Quiz about 20230807-AM1

Question 1

Find the mean of for the data $$14,\ 19,\ 12,\ 24,\ x,\ y,\ 14,\ 11,\ 19,\ 27$$
where the mode is $$14$$ and the median is $$15$$ .

Accepted Answer

17

Answer

14

Answer

15

Answer

16

Question 2

If $$f\left(x\right)=x^3-2x^2-x+5$$ ,
find the remainder when the polynomial $$g\left(x\right)=f\left(f\left(x\right)\right)$$ is divided by $$\left(x-2\right)$$ .

Accepted Answer

11

Answer

5

Answer

7

Answer

9

Question 3

Given that $$a\log_{520}2+b\log_{520}5+c\log_{520}13=3$$ ,
find the value of $$a+b+c$$ .

Accepted Answer

15

Answer

3

Answer

5

Answer

14

Question 4

If $$\left(1+x\right)\left(1+x^2\right)\left(1+x^4\right)\cdots\left(1+x^{1024}\right)=1+x+x^2+x^3+\cdots+x^n$$ ,
find the value of $$n$$ .

Accepted Answer

2047

Answer

1023

Answer

1025

Answer

2049

Question 5

Given that the coefficient of $$x^2$$ in the expansion of $$\left(\frac{2}{x^2}+3x\right)^n$$ is $$81648$$ ,
find the value of $$n$$ .

Accepted Answer

8

Answer

9

Answer

7

Answer

6

Question 6

How many solutions to the equation $$\cos2023x=-0.5$$ are there in the interval $$\left(0\degree,180\degree\right)$$ ?

Accepted Answer

2023

Answer

2022

Answer

4044

Answer

4046

Question 7

Solve $$\sin5x=\sin x+\sin2x$$ , $$0

Accepted Answer

$$\frac{\pi}{9},\ \frac{\pi}{2},\ \frac{5\pi}{9},\ \frac{7\pi}{9}$$

Answer

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

Answer

$$\frac{\pi}{2},\ \frac{5\pi}{9},\ \frac{7\pi}{9}$$

Answer

$$\frac{\pi}{9},\ \frac{5\pi}{9},\ \frac{7\pi}{9}$$

Question 8

Find the acute angle between the lines $$2x-6y+13=0$$ and $$3y-2x+7=0$$ .

Accepted Answer

$$15.26\degree$$

Answer

$$37.87\degree$$

Answer

$$52.13\degree$$

Answer

$$74.74\degree$$

Question 9

The mid-point of the three sides of $$\Delta ABC$$ are $$\left(2,0\right)$$ , $$\left(2,3\right)$$ and $$\left(8,7\right)$$ .
Find the area of $$\Delta ABC$$ .

Accepted Answer

36

Answer

9

Answer

18

Answer

27

Question 10

Find the equation of the circle passing through the points $$\left(2,-7\right)$$ , $$\left(2,1\right)$$ and $$\left(-2,-3\right)$$ .

Accepted Answer

$$x^2+y^2-4x+6y-3=0$$

Answer

$$x^2+y^2+4x-6y-3=0$$

Answer

$$3x^2+3y^2+2x-4y+3=0$$

Answer

$$3x^2+3y^2-2x-4y+3=0$$

Question 11

If one root of $$8x^2-6x-a-3=0$$ is the square of the other root,
find the value of $$a$$ .

Accepted Answer

-4 or 24

Answer

2 or 24

Answer

2 or -2

Answer

-2 or -4

Question 12

A coin is tossed ten times.
What is the probability that the result will be nine tails in a row?

Accepted Answer

0.001953125

Answer

0.5

Answer

0.25

Answer

0.0009765625

Question 13

Given that $$f\left(x\right)=x^{100}-x^{99}+x^{98}-x^{97}+\cdots+x^2-x+1$$ ,
find the coefficient of $$x^{99}$$ in $$f$$ .

Accepted Answer

0

Answer

-1

Answer

-99

Answer

-9702

Question 14

Find $$\lim_{x\rightarrow5}\ \frac{x^3+4x^2-5x}{x^2-25}$$ .

Accepted Answer

Not exist

Answer

$$\frac{1}{5}$$

Answer

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

Answer

$$\frac{3}{5}$$

Question 15

Find $$\lim_{x\rightarrow\infty}\ \left(1-\frac{3}{5x}\right)^{2x}.$$

Accepted Answer

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

Answer

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

Answer

$$e^{\frac{10}{3}}$$

Answer

$$e^{-\frac{10}{3}}$$

Question 16

Find the area of the region enclosed by the curve $$y=x-x^2$$ and the x-axis.

Accepted Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{8}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{1}{2}$$

20230807-AM1

16 questions

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