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. Adding Matrices
4p
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Order Matters
c^2 = a^2 - b^2

2. If A is acute a > h
y= +-(b/a) (x-h) + k
sin2 t + cos2 t =
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
one triangle

3. Addition Principle
nCrx^n-ry^r
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 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.

4. Conjugate Axis
2p
length from one covertex to the other 2b
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Center + P

5. sec t
Multiply Row By Column - Columns of first must be equal to rows of second
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
nCrx^n-ry^r
1/ cos t

6. Determinant
the longest axis of an ellipse 2a
2 events that can't be done together.
(x-h)^2 + (y-k)^2 = r^2
ad - bc

7. Law of Cosines
2p
c²=a²+b²-2abcosC
No triangle
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

8. Focus of ellipses
one triangle
the shortest axis of an ellipse 2b
(x-h)^2 + (y-k)^2 = r^2
c^2 = a^2 - b^2

9. sec2 t
2p
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
= 1 + tan2 t

10. 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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
Center + P
one triangle

11. Law of Sines
No triangle
sin2 t + cos2 t =
2 events that can't be done together.
sinA/a=sinB/b=sinC/c

12. If A is acute h<a<b
2p
Two Triangles
m X N - rows by columns
y= +-(a/b) (x-h) + k

13. Inclusion Exclusion Principle
m X N - rows by columns
Order Matters
n(A u B0 = n(A) + n(B) - n(A n B)
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

14. Focus of Hyperbola
2 events that can't be done together.
the longest axis of an ellipse 2a
c^2 = a^2 + b^2
(x-h)^2 + (y-k)^2 = r^2

15. Equation of Parabola
one triangle
1
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
1/ sin t

16. Area Of a Triangle
y= +-(b/a) (x-h) + k
1
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
length from one covertex to the other 2b

17. cot
the shortest axis of an ellipse 2b
cos t/ sin t
y= +-(b/a) (x-h) + k
one triangle

18. Binomial Theorem
the shortest axis of an ellipse 2b
nCrx^n-ry^r
No triangle
y= +-(b/a) (x-h) + k

19. If A is acute a<h
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
nPr= (n!)/(n-r)!
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
No triangle

20. Complement Principle
sinA/a=sinB/b=sinC/c
No triangle
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
= 1 + tan2 t

21. Transpose Matrices
center - p
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
one triangle
Given an m x n matrix A - its transpose is the n x m

22. Minor Axis
1
(side adjacent to given angle) sin (given angle) - h = b(sina)
one triangle
the shortest axis of an ellipse 2b

23. Cramer's rule
c^2 = a^2 - b^2
nCrx^n-ry^r
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
c²=a²+b²-2abcosC

24. Combinations

25. tan t
Order Matters
sec2 t
one triangle
sin t/ cos t

26. Permutations
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
nCrx^n-ry^r
n(A u B0 = n(A) + n(B) - n(A n B)
Order Matters

27. Asymptote of hyperbola that opens left and right.
(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
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

28. Probabilty
Order Matters
2p
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
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products

29. 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.
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
c²=a²+b²-2abcosC

30. Major Axis
one triangle
Order Matters
1/ cos t
the longest axis of an ellipse 2a

31. Inverse of 2X2 matrix
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.
_ _ 1/detA * | d -b | |-c a | - -
the longest axis of an ellipse 2a

32. Permutation Formula
length from one covertex to the other 2b
nPr= (n!)/(n-r)!
No triangle
order Doesn't Matter

33. 1=
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
sin2 t + cos2 t =
(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.

34. sin2 t + cos2 t =
1
nCr= (n!)/((n-r)! r!)
m X N - rows by columns
the longest axis of an ellipse 2a

35. Combination Formula
nCr= (n!)/((n-r)! r!)
(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
sin2 t + cos2 t =
Given an m x n matrix A - its transpose is the n x m

36. csc t
1/ sin t
the longest axis of an ellipse 2a
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2

37. Heron's Formula
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
2b²/a
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
y= +-(b/a) (x-h) + k

38. Focal Width of Ellipses
2b²/a
nPr= (n!)/(n-r)!
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

39. Directrix
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
nCr= (n!)/((n-r)! r!)
one triangle
center - p

40. Multiply Matrices
(x-h)^2 + (y-k)^2 = r^2
Multiply Row By Column - Columns of first must be equal to rows of second
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
one triangle

41. If A is obtuse a> b
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.
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
Order Matters
one triangle

42. matrices order
c^2 = a^2 + b^2
nCr= (n!)/((n-r)! r!)
m X N - rows by columns
sin t/ cos t

43. odds:
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
ratio
2p

44. Mutually Exclusive

45. Transverse Axis
sec2 t
Length of one vertex to the other 2a
nCr= (n!)/((n-r)! r!)
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

46. Focal Width
Two Triangles
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
4p
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

47. Ellipses Conic Section
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
Length of one vertex to the other 2a
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term

48. distance between focus and directrix
y= +-(b/a) (x-h) + k
Center + P
2p
Length of one vertex to the other 2a

49. Circle Conic Section
one triangle
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 = r^2
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions

50. 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
cos t/ sin t
length from one covertex to the other 2b
y= +-(b/a) (x-h) + k