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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. Focus of Parabola
Center + P
c^2 = a^2 - b^2
length from one covertex to the other 2b
n(A u B0 = n(A) + n(B) - n(A n B)

2. 1 + tan2 t =
2 events that can't be done together.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
sec2 t
= 1 + tan2 t

3. If A is acute a<h
No triangle
one triangle
Length of one vertex to the other 2a
sec2 t

4. Transverse Axis
Length of one vertex to the other 2a
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.
2 events that can't be done together.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

5. Inverse of 2X2 matrix
No triangle
(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
_ _ 1/detA * | d -b | |-c a | - -

6. Addition Principle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
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.
the longest axis of an ellipse 2a
one triangle

7. Adding Matrices
4p
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.
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
1

8. sec t
ad - bc
1/ cos t
2 events that can't be done together.
Order Matters

9. sec2 t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
order Doesn't Matter
1/ sin t
= 1 + tan2 t

10. distance between focus and directrix
nPr= (n!)/(n-r)!
n(A u B0 = n(A) + n(B) - n(A n B)
= 1 + tan2 t
2p

11. Focus of ellipses
c^2 = a^2 - b^2
(x-h)^2 + (y-k)^2 = r^2
nCr= (n!)/((n-r)! r!)
n(A u B0 = n(A) + n(B) - n(A n B)

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

13. h =
Center + P
Length of one vertex to the other 2a
y= +-(a/b) (x-h) + k
(side adjacent to given angle) sin (given angle) - h = b(sina)

14. Probabilty
Center + P
(x-h)^2 + (y-k)^2 = r^2
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

15. Permutation Formula
No triangle
nPr= (n!)/(n-r)!
_ _ 1/detA * | d -b | |-c a | - -
Center + P

16. Major Axis
2b²/a
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the longest axis of an ellipse 2a
one triangle

17. Circle Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
Two Triangles
(x-h)^2 + (y-k)^2 = r^2

18. Conjugate Axis
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
1/ sin t
length from one covertex to the other 2b
the shortest axis of an ellipse 2b

19. 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
one triangle
ad - bc
nCrx^n-ry^r

20. Combination Formula
nCr= (n!)/((n-r)! r!)
length from one covertex to the other 2b
sec2 t
2p

21. Asymptote of hyperbola that opens up and down
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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
No triangle

22. odds:
2b²/a
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
ratio

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

24. sin2 t + cos2 t =
y= +-(a/b) (x-h) + k
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
1

25. Law of Cosines
length from one covertex to the other 2b
No triangle
_ _ 1/detA * | d -b | |-c a | - -
c²=a²+b²-2abcosC

26. The Multiplication Principle
the longest axis of an ellipse 2a
nPr= (n!)/(n-r)!
1/ cos 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.

27. Complement Principle
1/ sin t
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)
Multiply Row By Column - Columns of first must be equal to rows of second

28. Law of Sines
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
4p
sinA/a=sinB/b=sinC/c

29. Solving Triangle if angle is obtuse
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
c^2 = a^2 - b^2
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

30. matrices order
1/ cos t
m X N - rows by columns
c^2 = a^2 - b^2
n(A u B0 = n(A) + n(B) - n(A n B)

31. Directrix
center - p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
sin2 t + cos2 t =
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

32. If A is acute a = h
nCrx^n-ry^r
Given an m x n matrix A - its transpose is the n x m
c²=a²+b²-2abcosC
one triangle

33. tan t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
4p
the shortest axis of an ellipse 2b
sin t/ cos t

34. Combinations

35. Permutations
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
the longest axis of an ellipse 2a
Order Matters

36. Area Of a Triangle
y= +-(a/b) (x-h) + k
the shortest axis of an ellipse 2b
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.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

37. Multiply Matrices
No 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
Multiply Row By Column - Columns of first must be equal to rows of second
2b²/a

38. Determinant
ad - bc
Two Triangles
_ _ 1/detA * | d -b | |-c a | - -
nCrx^n-ry^r

39. Focus of Hyperbola
the longest axis of an ellipse 2a
= 1 + tan2 t
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

40. csc t
1/ sin t
sin2 t + cos2 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

41. If A is obtuse a=< b
No triangle
y= +-(b/a) (x-h) + k
1/ cos t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

42. Focal Width
4p
2p
c²=a²+b²-2abcosC
the shortest axis of an ellipse 2b

43. Inclusion Exclusion Principle
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
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
No triangle

44. Equations of Hyperbola
(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
y= +-(b/a) (x-h) + k
1/ sin t
1

45. Binomial Theorem
y= +-(b/a) (x-h) + k
nCrx^n-ry^r
sinA/a=sinB/b=sinC/c
Center + P

46. Focal Width of Ellipses
n(A u B0 = n(A) + n(B) - n(A n B)
Order Matters
2b²/a
m X N - rows by columns

47. If A is obtuse a> b
one triangle
Center + P
y= +-(b/a) (x-h) + k
2b²/a

48. Asymptote of hyperbola that opens left and right.
(x-h)^2 + (y-k)^2 = r^2
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
y= +-(b/a) (x-h) + k
c²=a²+b²-2abcosC

49. Transpose Matrices
Given an m x n matrix A - its transpose is the n x m
Two Triangles
(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
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

50. If A is acute h<a<b
No triangle
(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
Two Triangles