
Pure math 2/3
Authored by Abdullahon Valihonov
Mathematics
11th Grade
Used 2+ times

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15 questions
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1.
MULTIPLE CHOICE QUESTION
5 mins • 6 pts
First simplify cos(3x)cos(x) using the expansions of cos(3x + x) and cos(3x − x), then integrate and solve expression.
2.
MULTIPLE CHOICE QUESTION
10 mins • 8 pts
The variables x and Θ satisfy the differential equation for 0 ≤ Θ < 10 and x > 0. It is given that x = 1 when Θ = 10
(i) Find
(ii) Solve the differential equation and calculate the value of x when Θ=π/3, giving your answer correct to 3 significant figures.
(i)
(ii) x= 1.46
(i)
(ii) x= -2.54
(i)
(ii) x=2.54
(i)
(ii) x = -2.54
3.
MULTIPLE CHOICE QUESTION
10 mins • 8 pts
Using the substitution x = , find value of I
3
1/2
1/6
no correct answer
4.
MULTIPLE CHOICE QUESTION
10 mins • 8 pts
In a certain chemical reaction the amount, x grams, of a substance is decreasing. The differential
equation relating x and t, the time in seconds since the reaction started, is where k is a positive constant. It is given that x = 100 at the start of the reaction.
(i) Solve the differential equation, obtaining a relation between x, t and k
(ii) Given that t=25 when x=80, find the value of t when x=40.
(i) ln x =
(ii) t = 64.1
(i) ln x =
(ii) t = 110
(i) ln x =
(ii) t = 110
(i) ln x =
(ii) t = 64.1
5.
MULTIPLE CHOICE QUESTION
20 sec • 1 pt
what is ?
1
no correct answer
6.
MULTIPLE SELECT QUESTION
30 sec • 2 pts
Match the one correct pair
tan^(-1) (x) - x +c
7.
MULTIPLE CHOICE QUESTION
10 sec • 5 pts
you want free points? then let's check if you are lucky, using integration find correct answer
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