Test your basic knowledge |

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. If A is obtuse a> b
one triangle
1/ cos t
y= +-(b/a) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

2. Permutations
Order Matters
y= +-(a/b) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -
ratio

3. Focus of Parabola
c^2 = a^2 + b^2
order Doesn't Matter
Center + P
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

4. sec t
nCr= (n!)/((n-r)! r!)
the shortest axis of an ellipse 2b
1/ cos t
Length of one vertex to the other 2a

5. Transpose Matrices
one triangle
Given an m x n matrix A - its transpose is the n x m
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Two Triangles

6. 1=
(x-h)^2 + (y-k)^2 = r^2
Length of one vertex to the other 2a
sin2 t + cos2 t =
y= +-(b/a) (x-h) + k

7. Area Of a Triangle
y= +-(b/a) (x-h) + k
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
ad - bc

8. Equation of Parabola
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
y= +-(a/b) (x-h) + k
(side adjacent to given angle) sin (given angle) - h = b(sina)

9. Complement Principle
nPr= (n!)/(n-r)!
c^2 = a^2 + b^2
center - p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

10. Inverse of 2X2 matrix
(x-h)^2 + (y-k)^2 = r^2
_ _ 1/detA * | d -b | |-c a | - -
Length of one vertex to the other 2a
sin t/ cos t

11. Conjugate Axis
1/ sin t
4p
length from one covertex to the other 2b
sinA/a=sinB/b=sinC/c

12. Binomial Theorem
length from one covertex to the other 2b
nCrx^n-ry^r
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

13. Focus of Hyperbola
y= +-(b/a) (x-h) + k
ad - bc
c^2 = a^2 + b^2
order Doesn't Matter

14. 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
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
2 events that can't be done together.
No triangle

15. Inclusion Exclusion Principle
n(A u B0 = n(A) + n(B) - n(A n B)
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
c^2 = a^2 + b^2
sec2 t

16. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nPr= (n!)/(n-r)!
ratio
sec2 t

17. Circle Conic Section
sec2 t
4p
nPr= (n!)/(n-r)!
(x-h)^2 + (y-k)^2 = r^2

18. Focal Width
ad - bc
4p
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
y= +-(a/b) (x-h) + k

19. h =
m X N - rows by columns
1
(side adjacent to given angle) sin (given angle) - h = b(sina)
Multiply Row By Column - Columns of first must be equal to rows of second

20. The Multiplication Principle
1/ sin t
= 1 + tan2 t
2 events that can't be done together.
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.

21. If A is acute a > h
n(A u B0 = n(A) + n(B) - n(A n B)
center - p
one triangle
Given an m x n matrix A - its transpose is the n x m

22. Minor Axis
sin2 t + cos2 t =
Length of one vertex to the other 2a
the shortest axis of an ellipse 2b
c^2 = a^2 - b^2

23. Equations of Hyperbola
1/ sin t
= 1 + tan2 t
1/ cos 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

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

25. Combination Formula
one triangle
nCr= (n!)/((n-r)! r!)
c²=a²+b²-2abcosC
Length of one vertex to the other 2a

26. Adding Matrices
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
nCr= (n!)/((n-r)! r!)
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.
one triangle

27. Major Axis
the longest axis of an ellipse 2a
one triangle
nPr= (n!)/(n-r)!
the shortest axis of an ellipse 2b

28. tan t
4p
sin t/ cos t
sinA/a=sinB/b=sinC/c
Length of one vertex to the other 2a

29. cot
cos t/ sin t
sin t/ cos t
n(A u B0 = n(A) + n(B) - n(A n B)
_ _ 1/detA * | d -b | |-c a | - -

30. If A is obtuse a=< 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
= 1 + tan2 t
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

31. Law of Sines
sinA/a=sinB/b=sinC/c
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Length of one vertex to the other 2a
sin t/ cos t

32. Probabilty
length from one covertex to the other 2b
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.
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

33. odds:
nCr= (n!)/((n-r)! r!)
ratio
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1/ sin t

34. csc 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
1/ sin t
Center + P
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

35. Law of Cosines
2b²/a
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
c²=a²+b²-2abcosC
nCrx^n-ry^r

36. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
Given an m x n matrix A - its transpose is the n x m
nCr= (n!)/((n-r)! r!)

37. Asymptote of hyperbola that opens up and down
sin2 t + cos2 t =
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 | - -
y= +-(a/b) (x-h) + k

38. matrices order
(x-h)^2 + (y-k)^2 = r^2
4p
m X N - rows by columns
sinA/a=sinB/b=sinC/c

39. 1 + tan2 t =
the longest axis of an ellipse 2a
c²=a²+b²-2abcosC
sec2 t
Given an m x n matrix A - its transpose is the n x m

40. Solving Triangle if angle is obtuse
1
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
(x-h)^2 + (y-k)^2 = r^2
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

41. Determinant
sec2 t
cos t/ sin t
sinA/a=sinB/b=sinC/c
ad - bc

42. sin2 t + cos2 t =
(side adjacent to given angle) sin (given angle) - h = b(sina)
ratio
c^2 = a^2 + b^2
1

43. Combinations

44. Mutually Exclusive

45. If A is acute a<h
cos t/ sin t
No triangle
Multiply Row By Column - Columns of first must be equal to rows of second
one triangle

46. Transverse Axis
Length of one vertex to the other 2a
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
sinA/a=sinB/b=sinC/c
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

47. Asymptote of hyperbola that opens left and right.
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
n(A u B0 = n(A) + n(B) - n(A n B)
(x-h)^2 + (y-k)^2 = r^2

48. Multiply Matrices
sec2 t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the longest axis of an ellipse 2a
Multiply Row By Column - Columns of first must be equal to rows of second

49. Directrix
m X N - rows by columns
nCrx^n-ry^r
center - p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

50. Focal Width of Ellipses
nPr= (n!)/(n-r)!
Order Matters
2b²/a
order Doesn't Matter