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. Permutation Formula
nPr= (n!)/(n-r)!
1/ sin t
2 events that can't be done together.
Order Matters

2. Asymptote of hyperbola that opens up and down
_ _ 1/detA * | d -b | |-c a | - -
y= +-(a/b) (x-h) + k
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
1

3. Inclusion Exclusion Principle
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
y= +-(b/a) (x-h) + k
n(A u B0 = n(A) + n(B) - n(A n B)

4. Law of Cosines
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 Doesn't Matter
c²=a²+b²-2abcosC

5. sec t
2 events that can't be done together.
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.
1/ cos t
one triangle

6. sin2 t + cos2 t =
sin2 t + cos2 t =
No triangle
c^2 = a^2 + b^2
1

7. The Multiplication Principle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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.
nPr= (n!)/(n-r)!
nCrx^n-ry^r

8. Focus of Hyperbola
Center + P
sin2 t + cos2 t =
c^2 = a^2 + b^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.

9. Probabilty
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.
1/ cos t
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

10. Combination Formula
nCr= (n!)/((n-r)! r!)
Multiply Row By Column - Columns of first must be equal to rows of second
nPr= (n!)/(n-r)!
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

11. distance between focus and directrix
2p
(side adjacent to given angle) sin (given angle) - h = b(sina)
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

12. Multiply Matrices
n(A u B0 = n(A) + n(B) - n(A n B)
1/ sin t
sin t/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second

13. Focal Width
_ _ 1/detA * | d -b | |-c a | - -
2 events that can't be done together.
4p
one triangle

14. Permutations
Length of one vertex to the other 2a
2p
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Order Matters

15. If A is obtuse a=< b
center - p
No triangle
nCr= (n!)/((n-r)! r!)
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.

16. Complement Principle
order Doesn't Matter
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
Order Matters
sinA/a=sinB/b=sinC/c

17. Addition 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.
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)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.
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

18. Adding Matrices
(side adjacent to given angle) sin (given angle) - h = b(sina)
nCrx^n-ry^r
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
_ _ 1/detA * | d -b | |-c a | - -

19. Asymptote of hyperbola that opens left and right.
sin2 t + cos2 t =
1/ cos t
ad - bc
y= +-(b/a) (x-h) + k

20. csc t
No triangle
1/ sin t
center - p
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

21. Equation of Parabola
nCrx^n-ry^r
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
nPr= (n!)/(n-r)!

22. Focus of ellipses
c^2 = a^2 - b^2
length from one covertex to the other 2b
m X N - rows by columns
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)

23. Directrix
nCrx^n-ry^r
center - p
cos t/ sin t
No triangle

24. matrices order
nCrx^n-ry^r
c^2 = a^2 + b^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
m X N - rows by columns

25. Heron's Formula
cos t/ sin 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
one triangle
m X N - rows by columns

26. Combinations

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

27. If A is acute a<h
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
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
No triangle
ratio

28. Transverse Axis
sin2 t + cos2 t =
2 events that can't be done together.
Length of one vertex to the other 2a
1/ sin t

29. odds:
sin t/ cos t
ratio
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
No triangle

30. Determinant
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Order Matters
2b²/a
ad - bc

31. tan t
No triangle
y= +-(b/a) (x-h) + k
sin t/ cos t
(x-h)^2 + (y-k)^2 = r^2

32. Focus of Parabola
length from one covertex to the other 2b
Center + P
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

33. Ellipses Conic Section
(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
one triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
c^2 = a^2 + b^2

34. Area Of a Triangle
sin t/ cos t
Given an m x n matrix A - its transpose is the n x m
the shortest axis of an ellipse 2b
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.

35. Focal Width of Ellipses
the shortest axis of an ellipse 2b
2b²/a
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
cos t/ sin t

36. sec2 t
No triangle
= 1 + tan2 t
sinA/a=sinB/b=sinC/c
_ _ 1/detA * | d -b | |-c a | - -

37. Binomial Theorem
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nCrx^n-ry^r
nPr= (n!)/(n-r)!
ratio

38. Inverse of 2X2 matrix
_ _ 1/detA * | d -b | |-c a | - -
2p
center - p
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

39. Law of Sines
_ _ 1/detA * | d -b | |-c a | - -
one triangle
sinA/a=sinB/b=sinC/c
the shortest axis of an ellipse 2b

40. Minor Axis
the shortest axis of an ellipse 2b
center - p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
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.

41. cot
ad - bc
Order Matters
cos t/ sin t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

42. Solving Triangle if angle is obtuse
ad - bc
c^2 = a^2 - b^2
c²=a²+b²-2abcosC
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS

43. Conjugate Axis
Two Triangles
1
length from one covertex to the other 2b
sec2 t

44. If A is acute h<a<b
(x-h)^2 + (y-k)^2 = r^2
Two Triangles
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

45. Circle Conic Section
_ _ 1/detA * | d -b | |-c a | - -
(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.
Given an m x n matrix A - its transpose is the n x m

46. h =
Length of one vertex to the other 2a
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
n(A u B0 = n(A) + n(B) - n(A n B)
(side adjacent to given angle) sin (given angle) - h = b(sina)

47. 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
one triangle
n(A u B0 = n(A) + n(B) - n(A n B)
Two Triangles

48. Cramer's rule
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= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
y= +-(b/a) (x-h) + k
_ _ 1/detA * | d -b | |-c a | - -

49. If A is acute a = h
n(A u B0 = n(A) + n(B) - n(A n B)
c^2 = a^2 + b^2
nCr= (n!)/((n-r)! r!)
one triangle

50. 1 + tan2 t =
sec2 t
1/ sin t
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger 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