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CALCULUS QUIZ-TRY-YOUR HAND

Total questions: 50

Worksheet time: 1hrs 15mins

Name
Class
Date
1.

y=2x9−x+56x6y=2x^9-x+\frac{5}{6x^6}  . Find the gradient of y.

a)

18x8−118x^8-1  

b)

18x8−x−5x718x^8-x-\frac{5}{x^7}  

c)

18x8−1−5x718x^8-1-\frac{5}{x^7}  

d)

18x8−1−5x518x^8-1-\frac{5}{x^5}  

2.

ddx(x3)\frac{\text{d}}{\text{d}x}\left(\sqrt[3]{x}\right)  

a)

−13  x23-\frac{1}{3\ \ \sqrt[3]{x^2}}  

b)

13  x23\frac{1}{3\ \ \sqrt[3]{x^2}}  

c)

3  x233\ \ \sqrt[3]{x^2}  

d)

x23\sqrt[3]{x^2}  

3.

Differentiate the following with respect of x.

y=(3x+8)5y=\left(3x+8\right)^5  

a)

15(3x+8)615\left(3x+8\right)^6  

b)

5(3x+8)45\left(3x+8\right)^4  

c)

(3x+8)4\left(3x+8\right)^4  

d)

15(3x+8)415\left(3x+8\right)^4  

4.

y=1x2+xy=\frac{1}{x^2}+\sqrt[]{x}  .Find dxdy\frac{\text{d}x}{\text{d}y}  .

a)

dxdy=−2x3+12x\frac{\text{d}x}{\text{d}y}=-\frac{2}{x^3}+\frac{1}{2\sqrt[]{x}}  

b)

dxdy=−2x−3+12x12\frac{\text{d}x}{\text{d}y}=-2x^{-3}+\frac{1}{2}x^{\frac{1}{2}}  

c)

dxdy=−2x−3+14x−12\frac{\text{d}x}{\text{d}y}=-2x^{-3}+\frac{1}{4}x^{-\frac{1}{2}}  

d)

dxdy=−2x−3\frac{\text{d}x}{\text{d}y}=-2x^{-3}  

5.

Differentiate x3−4x22x\frac{x^3-4x^2}{2x}  with respect to xx  .

a)

x2−2x^2-2  

b)

x2−2xx^2-2x  

c)

x−2x-2  

d)

x−2x2x-2x^2  

6.

Find d2xdy2\frac{\text{d}^2x}{\text{d}y^2}  for y=12x3+8x−6y=\frac{1}{2}x^3+8x-6  .

a)

32x2+8\frac{3}{2}x^2+8  

b)

3x3x  

c)

32x2\frac{3}{2}x^2  

d)

32x2+8x\frac{3}{2}x^2+8x  

7.

ddx(ln⁡ (3x−4)3)\frac{\text{d}}{\text{d}x}\left(\ln\ \left(3x-4\right)^3\right)  

a)

93x−4\frac{9}{3x-4}  

b)

33x−4\frac{3}{3x-4}  

c)

3(3x−4)2\frac{3}{\left(3x-4\right)^2}  

d)

1(3x−4)3\frac{1}{\left(3x-4\right)^3}  

8.

ddx(ln⁡ 42x−3)\frac{d}{dx}\left(\ln\ \sqrt[]{\frac{4}{2x-3}}\right)  

a)

−22x−3-\frac{2}{2x-3}  

b)

−12x−3-\frac{1}{2x-3}  

c)

12x−3\frac{1}{2x-3}  

d)

13−2x\frac{1}{3-2x}  

9.

ddx(ln⁡ 42x−3)\frac{d}{dx}\left(\ln\ \sqrt[]{\frac{4}{2x-3}}\right)  

a)

−22x−3-\frac{2}{2x-3}  

b)

−12x−3-\frac{1}{2x-3}  

c)

12x−3\frac{1}{2x-3}  

d)

13−2x\frac{1}{3-2x}  

10.

ddx(sin⁡2x)\frac{\text{d}}{\text{d}x}\left(\sin2x\right)  

a)

2cos⁡2x2\cos2x  

b)

−2cos⁡2x-2\cos2x  

c)

cos⁡2x\cos2x  

d)

2cos⁡3x2\cos3x  

11.

ddx (x4+6x−7)\frac{\text{d}}{\text{d}x}\ \left(x^4+6x-7\right)  

a)

4x3+64x^3+6  

b)

3x2+53x^2+5  

c)

x4+6x−7x^4+6x-7  

d)

4x5+6x24x^5+6x^2  

12.

ddx (x4+6x−7)\frac{\text{d}}{\text{d}x}\ \left(x^4+6x-7\right)  

a)

4x3+64x^3+6  

b)

3x2+53x^2+5  

c)

x4+6x−7x^4+6x-7  

d)

4x5+6x24x^5+6x^2  

13.

Differentiate with respect to x...

a)

6x2 + 6x

b)

6x + 2

c)

6x + 6

d)

6x2 + 6

14.
Differentiate 6x⅔.
a)
4x-⅓
b)
4x-⅔
c)
6x⅓
d)
4x⅓
15.
a)
3x2
b)
x3
c)
6x
d)
3x2 + x3
16.

Find the turning points of:

f(x)=x3+3x2-9x+1 (hint dy/dx=0)

a)

(-3,28) and (1,-4)

b)

(3,28) and (1,4)

c)

(1,28) and (-3,-4)

d)

(3,28) and (-1,-4)

17.

What is the derivative of xn?

a)

(n-1)xn

b)

nxn+1

c)

(n+1)xn-1

d)

nxn-1

18.

Which of the following is the indefinite integral of x32+7\frac{x^3}{2}+7 ?

a)

3x22\frac{3x^2}{2}  

b)

3x22+7x+c\frac{3x^2}{2}+7x+c  

c)

x48+7x+c\frac{x^4}{8}+7x+c  

d)

x48+c\frac{x^4}{8}+c  

19.

Integrate x\sqrt{x} with respect to x

a)

x12+cx^{\frac{1}{2}}+c  

b)

12x−12+ c\frac{1}{2}x^{-\frac{1}{2}}+\ c  

c)

23x32+ c\frac{2}{3}x^{\frac{3}{2}}+\ c  

d)

32x32+ c\frac{3}{2}x^{\frac{3}{2}}+\ c  

20.

∫ 1x+ 1x2 dx\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx  

a)

x−1 + x−2+ cx^{-1}\ +\ x^{-2}+\ c  

b)

x0 − x−1+ cx^0\ -\ x^{-1}+\ c  

c)

ln⁡x+ x−1+ c\ln x+\ x^{-1}+\ c  

d)

ln⁡x− x−1+ c\ln x-\ x^{-1}+\ c  

21.

∫5x4dx\int5x^4dx  

a)

x5x^5  

b)

54x5+C\frac{5}{4}x^5+C  

c)

x5+Cx^5+C  

d)

20x320x^3  + C

22.

∫(x2−2x)dx\int\left(x^2-2x\right)dx  

a)

13x3−x2+C\frac{1}{3}x^3-x^2+C  

b)

x2 −2x+Cx^{2\ }-2x+C  

c)

2x−22x-2  

d)

13x3−x2\frac{1}{3}x^3-x^2

23.

∫6x(x+2)dx\int6x\left(x+2\right)dx  

a)

6x2+12x+C6x^2+12x+C  

b)

x2 −2x+Cx^{2\ }-2x+C  

c)

3x2+6x+C3x^2+6x+C  

d)

2x3+6x2+C2x^3+6x^2+C

24.

∫(6x−1)dx\int\left(6\sqrt{x}-1\right)dx  

a)

6x32+x+C6x^{\frac{3}{2}}+x+C  

b)

4x32−x+C4x^{\frac{3}{2}}-x+C  

c)

3x−12−x+C3x^{-\frac{1}{2}}-x+C  

d)

I didn't look at my notes to see how to do this one.

25.

∫(1x2+6x3)dx\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx  

a)

−x−1−3x−2+C-x^{-1}-3x^{-2}+C  

b)

x−3−3+6x−4−4+C\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C  

c)

−x−1−3x−2-x^{-1}-3x^{-2}  

d)

−x−3x2+C-x-3x^2+C  

26.

∫(5x2−7x+6)dx\int\left(5x^2-7x+6\right)dx  

a)

53x−72x+6x+C\frac{5}{3}x-\frac{7}{2}x+6x+C  

b)

x+x+x+x+x+Cx+x+x+x+x+C  

c)

x3−3x2+6x+Cx^3-3x^2+6x+C  

d)

53x3−72x2+6x+C\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C  

27.

∫4sin⁡(−x)dx\int4\sin\left(-x\right)dx  

a)

4cos⁡(x)+C4\cos\left(x\right)+C  

b)

−4sin⁡(−x)+C-4\sin\left(-x\right)+C  

c)

4cos⁡(−x)+C4\cos\left(-x\right)+C  

d)

−4cos⁡(−x)+C-4\cos\left(-x\right)+C  

28.

∫(5x3−16e−4x+1x)dx\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx  

a)

2x52+4x−4x+ln⁡∣x∣+C2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C  

b)

5x13−4e−4x+1+C5x^{\frac{1}{3}}-4e^{-4x}+1+C  

c)

52x32−16e−4x+ln⁡∣x∣+C\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C  

d)

Got lazy with fake answers

29.

∫8x−3dx\int8x^{-3}dx  

a)

−2x−4+C-2x^{-4}+C  

b)

4x−3+C4x^{-3}+C  

c)

8−3x−2\frac{8}{-3}x^{-2}  

d)

−4x−2+C-4x^{-2}+C  

30.

∫(x−1−1)dx\int\left(x^{-1}-1\right)dx  

a)

ln⁡∣x∣−x+C\ln\left|x\right|-x+C  

b)

x−2−2−x+C\frac{x^{-2}}{-2}-x+C  

c)

ln⁡∣x∣−1+C\ln\left|x\right|-1+C  

d)

1−x+C1-x+C  

31.

∫0dx\int0dx  

a)

1x+C\frac{1}{x}+C  

b)

Not PossibleNot\ Possible  

c)

x+Cx+C  

d)

CC  

32.

Find the answer of ∫x2+4x dx?

a)

X3/2+2x2

b)

X2+4x

c)

x2/2 +3x+C

d)

x3 /3+2x2+C

33.

Integrate ∫x13dx\int_{ }^{ }x^{\frac{1}{3}}dx  

a)

=43x43+c=\frac{4}{3}x^{\frac{4}{3}}+c  

b)

=32x23+c=\frac{3}{2}x^{\frac{2}{3}}+c  

c)

=13x−23+c=\frac{1}{3}x^{-\frac{2}{3}}+c  

d)

=34x43+c=\frac{3}{4}x^{\frac{4}{3}}+c  

34.

Integrate ∫sin⁡x dx\int_{ }^{ }\sin x\ dx  

a)

=tan⁡x+c=\tan x+c  

b)

=−cos⁡x+c=-\cos x+c  

c)

=−sec⁡x+c=-\sec x+c  

d)

=cosec⁡ x +c=\operatorname{cosec}\ x\ +c  

35.

∫12xdx\int_{ }^{ }\frac{\text{1}}{\text{2x}}dx  

a)

=ln⁡2x+c=\ln2x+c  

b)

=2 ln⁡2x+c=2\ \ln2x+c  

c)

=12ln⁡2x+c=\frac{1}{2}\ln2x+c  

d)

=1ln⁡2x+c=\frac{1}{\ln2x}+c  

36.

∫tan⁡xdx \int\tan x_{ }dx\  

a)

ln⁡∣cos⁡∣+C\ln\left|\cos\right|+C  

b)

−ln⁡∣cos⁡x∣+C-\ln\left|\cos x\right|+C  

c)

ln⁡∣sin⁡x∣+c\ln\left|\sin x\right|+c  

d)

tan⁡2x2+c\frac{\tan^2x}{2}+c  

37.

∫(4x−ex)dx\int\left(\frac{4}{x}-e_{ }^x\right)dx  

a)

4x2−xex+C\frac{4}{x^2}-xe^x+C  

b)

4ln⁡∣x∣−ex+C4\ln\left|x\right|-e^x+C  

c)

4ln⁡(x)−ex+C4\ln\left(x\right)-e^x+C  

d)


4ln⁡∣x∣+ex+C4\ln\left|x\right|+e^x+C  

38.

What is the stationary point for the curve

y=x2−4y=x^2-4  

a)

A minimum at ( 0, -4)

b)

A maximum at (0, -4)

c)

A minimum at (0,4)

d)

A maximum at (0,4)

39.

Stationary point occur when....

a)

x = 0

b)

dydx=0\frac{\text{d}y}{\text{d}x}=0

c)

dxdy=0\frac{\text{d}x}{\text{d}y}=0

d)

d2ydx2=0\frac{d^2y}{dx^2}=0

40.

Inflection point is a nature for stationary point when...

a)

d2ydx2<0\frac{d^2y}{dx^2}<0

b)

d2ydx2>0\frac{d^2y}{dx^2}>0

c)

d2ydx2=0\frac{d^2y}{dx^2}=0

d)

d2ydx2≠0\frac{d^2y}{dx^2}\ne0

41.

The nature of the point is maximum, if 

a)

d2xdy2<0\frac{\text{d}^2x}{\text{d}y^2}<0   

b)

d2xdy2=0\frac{\text{d}^2x}{\text{d}y2}=0  

c)

d2xdy2>0\frac{\text{d}^2x}{\text{d}y^2}>0  

42.

If   d2xdy2>0\frac{\text{d}^2x}{\text{d}y^2}>0  , turning point is a 

a)

maximum point

b)

minimum point

c)

point of inflexion 

43.

y=x2−4y=x^2-4  

What is the maximum or minimum point for the curve?

a)

minimum at ( 0, -4)

b)

minimum at ( 0, 4)

c)

maximum at ( 0, -4)

d)

maximum at ( 0, 4)

44.

∫ 3x+2x2−1dx\int\ \frac{3x+2}{x^2-1}dx  

a)

ln⁡∣x2−1∣\ln\left|x^2-1\right|  

b)

12ln⁡∣x+1∣+52ln⁡∣x−1∣+c\frac{1}{2}\ln\left|x+1\right|+\frac{5}{2}\ln\left|x-1\right|+c  

c)

32ln⁡∣x−1∣+12ln⁡∣x+1∣+c\frac{3}{2}\ln\left|x-1\right|+\frac{1}{2}\ln\left|x+1\right|+c  

d)

52ln⁡∣x+1∣+12ln⁡∣(x−1)2∣+c\frac{5}{2}\ln\left|x+1\right|+\frac{1}{2}\ln\left|\left(x-1\right)^2\right|+c

45.

Break this into partial fractions.

a)
b)
c)
d)
46.

Use the substitution u=x2u=x^2   to evaluate the integral.

a)

2x

b)

e16−1e^{16}-1  

c)

ex2+ce^{x^2}+c  

d)

64

47.

Choose the correct approach to solve this question.

a)

SUBSTITUTION

b)

BY PARTS

c)

PARTIAL FRACTION

d)

INVERSE

48.

Choose the correct approach to solve this question.

a)

SUBSTITUTION

b)

BY PARTS

c)

PARTIAL FRACTION

d)

INVERSE

49.

Find A, B, and C

a)

A=-2, B=3, C=5

b)

A=-9, B=1, C=0

c)

A=1, B=1, C=6

d)

A=-1, B=1, C=5

50.

Set up this function as a partial fraction

(Pg. 63 in the workbooks)

a)

∫2x+2+6x+5dx\int_{ }^{ }\frac{2}{x+2}+\frac{6}{x+5}dx

b)

∫7x+2+3x+5dx\int_{ }^{ }\frac{7}{x+2}+\frac{3}{x+5}dx

c)

∫3x+2+7x+5dx\int_{ }^{ }\frac{3}{x+2}+\frac{7}{x+5}dx

d)

∫6x+2+2x+5dx\int_{ }^{ }\frac{6}{x+2}+\frac{2}{x+5}dx

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