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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. h =
4p
(side adjacent to given angle) sin (given angle) - h = b(sina)
(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
2p

2. sin2 t + cos2 t =
If A is a subset of a universal set U - then n(A) p n(U) - n(_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
center - p
1

3. Minor Axis
1/ cos t
the shortest axis of an ellipse 2b
1/ sin t
nCr= (n!)/((n-r)! r!)

4. Equation of Parabola
2b²/a
Multiply Row By Column - Columns of first must be equal to rows of second
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

5. distance between focus and directrix
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
2p
one triangle

6. 1=
sin2 t + cos2 t =
c^2 = a^2 + b^2
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.
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

7. Heron's Formula
c²=a²+b²-2abcosC
1
No 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. Transverse Axis
Length of one vertex to the other 2a
the longest axis of an ellipse 2a
n(A u B0 = n(A) + n(B) - n(A n B)
the shortest axis of an ellipse 2b

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

10. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2 = r^2
(side adjacent to given angle) sin (given angle) - h = b(sina)

11. Circle Conic Section
(x-h)^2 + (y-k)^2 = r^2
one triangle
4p
length from one covertex to the other 2b

12. If A is obtuse a> b
n(A u B0 = n(A) + n(B) - n(A n B)
y= +-(a/b) (x-h) + k
sec2 t
one triangle

13. 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
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
sec2 t
nPr= (n!)/(n-r)!

14. Directrix
= 1 + tan2 t
c^2 = a^2 - b^2
c²=a²+b²-2abcosC
center - p

15. Permutations
Given an m x n matrix A - its transpose is the n x m
Order Matters
c²=a²+b²-2abcosC
m X N - rows by columns

16. Determinant
(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
ad - bc
one triangle
c²=a²+b²-2abcosC

17. sec2 t
nCrx^n-ry^r
2 events that can't be done together.
sinA/a=sinB/b=sinC/c
= 1 + tan2 t

18. Combinations

19. Major Axis
y= +-(b/a) (x-h) + k
Order Matters
c^2 = a^2 + b^2
the longest axis of an ellipse 2a

20. csc t
No triangle
1/ sin t
Center + P
(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. 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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
one triangle

22. Focus of ellipses
c^2 = a^2 - b^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
sec2 t
cos t/ sin t

23. Equations of Hyperbola
1/ sin t
No triangle
length from one covertex to the other 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

24. Area Of a Triangle
Length of one vertex to the other 2a
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Multiply Row By Column - Columns of first must be equal to rows of second
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.

25. Asymptote of hyperbola that opens up and down
one triangle
one triangle
y= +-(a/b) (x-h) + k
Multiply Row By Column - Columns of first must be equal to rows of second

26. 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
ratio
Given an m x n matrix A - its transpose is the n x m
one triangle

27. Combination Formula
nCr= (n!)/((n-r)! r!)
4p
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.

28. tan t
c²=a²+b²-2abcosC
nCrx^n-ry^r
sin t/ cos t
1/ cos t

29. cot
one triangle
cos t/ sin t
1/ cos t
Length of one vertex to the other 2a

30. Solving Triangle if angle is obtuse
y= +-(b/a) (x-h) + k
ad - bc
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Center + P

31. 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
one triangle
nPr= (n!)/(n-r)!
No triangle

32. Mutually Exclusive

33. Conjugate Axis
m X N - rows by columns
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
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.

34. Transpose Matrices
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 shortest axis of an ellipse 2b
the longest axis of an ellipse 2a

35. Law of Sines
center - p
sinA/a=sinB/b=sinC/c
ad - bc
nPr= (n!)/(n-r)!

36. Inverse of 2X2 matrix
y= +-(a/b) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
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.
4p

37. Law of Cosines
Multiply Row By Column - Columns of first must be equal to rows of second
c²=a²+b²-2abcosC
nCrx^n-ry^r
order Doesn't Matter

38. Inclusion Exclusion Principle
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
n(A u B0 = n(A) + n(B) - n(A n B)
4p

39. odds:
order Doesn't Matter
(side adjacent to given angle) sin (given angle) - h = b(sina)
ratio
1

40. Permutation Formula
No triangle
y= +-(a/b) (x-h) + k
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.
nPr= (n!)/(n-r)!

41. Focal Width of Ellipses
c²=a²+b²-2abcosC
(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
ad - bc
2b²/a

42. Complement Principle
2 events that can't be done together.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Two Triangles
c²=a²+b²-2abcosC

43. If A is obtuse a=< b
2 events that can't be done together.
No triangle
sec2 t
cos t/ sin t

44. If A is acute a<h
No triangle
4p
sin t/ cos t
ratio

45. Focal Width
m X N - rows by columns
= 1 + tan2 t
Order Matters
4p

46. If A is acute a > h
one triangle
c^2 = a^2 - b^2
If A is a subset of a universal set U - then n(A) p n(U) - n(_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

47. Focus of Hyperbola
center - p
c^2 = a^2 + b^2
sinA/a=sinB/b=sinC/c
_ _ 1/detA * | d -b | |-c a | - -

48. If A is acute h<a<b
Length of one vertex to the other 2a
Two Triangles
sin2 t + cos2 t =
c²=a²+b²-2abcosC

49. Multiply Matrices
(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
sin t/ cos t
nCr= (n!)/((n-r)! r!)

50. matrices order
m X N - rows by columns
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/ cos t
sin t/ cos t