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. Equations of Hyperbola
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.
(x-h)^2 + (y-k)^2 = r^2
m X N - rows by columns
(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

2. cot
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
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
= 1 + tan2 t
cos t/ sin t

3. Conjugate Axis
length from one covertex to the other 2b
one triangle
ad - bc
Given an m x n matrix A - its transpose is the n x m

4. Asymptote of hyperbola that opens up and down
n(A u B0 = n(A) + n(B) - n(A n B)
2p
y= +-(a/b) (x-h) + k
one triangle

5. Permutations
Order Matters
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
length from one covertex to the other 2b
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

6. tan t
sin t/ cos t
nCr= (n!)/((n-r)! r!)
y= +-(a/b) (x-h) + k
2 events that can't be done together.

7. If A is acute h<a<b
Two Triangles
(side adjacent to given angle) sin (given angle) - h = b(sina)
cos t/ sin t
m X N - rows by columns

8. Directrix
center - p
sec2 t
1
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

9. Focus of Hyperbola
cos t/ sin t
c^2 = a^2 + b^2
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
2p

10. csc t
1/ sin t
Two Triangles
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

11. Combinations

12. If A is acute a<h
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
_ _ 1/detA * | d -b | |-c a | - -
4p

13. Solving Triangle if angle is obtuse
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
c^2 = a^2 + b^2
_ _ 1/detA * | d -b | |-c a | - -
1/ cos t

14. If A is acute a = h
sec2 t
1
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
one triangle

15. Transverse Axis
Length of one vertex to the other 2a
cos t/ sin t
Order Matters
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

16. Binomial Theorem
nCrx^n-ry^r
Given an m x n matrix A - its transpose is the n x m
sin t/ cos t
sinA/a=sinB/b=sinC/c

17. 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
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
c^2 = a^2 - b^2

18. Focus of Parabola
Length of one vertex to the other 2a
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Center + P
Order Matters

19. Adding Matrices
ratio
(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
1/ sin t

20. Addition Principle
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 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
nCrx^n-ry^r
sin2 t + cos2 t =

21. Circle Conic Section
2p
center - p
(x-h)^2 + (y-k)^2 = r^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.

22. 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.
2p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

23. Law of Cosines
c²=a²+b²-2abcosC
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
center - p
nCrx^n-ry^r

24. sec2 t
1/ cos t
cos t/ sin t
= 1 + tan2 t
n(A u B0 = n(A) + n(B) - n(A n B)

25. Heron's Formula
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
sinA/a=sinB/b=sinC/c
Two Triangles

26. Complement Principle
4p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
y= +-(b/a) (x-h) + k
order Doesn't Matter

27. matrices order
(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
nPr= (n!)/(n-r)!
m X N - rows by columns
2p

28. Permutation Formula
order Doesn't Matter
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
ratio
nPr= (n!)/(n-r)!

29. Equation of Parabola
2 events that can't be done together.
(side adjacent to given angle) sin (given angle) - h = b(sina)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
sec2 t

30. Inclusion Exclusion Principle
Given an m x n matrix A - its transpose is the n x m
_ _ 1/detA * | d -b | |-c a | - -
n(A u B0 = n(A) + n(B) - n(A n B)
2 events that can't be done together.

31. Transpose Matrices
2 events that can't be done together.
Given an m x n matrix A - its transpose is the n x m
2b²/a
y= +-(a/b) (x-h) + k

32. odds:
ratio
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
1
the shortest axis of an ellipse 2b

33. 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
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
1/ sin t
one triangle

34. If A is obtuse a> b
_ _ 1/detA * | d -b | |-c a | - -
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
one triangle
ad - bc

35. Ellipses Conic Section
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nCrx^n-ry^r
n(A u B0 = n(A) + n(B) - n(A n B)
(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

36. Inverse of 2X2 matrix
one triangle
= 1 + tan2 t
_ _ 1/detA * | d -b | |-c a | - -
Given an m x n matrix A - its transpose is the n x m

37. Determinant
1
sin2 t + cos2 t =
ad - bc
m X N - rows by columns

38. Focal Width
y= +-(b/a) (x-h) + k
4p
m X N - rows by columns
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

39. Multiply Matrices
Two Triangles
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
Multiply Row By Column - Columns of first must be equal to rows of second

40. 1=
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
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
sin2 t + cos2 t =
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

41. sin2 t + cos2 t =
nCr= (n!)/((n-r)! r!)
1
y= +-(b/a) (x-h) + k
c²=a²+b²-2abcosC

42. Asymptote of hyperbola that opens left and right.
ad - bc
y= +-(b/a) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
the shortest axis of an ellipse 2b

43. Mutually Exclusive

44. Cramer's rule
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
nCrx^n-ry^r
one triangle
4p

45. h =
sin2 t + cos2 t =
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
(side adjacent to given angle) sin (given angle) - h = b(sina)
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

46. Minor Axis
(side adjacent to given angle) sin (given angle) - h = b(sina)
m X N - rows by columns
1/ cos t
the shortest axis of an ellipse 2b

47. Area Of a Triangle
sin2 t + cos2 t =
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
Two Triangles
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

48. 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
ratio
(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

49. sec t
sin2 t + cos2 t =
m X N - rows by columns
(x-h)^2 + (y-k)^2 = r^2
1/ cos t

50. 1 + tan2 t =
sec2 t
y= +-(b/a) (x-h) + k
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
No triangle