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Pure math 2/3

Authored by Abdullahon Valihonov

Mathematics

11th Grade

Used 2+ times

Pure math 2/3
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15 questions

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1.

MULTIPLE CHOICE QUESTION

5 mins • 6 pts

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First simplify cos(3x)cos(x) using the expansions of cos(3x + x) and cos(3x − x), then integrate and solve expression.

3 3 8\frac{3\ \sqrt[\ ]{3}}{8}

5 3 8\frac{5\ \sqrt[\ ]{3}}{8}

8 3 3\frac{8\ \sqrt[\ ]{3}}{3}

8 3 5\frac{8\ \sqrt[\ ]{3}}{5}

2.

MULTIPLE CHOICE QUESTION

10 mins • 8 pts

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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 d(tan⁡2θ)dθ\frac{d\left(\tan^2\theta\right)}{d\theta}
(ii)  Solve the differential equation and calculate the value of x when Θ=π/3, giving your answer correct to 3 significant figures.

(i) tan⁡θ2cos⁡2θ\frac{\tan\theta}{2\cos^2\theta}
(ii) x= 1.46

(i) 2tan⁡θcos⁡2θ\frac{2\tan\theta}{\cos^2\theta}
(ii) x= -2.54

(i) 2tan⁡θcos⁡2θ\frac{2\tan\theta}{\cos^2\theta}
(ii) x=2.54

(i) tan⁡θ2cos⁡2θ\frac{\tan\theta}{2\cos^2\theta}

(ii) x = -2.54

3.

MULTIPLE CHOICE QUESTION

10 mins • 8 pts

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Using the substitution x = cos⁡2(θ)\cos^2\left(\theta\right) , 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 dydx=−kxt \frac{\text{d}y}{\text{d}x}=-kx\sqrt[\ ]{t} 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 = −23kt t +ln⁡100-\frac{2}{3}kt\ \sqrt[\ ]{t}+\ln100

(ii) t = 64.1

(i) ln x = 23kt t +ln⁡100\frac{2}{3}kt\ \sqrt[\ ]{t}+\ln100

(ii) t = 110

(i) ln x = −23kt t +ln⁡100-\frac{2}{3}kt\ \sqrt[\ ]{t}+\ln100

(ii) t = 110

(i) ln x = 23kt t +ln⁡100\frac{2}{3}kt\ \sqrt[\ ]{t}+\ln100

(ii) t = 64.1

5.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

what is d (ey)d x\frac{\text{d}\ \left(e^y\right)}{\text{d}\ x} ?

1

no correct answer

eydxdye^y\frac{\text{d}x}{\text{d}y}

eye^y

6.

MULTIPLE SELECT QUESTION

30 sec • 2 pts

Match the one correct pair

∫  (1x2+1) dx\int_{\ }^{\ }\left(\frac{1}{x^2+1}\right)\ dx

∫  cos⁡x dx\int_{\ }^{\ }\cos x\ dx

∫  sin⁡x dx\int_{\ }^{\ }\sin x\ dx

∫  ln⁡x dx\int_{\ }^{\ }\ln x\ dx

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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