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Test your basic knowledge |
CLEP Pre - Calculus 2
Start Test
Study First
Subjects
:
clep
,
math
,
calculus
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. Conjugate Axis
nPr= (n!)/(n-r)!
length from one covertex to the other 2b
the longest axis of an ellipse 2a
c²=a²+b²-2abcosC
2. Focus of Hyperbola
1
c^2 = a^2 + b^2
1/ sin t
(x-h)^2 + (y-k)^2 = r^2
3. sec t
_ _ 1/detA * | d -b | |-c a | - -
1/ cos t
2 events that can't be done together.
4p
4. Adding Matrices
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
ratio
2p
5. If A is acute h<a<b
y= +-(b/a) (x-h) + k
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.
cos t/ sin t
Two Triangles
6. Permutations
Order Matters
sin2 t + cos2 t =
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
2b²/a
7. If A is acute a = h
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
2b²/a
one triangle
Center + P
8. Inclusion Exclusion Principle
c^2 = a^2 - b^2
4p
ratio
n(A u B0 = n(A) + n(B) - n(A n B)
9. Determinant
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)
2b²/a
ad - bc
10. Law of Cosines
c²=a²+b²-2abcosC
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
Multiply Row By Column - Columns of first must be equal to rows of second
No triangle
11. sin2 t + cos2 t =
1
nPr= (n!)/(n-r)!
cos t/ sin t
sin t/ cos t
12. The Multiplication Principle
(side adjacent to given angle) sin (given angle) - h = b(sina)
sinA/a=sinB/b=sinC/c
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
13. h =
1/ sin t
(side adjacent to given angle) sin (given angle) - h = b(sina)
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
14. Combinations
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15. Inverse of 2X2 matrix
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
_ _ 1/detA * | d -b | |-c a | - -
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
16. odds:
ratio
Center + P
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
17. Heron's Formula
length from one covertex to the other 2b
ad - bc
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)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
18. csc t
one triangle
1/ sin t
length from one covertex to the other 2b
nPr= (n!)/(n-r)!
19. Focus of ellipses
c^2 = a^2 - b^2
nCr= (n!)/((n-r)! r!)
Center + P
Given an m x n matrix A - its transpose is the n x m
20. Focal Width
(x-h)^2 + (y-k)^2 = r^2
2p
order Doesn't Matter
4p
21. cot
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.
No triangle
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
cos t/ sin t
22. matrices order
sec2 t
nPr= (n!)/(n-r)!
2b²/a
m X N - rows by columns
23. If A is acute a<h
center - p
Multiply Row By Column - Columns of first must be equal to rows of second
No triangle
n(A u B0 = n(A) + n(B) - n(A n B)
24. Asymptote of hyperbola that opens left and right.
y= +-(b/a) (x-h) + k
nCrx^n-ry^r
one triangle
cos t/ sin t
25. Binomial Theorem
nCrx^n-ry^r
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
4p
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
26. Addition Principle
one triangle
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.
c^2 = a^2 - b^2
27. Transverse Axis
nCrx^n-ry^r
sin2 t + cos2 t =
sin t/ cos t
Length of one vertex to the other 2a
28. distance between focus and directrix
2p
1/ cos t
m X N - rows by columns
order Doesn't Matter
29. 1=
sec2 t
c²=a²+b²-2abcosC
order Doesn't Matter
sin2 t + cos2 t =
30. If A is acute a > h
Given an m x n matrix A - its transpose is the n x m
c^2 = a^2 - b^2
ratio
one triangle
31. Area Of a 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
Two Triangles
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
= 1 + tan2 t
32. Major Axis
No triangle
the longest axis of an ellipse 2a
2 events that can't be done together.
= 1 + tan2 t
33. tan t
2p
Length of one vertex to the other 2a
sin t/ cos t
Multiply Row By Column - Columns of first must be equal to rows of second
34. Solving Triangle if angle is obtuse
the longest axis of an ellipse 2a
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
nCr= (n!)/((n-r)! r!)
c^2 = a^2 + b^2
35. Ellipses Conic Section
2 events that can't be done together.
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
cos t/ sin t
36. Focal Width of Ellipses
To find an obtuse angle you need to use the Law of Cosines and when given SSS or SAS
2b²/a
center - p
y= +-(b/a) (x-h) + k
37. Mutually Exclusive
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38. If A is obtuse a> b
one triangle
nPr= (n!)/(n-r)!
_ _ 1/detA * | d -b | |-c a | - -
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
39. Transpose Matrices
ratio
Given an m x n matrix A - its transpose is the n x m
Two Triangles
A = 1/2ac sin B - where a and c are the lengths of two sides and B is the angle between them.
40. Permutation Formula
sin2 t + cos2 t =
nPr= (n!)/(n-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
y= +-(b/a) (x-h) + k
41. Asymptote of hyperbola that opens up and down
nPr= (n!)/(n-r)!
2b²/a
y= +-(a/b) (x-h) + k
one triangle
42. Directrix
center - p
n(A u B0 = n(A) + n(B) - n(A n B)
nPr= (n!)/(n-r)!
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
43. Cramer's rule
1/ sin t
X= Dx/ D - Y =Dy/ D - Z = Dz/ D - Replace column with products
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
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
44. Equation of Parabola
n(A u B0 = n(A) + n(B) - n(A n B)
one triangle
the shortest axis of an ellipse 2b
regular (opens up/down): 4p(y - k) = (x - h)2 - sideways (opens right/left):4p(x - h) = (y - k)2
45. Circle Conic Section
2p
(x-h)^2 + (y-k)^2 = r^2
Multiply Row By Column - Columns of first must be equal to rows of second
1/ sin t
46. Complement Principle
Multiply Row By Column - Columns of first must be equal to rows of second
(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)
If A is a subset of a universal set U - then n(A) p n(U) - n(_A)
47. Focus of Parabola
m X N - rows by columns
center - p
Center + P
No triangle
48. 1 + tan2 t =
sin2 t + cos2 t =
sec2 t
ad - bc
Order Matters
49. Law of Sines
(side adjacent to given angle) sin (given angle) - h = b(sina)
(x-h)^2 + (y-k)^2/a^2 b^2 = 1 a is always bigger term
y= +-(a/b) (x-h) + k
sinA/a=sinB/b=sinC/c
50. sec2 t
(x-h)^2 + (y-k)^2 = r^2
= 1 + tan2 t
to add or subtract matrices - simply add or subtract matrices only if the have the same dimensions
4p