2 + (y-k)^2 = r^2

27. Cramer's rule
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
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
(side adjacent to given angle) sin (given angle) - h = b(sina)
sec2 t

28. If A is acute h<a<b
y= +-(a/b) (x-h) + k
1
Two Triangles
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. sec 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
4p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
1/ cos t

30. Focus of Hyperbola
c^2 = a^2 + b^2
2p
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

31. Law of Cosines
c²=a²+b²-2abcosC
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Given an m x n matrix A - its transpose is the n x m
No triangle

32. If A is obtuse a> b
4p
one triangle
Multiply Row By Column - Columns of first must be equal to rows of second
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

33. Permutations
sec2 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.
Order Matters

34. matrices order
m X N - rows by columns
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.
Given an m x n matrix A - its transpose is the n x m
the longest axis of an ellipse 2a

35. Complement Principle
c^2 = a^2 + b^2
sin t/ cos t
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
c²=a²+b²-2abcosC

36. Ellipses Conic Section
2p
Given an m x n matrix A - its transpose is the n x m
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
sin t/ cos t

37. If A is acute a = h
(x-h)^2 + (y-k)^2 = r^2
order Doesn't Matter
one triangle
Length of one vertex to the other 2a

38. Major Axis
ad - bc
Given an m x n matrix A - its transpose is the n x m
the longest axis of an ellipse 2a
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

39. If A is acute a<h
(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
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.
one triangle
No triangle

40. Focal Width
sin t/ cos t
n(A u B0 = n(A) + n(B) - n(A n B)
4p
2b²/a

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
length from one covertex to the other 2b
one triangle
1

42. odds:
ratio
the shortest axis of an ellipse 2b
sin2 t + cos2 t =
order Doesn't Matter

43. Transverse Axis
c²=a²+b²-2abcosC
Order Matters
center - p
Length of one vertex to the other 2a

44. distance between focus and directrix
2p
Given an m x n matrix A - its transpose is the n x m
center - p
one triangle

45. Addition Principle
1/ sin t
length from one covertex to the other 2b
2p
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.

46. 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
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.
Order Matters
one triangle

47. If A is obtuse a=< b
Given an m x n matrix A - its transpose is the n x m
ad - bc
cos t/ sin t
No triangle

48. Circle Conic Section
sin t/ cos t
c^2 = a^2 + b^2
nPr= (n!)/(n-r)!
(x-h)^2 + (y-k)^2 = r^2

49. Equations of Hyperbola
2b²/a
(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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

50. 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.
Length of one vertex to the other 2a
No triangle
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products