verify that P⇒Q is true, then verify that the contrapositive statement \overline{P}⇒\overline{Q} is also true.

If an animal does not have a shell then it is not a turtle. True statement.

Given the true statements below, write the converse of each and decide whether or not the converse is also true.

If something tastes sweet, it contains a lot of sugar. False.

Integration by substitution

\frac{\left(1+x^2\right)^5}{10}+C

Integration by parts.

I=\frac{e^{3x}\left(3\cos2x+2\sin⁡2x\right)}{13}+C

Given the true statements below, write the converse of each and decide whether or not the converse is also true.

If it is cold, then it is snowing. False.

Write the contrapositive for: "If a drink is cold then it is refreshing"

If a drink is not refreshing then it is not cold.

Write the converse of the statement.

If an animalcan fly, it has wings.

Integration by substitution

-\frac{2\left(x+2\right)\sqrt{1-x}}{3}+C

State whether the statement and its contrapositive are both true or both false.

If you are not good at basketball then you are not tall. Both false.

verify that P⇒Q is true, then verify that the contrapositive statement \overline{P}⇒\overline{Q} is also true.

If there is not lightning then there is not thunder. True statement.

Write the contrapositive statement \overline{Q}⇒\overline{P}

If you are not happy then you don’t smile

Write the converse of the statement.

If a shape is a quadrilateral, then it has four sides.

Decompose into partial fractions.

\frac{2}{(1-x)}+\frac{2}{(1+x)}

State whether the statement and its contrapositive are both true or both false.

If an animal is not a bird then it does not lay eggs. Both false.

For the contrapositive "If a shape does not have four sides, it is not a trapezium", what is the original statement.

If a shape is a trapezium, then it has 4 sides.

Integration by substitution

\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C

Integration by parts.

\frac{x^4}{4}\ln x-\frac{x^4}{16}+C

Write the contrapositive for: "If a shape is a triangle, then it has 3 sides".

If a shape does not have 3 sides then it is not a triangle.

Integration by parts.

\frac{xe^{3x}}{3}-\frac{e^{3x}}{9}+C

For the contrapositive "If grass is not green, then it has not been raining", what is the original statement.

If it has been raining, then the grass is green

Integration using partial fractions.

\frac{1}{2\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C

Integration of functions with a quadratic denominator

x+2\ln\left|x\right|-\frac{1}{x}+C

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Year 12 Mathematics Extension 2 Quiz 1 Proofs language and Integration 2021

38 termsStudBud Administration110 plays

#math #extension 2 #reviewfortrials

Flashcards38 cardsFPractice quizPHost liveL

Questions 38

Answers

1
verify that P⇒Q is true, then verify that the contrapositive statement \overline{P}⇒\overline{Q} is also true.
If an animal does not have a shell then it is not a turtle. True statement.
If an animal does have a shell then it is not a turtle. True statement.
If an animal does not have a shell then it is not a turtle. True is false.
If an animal does not have a shell then it is a turtle. True statement.
2
Given the true statements below, write the converse of each and decide whether or not the converse is also true.
If something tastes sweet, it contains a lot of sugar. False.
If something tasted sweet, it was a doughnut. False.
If something didn't taste sweet, it contains a lot of sugar. False.
If something tastes sweet, it contains a lot of sugar. True.
3
What do you call a baby goat?
Baby Goat
Kid
Goat
Grace James Binney
4
What are the primary colors?
Blue, Green, Yellow
Red, Green, Yellow
Green, Blue, Red
Yellow, Blue, Red
5
Integration by substitution
\frac{\left(1+x^2\right)^5}{10}+C
\frac{\left(1+x^2\right)^{10}}{10}+C
\frac{\left(1+x^2\right)^5}{5}+C
\frac{\left(1+x^2\right)^5}{10}
6
What game is this?
Mario Kart
Centipede
Ms Pac Man
Donkey Kong
7
Integration by parts.
I=\frac{e^{3x}\left(3\cos2x+3\sin⁡2x\right)}{13}+C
I=\frac{e^{3x}\left(2\cos2x+2\sin⁡2x\right)}{13}+C
I=e^{3x}\left(3\cos2x+2\sin⁡2x\right)+C
I=\frac{e^{3x}\left(3\cos2x+2\sin⁡2x\right)}{13}+C
8
Who is this?
Bill Gates
Tim Berners-Lee
Steve Jobs
9
Given the true statements below, write the converse of each and decide whether or not the converse is also true.
If it is cold, then it is snowing. True.
If it is, then it is snowing. False.
If it is cold, then it was snowing. False.
If it is cold, then it is snowing. False.
10
Write the contrapositive for: "If a drink is cold then it is refreshing"
If a drink is refreshing then it is not cold.
If a drink is not refreshing then it is cold.
If a drink is not refreshing then it is not cold.
If a drink is refreshing then it is cold.
11
Write the converse of the statement.
If an animalcan fly, it has wings.
If an animal has wings, it can fly.
If it can fly, it is an anumal.
If an animal can fly, it has wigs.
12
Integration by substitution
-\frac{2\left(x+2\right)\sqrt{1-x}}{3}+C
-2\left(x+2\right)\sqrt{1-x}
-\frac{\left(x+2\right)\sqrt{1-x}}{3}+C
\frac{2\left(x+2\right)\sqrt{1-x}}{3}+C
13
State whether the statement and its contrapositive are both true or both false.
If you are not good at basketball then you are not tall. Both true.
If you are good at basketball then you are not tall. Both false.
If you are not good at basketball then you are not tall. Both false.
If you are not good at basketball then you are tall. Both false.
14
Cats are feline, dogs are canine, cows are....?
Bovine
Cownine
Horse
Milky
15
verify that P⇒Q is true, then verify that the contrapositive statement \overline{P}⇒\overline{Q} is also true.
If there is lightning then there is not thunder. False statement.
If there is not lightning then there is thunder. True statement.
If there is not lightning then there is not thunder. True statement.
If there is lightning then there is not thunder. True statement.
16
How many plays did Shakespeare write?
35
38
37
36
17
What is the highest mountain on earth?
Mount Kilimanjaro
Mount Bulla
Mount Everest
Mount Fuji
18
Write the contrapositive statement \overline{Q}⇒\overline{P}
If you are happy then you smile
If you are not happy then you smile
If you are happy then you don’t smile
If you are not happy then you don’t smile
19
How many edges does a cube have?
8
10
14
12
20
Decide whether equivalence holds for the statement below. If so, write A⇔B
This is not an equivalence
A⇔Bis true.
B⇒Ais not true.
A⇒Bis true.
21
How often does the moon orbit the Earth?
every 365 days
every 30 days
every 7 days
every 27 days
22
Recurrence relationships
x^{n-1}e^x-nI_{n-1}
x^ne^x-nI_{n-1}
x^ne^{x-1}-nI_{n-1}
x^ne^x-I_{n-1}
23
Where is this?
Paris
New York
Wellington
London
24
Write the converse of the statement.
If a shape is a quadrilateral, then it has five sides.
If a shape is a quadrilateral, then it has four sides.
If a shape is a palindrome, then it has four sides.
If a shape is not a quadrilateral, then it has four sides.
25
Decompose into partial fractions.
\frac{2}{(1-x)}+\frac{2}{(1-x)}
\frac{2}{(1-x)}+\frac{2}{(1+x)}
\frac{2}{(1+x)}+\frac{2}{(1+x)}
\frac{2}{(1-x)}-\frac{2}{(1+x)}
26
Decide whether equivalence holds for the statement below. If so, write A⇔B
This is not an equivalence
A⇔Bis true.
B⇒Ais not true.
A⇒Bis true.
27
Find the converse and decide whether or not it is an equivalence. If so, write it in the form.PiffQ.
This is not an equivalence
A⇒Bis true.
B⇒Ais not true.
A⇔Bis true.
28
State whether the statement and its contrapositive are both true or both false.
If an animal is a bird then it does not lay eggs. Both true.
If an animal is not a bird then it can lay eggs. Both false.
If an animal is not a bird then it does not lay eggs. Both false.
If an animal is a bird then it does not lay eggs. Both false.
29
For the contrapositive "If a shape does not have four sides, it is not a trapezium", what is the original statement.
If a shape is a trapezium, then it has 4 sides.
If a shape is not a trapezium, then it has 4 sides.
If a shape is a trapezium, then it may or may not have 4 sides.
If a shape is a trapezium, then it does not have 4 sides.
30
Integration of functions with a quadratic denominator
\tan^{-1}\left(x\right)+C
-\tan^{-1}\left(x\right)+C
x-\tan^{-1}\left(x\right)+C
x-C
31
Integration by substitution
\tan^{-1}\left(\frac{x}{a}\right)+C
\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C
a\tan^{ }\left(\frac{x}{a}\right)+C
\frac{1}{a}\tan^{-1}\left(a\right)+C
32
Integration by parts.
\frac{x^4}{4}\ln x-\frac{x^4}{16}+C
x^4\ln x-\frac{x^4}{16}+C
16\ln x-\frac{x^4}{16}+C
\frac{x^4}{4}\ln x-\frac{x^4}{4}+C
33
Write the contrapositive for: "If a shape is a triangle, then it has 3 sides".
If a shape has 3 sides then it is not a triangle.
If a shape does not have 3 sides then it is a triangle.
If a shape has 3 sides then it is a triangle.
If a shape does not have 3 sides then it is not a triangle.
34
Integration by parts.
\frac{xe^{3x}}{9}-\frac{e^{3x}}{9}+C
\frac{xe^{3x}}{3}-\frac{e^{3x}}{3}+C
\frac{xe^{3x}}{3}+\frac{e^{3x}}{9}+C
\frac{xe^{3x}}{3}-\frac{e^{3x}}{9}+C
35
For the contrapositive "If grass is not green, then it has not been raining", what is the original statement.
If there is grass, then there is rain.
If it has been raining, then the grass is grass.
If it has been raining, then the grass is green
If it has rain, then it is grass.
36
Integration using partial fractions.
\frac{1}{\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C
\frac{1}{2\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C
\frac{1}{2}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C
\frac{1}{2\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2|)+C
37
Find the converse and decide whether or not it is an equivalence. If so, write it in the form.PiffQ.
P⇒Qis true.
PiffQ
This is not an equivalence
AiffQ
38
Integration of functions with a quadratic denominator
x+2\ln\left|x\right|-\frac{1}{x}+C
2x\ln\left|x\right|-\frac{1}{x}+C
2\ln\left|x\right|-\frac{1}{x}+C
x+2\ln\left|x\right|-x+C

Year 12 Mathematics Extension 2 Quiz 1 Proofs language and Integration 2021 Flashcards | StudBud

Year 12 Mathematics Extension 2 Quiz 1 Proofs language and Integration 2021

38 termsStudBud Administration110 plays

#math #extension 2 #reviewfortrials

Flashcards38 cardsFPractice quizPHost liveL

Questions 38

Answers

1
verify that P⇒Q is true, then verify that the contrapositive statement \overline{P}⇒\overline{Q} is also true.
If an animal does not have a shell then it is not a turtle. True statement.
If an animal does have a shell then it is not a turtle. True statement.
If an animal does not have a shell then it is not a turtle. True is false.
If an animal does not have a shell then it is a turtle. True statement.
2
Given the true statements below, write the converse of each and decide whether or not the converse is also true.
If something tastes sweet, it contains a lot of sugar. False.
If something tasted sweet, it was a doughnut. False.
If something didn't taste sweet, it contains a lot of sugar. False.
If something tastes sweet, it contains a lot of sugar. True.
3
What do you call a baby goat?
Baby Goat
Kid
Goat
Grace James Binney
4
What are the primary colors?
Blue, Green, Yellow
Red, Green, Yellow
Green, Blue, Red
Yellow, Blue, Red
5
Integration by substitution
\frac{\left(1+x^2\right)^5}{10}+C
\frac{\left(1+x^2\right)^{10}}{10}+C
\frac{\left(1+x^2\right)^5}{5}+C
\frac{\left(1+x^2\right)^5}{10}
6
What game is this?
Mario Kart
Centipede
Ms Pac Man
Donkey Kong
7
Integration by parts.
I=\frac{e^{3x}\left(3\cos2x+3\sin⁡2x\right)}{13}+C
I=\frac{e^{3x}\left(2\cos2x+2\sin⁡2x\right)}{13}+C
I=e^{3x}\left(3\cos2x+2\sin⁡2x\right)+C
I=\frac{e^{3x}\left(3\cos2x+2\sin⁡2x\right)}{13}+C
8
Who is this?
Bill Gates
Tim Berners-Lee
Steve Jobs
9
Given the true statements below, write the converse of each and decide whether or not the converse is also true.
If it is cold, then it is snowing. True.
If it is, then it is snowing. False.
If it is cold, then it was snowing. False.
If it is cold, then it is snowing. False.
10
Write the contrapositive for: "If a drink is cold then it is refreshing"
If a drink is refreshing then it is not cold.
If a drink is not refreshing then it is cold.
If a drink is not refreshing then it is not cold.
If a drink is refreshing then it is cold.
11
Write the converse of the statement.
If an animalcan fly, it has wings.
If an animal has wings, it can fly.
If it can fly, it is an anumal.
If an animal can fly, it has wigs.
12
Integration by substitution
-\frac{2\left(x+2\right)\sqrt{1-x}}{3}+C
-2\left(x+2\right)\sqrt{1-x}
-\frac{\left(x+2\right)\sqrt{1-x}}{3}+C
\frac{2\left(x+2\right)\sqrt{1-x}}{3}+C
13
State whether the statement and its contrapositive are both true or both false.
If you are not good at basketball then you are not tall. Both true.
If you are good at basketball then you are not tall. Both false.
If you are not good at basketball then you are not tall. Both false.
If you are not good at basketball then you are tall. Both false.
14
Cats are feline, dogs are canine, cows are....?
Bovine
Cownine
Horse
Milky
15
verify that P⇒Q is true, then verify that the contrapositive statement \overline{P}⇒\overline{Q} is also true.
If there is lightning then there is not thunder. False statement.
If there is not lightning then there is thunder. True statement.
If there is not lightning then there is not thunder. True statement.
If there is lightning then there is not thunder. True statement.
16
How many plays did Shakespeare write?
35
38
37
36
17
What is the highest mountain on earth?
Mount Kilimanjaro
Mount Bulla
Mount Everest
Mount Fuji
18
Write the contrapositive statement \overline{Q}⇒\overline{P}
If you are happy then you smile
If you are not happy then you smile
If you are happy then you don’t smile
If you are not happy then you don’t smile
19
How many edges does a cube have?
8
10
14
12
20
Decide whether equivalence holds for the statement below. If so, write A⇔B
This is not an equivalence
A⇔Bis true.
B⇒Ais not true.
A⇒Bis true.
21
How often does the moon orbit the Earth?
every 365 days
every 30 days
every 7 days
every 27 days
22
Recurrence relationships
x^{n-1}e^x-nI_{n-1}
x^ne^x-nI_{n-1}
x^ne^{x-1}-nI_{n-1}
x^ne^x-I_{n-1}
23
Where is this?
Paris
New York
Wellington
London
24
Write the converse of the statement.
If a shape is a quadrilateral, then it has five sides.
If a shape is a quadrilateral, then it has four sides.
If a shape is a palindrome, then it has four sides.
If a shape is not a quadrilateral, then it has four sides.
25
Decompose into partial fractions.
\frac{2}{(1-x)}+\frac{2}{(1-x)}
\frac{2}{(1-x)}+\frac{2}{(1+x)}
\frac{2}{(1+x)}+\frac{2}{(1+x)}
\frac{2}{(1-x)}-\frac{2}{(1+x)}
26
Decide whether equivalence holds for the statement below. If so, write A⇔B
This is not an equivalence
A⇔Bis true.
B⇒Ais not true.
A⇒Bis true.
27
Find the converse and decide whether or not it is an equivalence. If so, write it in the form.PiffQ.
This is not an equivalence
A⇒Bis true.
B⇒Ais not true.
A⇔Bis true.
28
State whether the statement and its contrapositive are both true or both false.
If an animal is a bird then it does not lay eggs. Both true.
If an animal is not a bird then it can lay eggs. Both false.
If an animal is not a bird then it does not lay eggs. Both false.
If an animal is a bird then it does not lay eggs. Both false.
29
For the contrapositive "If a shape does not have four sides, it is not a trapezium", what is the original statement.
If a shape is a trapezium, then it has 4 sides.
If a shape is not a trapezium, then it has 4 sides.
If a shape is a trapezium, then it may or may not have 4 sides.
If a shape is a trapezium, then it does not have 4 sides.
30
Integration of functions with a quadratic denominator
\tan^{-1}\left(x\right)+C
-\tan^{-1}\left(x\right)+C
x-\tan^{-1}\left(x\right)+C
x-C
31
Integration by substitution
\tan^{-1}\left(\frac{x}{a}\right)+C
\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C
a\tan^{ }\left(\frac{x}{a}\right)+C
\frac{1}{a}\tan^{-1}\left(a\right)+C
32
Integration by parts.
\frac{x^4}{4}\ln x-\frac{x^4}{16}+C
x^4\ln x-\frac{x^4}{16}+C
16\ln x-\frac{x^4}{16}+C
\frac{x^4}{4}\ln x-\frac{x^4}{4}+C
33
Write the contrapositive for: "If a shape is a triangle, then it has 3 sides".
If a shape has 3 sides then it is not a triangle.
If a shape does not have 3 sides then it is a triangle.
If a shape has 3 sides then it is a triangle.
If a shape does not have 3 sides then it is not a triangle.
34
Integration by parts.
\frac{xe^{3x}}{9}-\frac{e^{3x}}{9}+C
\frac{xe^{3x}}{3}-\frac{e^{3x}}{3}+C
\frac{xe^{3x}}{3}+\frac{e^{3x}}{9}+C
\frac{xe^{3x}}{3}-\frac{e^{3x}}{9}+C
35
For the contrapositive "If grass is not green, then it has not been raining", what is the original statement.
If there is grass, then there is rain.
If it has been raining, then the grass is grass.
If it has been raining, then the grass is green
If it has rain, then it is grass.
36
Integration using partial fractions.
\frac{1}{\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C
\frac{1}{2\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C
\frac{1}{2}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2+\sqrt{5}|)+C
\frac{1}{2\sqrt{5}}(\ln⁡|x-2-\sqrt{5}|-\ln⁡|x-2|)+C
37
Find the converse and decide whether or not it is an equivalence. If so, write it in the form.PiffQ.
P⇒Qis true.
PiffQ
This is not an equivalence
AiffQ
38
Integration of functions with a quadratic denominator
x+2\ln\left|x\right|-\frac{1}{x}+C
2x\ln\left|x\right|-\frac{1}{x}+C
2\ln\left|x\right|-\frac{1}{x}+C
x+2\ln\left|x\right|-x+C