Free Printable Level 11 MCQ

1.

$\sin^{-1}\left(\sin4\right)=?$

a)

$\pi-4$

b)

$4$

c)

$4-\pi$

d)

$4-2\pi$

2.

$\cos^{-1}\left(\cos8\right)$

a)

$8-2\pi$

b)

$8$

c)

$8-\pi$

d)

$2\pi-8$

3.

If the equation's solution for $\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$ is $\frac{a}{b}$ , find the value of a+b.

(a)

4.

If $\sin^{-1}\left(\sin\ x\right)=\pi-x$ , then x belongs to

a)

$\left[\frac{\pi}{2},\frac{3\pi}{2}\right]$

b)

$\left[0,\frac{\pi}{2}\right]$

c)

$\left[\frac{3\pi}{2},2\pi\right]$

d)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

5.

Calculate $\sin^{-1}\left(\frac{1}{\sqrt[]{5}}\right)+\cot^{-1}\left(3\right)$

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{3}$

c)

$\frac{\sqrt[]{50}}{10}$

d)

$\frac{\pi}{6}$

6.

Given that $\int_2^6\ k\left(x\right)dx\ =\ -5,\$ find the value of $p$ if $\int_2^6\ \left[2p+3k\left(x\right)\right]dx=33$ .

(a)

7.

$\int_0^1\ \frac{x}{\left(x^2+1\right)^{2\ }}dx\ =\frac{1}{a}$ ,

find the value of a

(a)

8.

Find the value for the definite integral $\int_{-4}^2\ \sqrt{17+4x}\ dx\ =\ \frac{a}{b}$ . What is the value of a+b ?

a+b为多少（整数)？

(a)

9.

Given that $\int_{-1}^3f\left(x\right)dx=4$ and $\int_{-1}^3\ g\left(x\right)\ dx=9$ , then find the value of $\left[\int_{-1}^3\ 5f\left(x\right)\ dx\ \ +\int_3^{-1}\ g\left(x\right)\ dx\right]$

a)

11

b)

29

c)

20

d)

15

10.

A curve has the gradient function of $\frac{10}{\left(5x-3\right)^2}$ . If the curve passes through the point $\left(1,2\right)$ , find the equation of the curve. 某曲线的斜率为 $\frac{10}{\left(5x-3\right)^{2\ }}$ 和经过点 $\left(1,2\right)$ . 求该曲线方程式。

a)

$y=-\frac{2}{\left(5x-3\right)}+3$

b)

$y=\frac{2}{\left(5x+3\right)}+3$

c)

$y=-\frac{10}{\left(5x-3\right)}+c$

d)

$y=\frac{2}{\left(5x-3\right)}+c$

11.

$\int_0^1\ x\left(2x^2-1\right)^{10}\ dx$

a)

$\frac{1}{22}$

b)

$\frac{1}{11}$

c)

$-\frac{1}{11}$

d)

$\frac{1}{44}$

12.

Find the value of

$\int_{-\frac{\pi}{2}}^0\ \sin x\cos x\ dx$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$-\frac{1}{4}$

d)

$\frac{1}{4}$

13.

Find the value

$\int_0^{\frac{\pi}{2}}\ \cos^2x\ \sin x\ dx$

a)

$\frac{1}{3}$

b)

$\frac{1}{2}$

c)

$\frac{1}{4}$

d)

$\frac{1}{5}$

14.

Find the area of the region bounded by the given curves. $y=16-x^2$ and $y=x^2-16$

a)

$\frac{512}{3}unit^2$

b)

$\frac{352}{3}unit^2$

c)

$\frac{252}{3}\ unit^2$

d)

$\frac{152}{3\ }unit^2$

15.

A particle moves along a straight line and passes through a fixed point O with a velocity of $-12ms^{-1}$ . Its acceleration, $a\ ms^{-2}$ , t seconds after passing O is given by $a=4t-2$ . Find the total distance travelled by the particle in the first 5 seconds.

a)

$\frac{157}{3}m$

b)

$\frac{127}{3\ }m$

c)

$\frac{86}{3}m$

d)

$65\ m$

16.

A particle moves along a straight line and passes through a fixed point O such that its velocity, $v\ ms^{-1}$ . t seconds after passing through O is given by $v=8-2t$ . Find the maximum displacement, s of the particle.

a)

$16m$

b)

$12m$

c)

$20m$

d)

$24m$

17.

A particle moves along a straight line and passes through a fixed point O. The velocity, $v\ ms^{-1}$ of the particle is given by $v=3t^2-2t-21$ , where t is the time in seconds, after passing through O. Find the total distance travelled by the particle is the first 5 seconds.

a)

85 m

b)

5 m

c)

40 m

d)

45 m

18.

Given that $a=\int_0^2\ x^2dx$ , $b=\int_0^2\ x^3\ dx$ , $c=\int_0^2\sin\ x\ dx$ , which of the following is true?

a)

$c<a<b$

b)

$b<c<a$

c)

$a<b<c$

d)

$a<c<b$

19.

$\int_0^{\frac{3}{2}}\ \sqrt{9-4x^2\ }dx$ 可以看成为

a)

半径为 $\frac{3}{2}$ 的圆的面积的二分之一

b)

半径为 $\frac{3}{2}$ 的圆的面积的八分之一

c)

半径为 $\frac{3}{2}$ 的圆的面积的三分之一

d)

半径为 $\frac{3}{2}$ 的圆的面积的四分之一

20.

The diagram shows part of the curves undefined andundefined which intersect at P. Find the area undefined of the shaded region. （A是整数）

(a)

21.

The diagram shows the curve $y=x^2$ , the straight lines $y=16$ and $x=1$ . The volume generated when the shaded region is revolved through $360\degree$ about the x-axis is $P\frac{2}{5}\pi\ \ unit^3$ . What is the value of P? （键入P的整数值）。

(a)

22.

a)

$\frac{2}{3}x^{\frac{3}{2}}+\frac{6}{13}x^{\frac{13}{6}}+c$

b)

$\frac{3}{2}x^{\frac{2}{3}}+\frac{13}{6}x^{\frac{6}{13}}+c$

c)

$\frac{4}{3}x^{\frac{3}{4}}+\frac{12}{5}x^{\frac{5}{12}}+c$

d)

$\frac{3}{4}x^{\frac{4}{3}}+\frac{5}{12}x^{\frac{12}{5}}+c$

23.

The diagram show part of the curve $y=\frac{8}{x^2}$ and the straight line $y=x$ which intersect at $p$ . Find the area, $A\ unit^2$ of the shaded region.

a)

$\frac{14}{3}\ unit^2$

b)

$4\ unit^2$

c)

$\frac{11}{4}\ unit^2$

d)

$\frac{13}{2}\ unit^2$

24.

The diagram shows part of the curve $y^2=x-3$ and the straight line $y=2$ . Find the volume generated when the shaded region is revolved through $360\degree$ about the y-axis.

a)

$\frac{202}{5}\pi\ unit^3$

b)

$\frac{192}{5}\pi\ unit^3$

c)

$\frac{182}{5}\pi\ unit^3$

d)

$\frac{172}{5}\pi\ unit^3$

25.

Find the area of the shaded region

a)

$\frac{1}{3}$

b)

$\frac{1}{4}$

c)

$\frac{1}{2}$

d)

$\frac{1}{6}$

26.

$\sin\ \left(\frac{\pi}{3}-\sin^{-1}\left(-\frac{1}{2}\right)\right)$ is equal to

a)

$1$

b)

$\frac{1}{3}$

c)

$\frac{1}{4}$

d)

$\frac{1}{2}$

27.

Find the value of $\sin^{-1}\ \left(\cos\ \frac{33}{5}\pi\right)$

a)

$-\frac{\pi}{10}$

b)

$\frac{7}{5}\pi$

c)

$-\frac{\pi}{4}$

d)

$\frac{2}{5}\pi$

28.

Evaluate $\sin\ \frac{1}{2}\cos^{-1}\ \frac{4}{5}$

a)

$\frac{\sqrt[]{10}}{10}$

b)

$\frac{3}{5}$

c)

$1$

d)

$-\frac{\sqrt[]{3}}{5}$

29.

Find the value of $\cos^2\ \frac{1}{2}\left(\cos^{-1}\ \frac{3}{5}\right)$

a)

$\frac{4}{5}$

b)

$-\frac{1}{4}$

c)

$-\frac{1}{2}$

d)

$\frac{1}{3}$

30.

$\lim_{x\rightarrow\infty}\ \left(\frac{x+6}{x+5}\right)^x=$

a)

$e$

b)

$e^{\frac{6}{5}}$

c)

$e^{-\frac{6}{5}}$

d)

$e^{\frac{5}{6}}$

31.

$\lim_{x\rightarrow\infty}\ \left(\frac{x-3}{x}\right)^{\frac{x}{2}}=$

a)

$e^{-\frac{3}{2}}$

b)

$e^{\frac{3}{2}}$

c)

$e^{\frac{2}{3}}$

d)

$e^{-\frac{2}{3}}$

32.

Given $y=\sqrt[]{\cos x+\sqrt[]{\cos x+\sqrt[]{\cos\ x+...\infty}}}$ , find the $\frac{\text{d}y}{\text{d}x}$

a)

$\frac{\sin\ x}{1-2y}$

b)

$\frac{2\ \sin\ x}{3y+2}$

c)

$\frac{\sin\ x}{2y+1}$

d)

$\frac{2y}{\sin\ x}$

33.

Given $y=\sqrt[]{\tan\ x+\sqrt[]{\tan\ x\ +\sqrt[]{\tan\ x+...\infty}}}$ , find the $\frac{\text{d}y}{\text{d}x}$

a)

$\frac{\sec^2x}{2y-1}$

b)

$\frac{y}{\sec^2x}$

c)

$\frac{y+1}{\sec^2x}$

d)

$\frac{\sec^2x}{y+2}$

34.

Given that $y^3-3xy^2=x^3+3x^2y$ ,find the value of $\frac{\text{d}y}{\text{d}x}$ at point (1,1)

a)

$-\frac{4}{3}$

b)

$-\frac{1}{2}$

c)

$-\frac{2}{3}$

d)

$-\frac{1}{4}$

35.

Differentiate of $y=\sin^{-1}\ \frac{4}{3x}$

a)

$-\frac{4\sqrt[]{x^2}}{x^2\ \sqrt[]{9x^2-16}}$

b)

$\frac{\sqrt[]{x^2}}{x^2\sqrt[]{9x^2-16}}$

c)

$-\frac{\sqrt[]{x^2}}{x\ \sqrt[]{9x^2-16}}$

d)

$\frac{2\sqrt[]{x^2}}{x^2\sqrt[]{16-9x^2}}$

36.

Derivative of $y=\cos^{-1}\ \left(\frac{3x+2}{7}\right)$

a)

$-\frac{3}{\sqrt[]{-9x^2-12x+45}}$

b)

$\frac{3}{\sqrt[]{-9x^2-12x+45}}$

c)

$-\frac{3}{\sqrt[]{9x^2+12x-45}}$

d)

$\frac{3}{\sqrt[]{9x^2+12x-45}}$

37.

Derivative of $y=\left(\sin^{-1}x\right)^2$

a)

$\frac{2\ \sin^{-1}x}{\sqrt[]{1-x^2}}$

b)

$\frac{2\ \sin^{-1}x}{\sqrt[]{1+x^2}}$

c)

$\frac{2\ \sin^{-1}x}{1-x^2}$

d)

$\frac{2\ \sin^{-1}x}{1+x^2}$

38.

Derivative of $y=\left(\cos^{-1}2x\right)^2$

a)

$-\frac{4\cos^{-1}2x}{\sqrt[]{1-4x^2}}$

b)

$\frac{4\ \cos^{-1}2x}{\sqrt[]{1-4x^2}}$

c)

$\frac{\cos^{-1}2x}{\sqrt[]{1-4x^2}}$

d)

$-\frac{\cos^{-1}2x}{\sqrt[]{1-4x^2}}$

39.

$\frac{d}{dx}\sqrt[]{16-x^2}\cdot\ \sin^{-1}\left(\frac{x}{4}\right)$

a)

$-\frac{x\sin\left(\frac{x}{4}\right)}{\sqrt[]{16-x^2}}+1$

b)

$\frac{x\sin^{-1}\left(\frac{x}{4}\right)}{\sqrt[]{16-x^2}}+1$

c)

$-\frac{x\ \sin^{-1}\left(\frac{x}{4}\right)}{\sqrt[]{16-x^2}}-1$

d)

$\frac{x\ \sin^{-1}\left(\frac{x}{4}\right)}{\sqrt[]{16-x^2}}-1$

40.

Given $\lim_{x\rightarrow\infty}\ \left(1-\frac{3}{x}\right)^{2x}=\frac{1}{e^k}$ , what is the value of k?

(a)

Level 11 MCQ

Total questions: 40

Worksheet time: 10hrs 0mins

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