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Mathematical quiz displaying formulas using LaTeX/MathML.

Introduction #

This quiz can only be presented correctly by a browser capable of displaying mathematical formulas, e. g. Mozilla.

This quiz tests your knowledge in the field of "Advanced Calculus".

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0

Qstn_name_number_1 #

1

Qstn_phrase_1 #

$ sin 0 = $

Correct_answer_1 #

0

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Qstn_name_number_2

2

Qstn_phrase_2

$ tan (\pi / 4) = $

Correct_answer_2

1

Hints_2

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Qstn_name_number_3

3

Qstn_phrase_3

$ cos (\pi) = $

Correct_answer_3

-1

Hints_3

Reward_3

Qstn_name_number_4

4

Qstn_phrase_4

$sin^2 x + cos^2 x=$

Correct_answer_4

1

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Reward_4

Qstn_name_number_5

5

Qstn_phrase_5

The sine function is an:
[a] increasing function
[b] decreasing function
[c] non-monotonous function

Correct_answer_5

[c]

Hints_5

Reward_5

Qstn_name_number_6

6

Qstn_phrase_6

Which of the following statements are associated (click 2 buttons):
[a] $ y = sin x $
[b] $ y = cos x $
[c] $ y = tan x $
[d] $ y' = sin x $
[e] $ y' = - cos x $
[f] $ y' = - sin x $
[g] $ y' = cos ^ 2 x $

Correct_answer_6

[b][f]

Hints_6

Reward_6

Qstn_name_number_7

7

Qstn_phrase_7

Which of the following statements are associated (click 2 buttons):
[a] $ y=ln x $
[b] $ y= e^x $
[c] $ y= \sqrt x$
[d] $ y' = x $
[e] $ y' = \sqrt x$
[f] $ y' = e^{-x} $
[g] $ y'=1/x^2 $
[h] $ y'=1/x$

Correct_answer_7

[a][h]

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Qstn_name_number_8

8

Qstn_phrase_8

Can $ ln(a/b) $ be rewritten:
[a] $ ln a + ln b $
[b] $ ln a \cdot ln b $
[c] Nothing simpler
Click a button..

Correct_answer_8

[c]

Hints_8

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Qstn_name_number_9

9

Qstn_phrase_9

Can $ ln(a+b) $ be rewritten:
[a] $ {ln a} / { ln b } $
[b] $ ln a - ln b $
[c] Nothing simpler

Correct_answer_9

[b]

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Qstn_name_number_10

10

Qstn_phrase_10

To which of the following expressions can you rewrite $ ( x ^ a ) ^ b $:
[a] $ x ^ { a + b } $
[b] $ x^a \cdot x^b $
[c] $ x ^ (a^b) $
[d] $ x ^ { a \cdot b } $

Correct_answer_10

[d]

Hints_10

Reward_10

Qstn_name_number_11

11

Qstn_phrase_11

Which of the following expressions corresponds to $ e ^{ a + b } $:
[a] $ e^a + e^b $
[b] $ e^a \cdot e^b $
[c] None of these expressions

Correct_answer_11

[b]

Hints_11

Reward_11

Qstn_name_number_12

12

Qstn_phrase_12

Is $ |5| $
[a] 5 or
[b] $ \pm 5 $

Correct_answer_12

[a]

Hints_12

Reward_12

Qstn_name_number_13

13

Qstn_phrase_13

Is $ \sqrt 9 $ equivalent to:
[a] 3
[b] $ \pm 3 $

Correct_answer_13

[a]

Hints_13

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Qstn_name_number_14

14

Qstn_phrase_14

Reduce the fraction $ \frac {x^2 - y^2} {x - y } $
Enter 3 characters separated by blanks:

Correct_answer_14

{.1 x+y }{ y+x }

Hints_14

Reward_14

Qstn_name_number_15

15

Qstn_phrase_15

Which of the following statements is/are correct:
[a] f is continuous $ \Leftrightarrow $ f is differentiable
[b] f is continuous $ \Rightarrow $ f is differentiable
[c] f is continuous $ \Leftarrow $ f is differentiable
[d] none of the assertions above.

Correct_answer_15

[c]

Hints_15

Reward_15

Qstn_name_number_16

16

Qstn_phrase_16

Correct_answer_16

Hints_16

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Qstn_name_number_17

17

Qstn_phrase_17

Correct_answer_17

Hints_17

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Qstn_name_number_18

18

Qstn_phrase_18

Correct_answer_18

Hints_18

Reward_18

Qstn_name_number_19

19

Qstn_phrase_19

Correct_answer_19

Hints_19

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Qstn_name_number_20

20

Qstn_phrase_20

Correct_answer_20

Hints_20

Reward_20

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