Quiz about Yr2 holiday work

Question 1

$$\frac{ ext{d}}{ ext{d}x}\left(e^x ight)$$

Accepted Answer

$$e^x$$

Answer

$$-e^x$$

Answer

$$\frac{1}{e^x}$$

Answer

$$-\frac{1}{e^x}$$

Question 2

Differentiate y = ln (5x - 7)

Accepted Answer

_ 5 _5x-7

Answer

_ 1 _5x-7

Answer

ln5

Answer

ln5x - ln 7

Question 3

All the equations was TRUE accept...

Accepted Answer

$$\frac{ ext{d}A}{ ext{d}x}=\frac{ ext{d}x}{ ext{d}A} imes\frac{ ext{d}A}{ ext{d}t}$$

Answer

$$\frac{ ext{d}y}{ ext{d}x}=\frac{ ext{d}y}{ ext{d}t} imes\frac{ ext{d}t}{ ext{d}x}$$

Answer

$$\frac{ ext{d}V}{ ext{d}t}=\frac{ ext{d}V}{ ext{d}x} imes\frac{ ext{d}x}{ ext{d}t}$$

Answer

$$\frac{ ext{dA}}{ ext{d}t}=\frac{ ext{d}A}{ ext{d}x} imes\frac{ ext{d}x}{ ext{d}t}$$

Question 4

Stationary point occur when....

Accepted Answer

$$\frac{ ext{d}y}{ ext{d}x}=0$$

Answer

x = 0

Answer

$$\frac{ ext{d}x}{ ext{d}y}=0$$

Answer

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

Question 5

Find the derivative.

Accepted Answer

x⁴cosx + 4x³sinx

Answer

x⁴cosx - 4x³sinx

Answer

4x3cosx

Answer

-4x3cosx

Question 6

find y' for y= sin(2x²)

Accepted Answer

4xcos(2x²)

Answer

4sin(2x2)

Answer

2xcos(2x²)

Answer

xcos(4x2)

Question 7

Question 7.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 8

Find f '(x) if f(x) = x⁴sinx

Accepted Answer

x⁴cosx + 4x³sinx

Answer

4x3cosx

Answer

x4cosx

Answer

-x⁴cosx + 4x³sinx

Question 9

Find the second derivative of the function:
f (x) = sin (5x⁶)

Accepted Answer

f ''(x) = 150x⁴ cos 5x⁶ - 900x¹⁰ sin 5x⁶

Answer

f ''(x) = 30x⁴ cos 5x⁶ + 30x¹⁰ sin 5x⁶

Answer

f ''(x) = 180x⁴ cos 5x⁶ - 900x¹⁰ sin 5x⁶

Answer

f ''(x) = 150x⁴ cos 5x⁶ + 900x¹⁰ sin 5x⁶

Question 10

Find dy/dx for
y = (x² + 1)³

Accepted Answer

dy/dx = 6x(x² + 1)²

Answer

dy/dx = 3(x² + 1)²

Answer

dy/dx = 3(2x)²

Answer

dy/dx = 2x(x² + 1)²

Question 11

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

Accepted Answer

y = 500x - 400

Answer

y = 500x + 400

Answer

y = 100x + 400

Answer

y = -500 x - 400

Question 12

Find the derivative:
y=5x²e^3x

Accepted Answer

y'=5xe^3x(3x+2)

Answer

y'=10xe^3x(2x+3)

Answer

y'=10ex^3x(3x+2)

Answer

y'=5xe^3x(2x+3)

Question 13

Find the derivative:
y = 3ln(x²-3)

Accepted Answer

6x/(x2-3)

Answer

3/(x2-3)

Answer

3x/(x2-3)

Answer

9x/(x2-3)

Question 14

Find the derivative of the given equation
f(x) = 7

Accepted Answer

0

Answer

7

Answer

7x

Answer

14

Question 15

Find the derivative of the given equation
f(x) = 1/x²

Accepted Answer

-2x-3

Answer

1/2x

Answer

-2x

Answer

2x

Question 16

If a function has a derivative that is negative, what does that tell you?

Accepted Answer

The function is decreasing

Answer

The function is increasing

Question 17

The derivative of a function is its

Accepted Answer

Instantaneous rate of change

Answer

Sign

Answer

Maximum/Minimum

Answer

Common Denominator

Question 18

If the position function for a particle is s(t) = -t² - t, what is the expression for the instantaneous velocity for the particle?

Accepted Answer

v(t) -2t - 1

Answer

v(t) = -2

Answer

v(t) = t3

Answer

v(t) = -t

Question 19

What rule should be used in deriving h(x) = 2(x - 4)³

Accepted Answer

Chain rule

Answer

Power rule

Answer

Product rule

Answer

Quotient rule

Question 20

Find the derivative of
f(x) = (x⁶ + 4)⁵

Accepted Answer

f '(x) = 30x⁵(x⁶ + 4)⁴

Answer

f '(x) = 5x⁵(x⁴ + 4)⁴

Answer

f '(x) = 6x⁵(x⁶ + 4)⁴

Answer

f '(x) = 30x⁶(x⁶ + 4)⁴

Question 21

Find the derivative of f(x)=(x³-2x)²

Accepted Answer

6x⁵ - 16x³+8x

Answer

6x⁵ - 12x³+8x

Answer

x⁶-4x⁴+4x²

Answer

6x⁵ - 16x^3-8x

Question 22

Differentiate f(x) = (9 - 4x²)^-1

Accepted Answer

8x/(9 - 4x²)²

Answer

8x/(9 - 4x²)^-2

Answer

-8x/(9 - 4x²)^-2

Answer

-8x(9 - 4x²)²

Question 23

Question 23.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 24

Question 24.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 25

Question 25.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 26

Differentiate:
f(x) = x⁷ (5 + 8x)³

Accepted Answer

f '(x) = x⁶ (5 + 8x)² (35 + 80x)

Answer

f '(x) = x² (5 + 8x)⁶ (35 + 80x)

Answer

f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

Answer

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Question 27

Find the derivative.

y = x²/ (3x-1)

Accepted Answer

y' = (3x² - 2x) / (3x-1)²

Answer

y' = (3x-1) / (3x-1)²

Answer

y' = (6x+1)²/ (3x-1)²

Answer

y' = (6x-1) / (3x-1)²

Question 28

Given that y = (x+2)/(x-3), find y'.

Accepted Answer

y' = -5/(x-3)²

Answer

y' = -1/(x-3)²

Answer

y' = (2x-5)/(x-3)²

Answer

y' = (2x-1)/(x-3)²

Question 29

Find the derivative of g(x)=(3x-2)/(x²+2)

Accepted Answer

(-3x²+4x +6)/(x²+2)²

Answer

3/(2x)

Answer

(-3x²-4x +6)/(x²+2)²

Answer

(-3x²+10)/(x²+2)²

Question 30

Find

$$\frac{ ext{d}y}{ ext{d}x}$$ if $$y=\frac{x}{Sinx}$$

Accepted Answer

$$\frac{Sinx-x\ Cosx}{Sin^2x}$$

Answer

$$\frac{Cosx-Sinx}{x^2}$$

Answer

$$\frac{x-Sinx}{Cos^2x}$$

Answer

$$\frac{1}{Cosx}$$

Question 31

find y' for y= sin(2x²)

Accepted Answer

4xcos(2x²)

Answer

4sin(2x2)

Answer

2xcos(2x²)

Answer

xcos(4x2)

Question 32

The interval in which

$$y=x^2e^{-x}$$ is increasing is

Accepted Answer

(D) $$\left(0,\ 2\right)$$

Answer

(A) $$\left(-\infty,\ \infty\right)$$

Answer

(B) $$\left(-2,\ 0\right)$$

Answer

(C) $$\left(2,\ \infty\right)$$

Question 33

The population of a town x years after 2000 is modeled by P(x).  What is the best interpretation of P'(10) = 50.

Accepted Answer

In 2010, the population was increasing 50 people per year.

Answer

In 2010, the population was 50 people.

Answer

It took 10 years for the population to increase by 50 people.

Answer

The average change in population over the 10 years was 50 people per year.

Question 34

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec. How fast is the height of the water changing when the water is 2 ft deep?

Accepted Answer

-9/(8pi) ft/sec

Answer

9/(8pi) ft/sec

Answer

-8/(9pi) ft/sec

Answer

8/(9pi) f/tsec

Question 35

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

Accepted Answer

100ft x 200ft

Answer

102ft x 196 ft

Answer

50 ft x 300 ft

Answer

50 ft x 175 ft

Question 36

Find the derivative
f(t) = (t² + 2t)⁵

Accepted Answer

f'(t) = 5(t² + 2t)⁴(2t + 2)

Answer

f'(t) = 5(2t+2)⁴

Answer

f'(t) = 5(t² + 2t)⁴

Answer

f'(t) = 5(t² + 2t)⁴(2t)

Question 37

Question 37.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 38

find y' for y=(e^5x)+1

Accepted Answer

5e5x

Answer

5e5x+1

Answer

e5x

Answer

1

Question 39

find y' for y= sin(2x²)

Accepted Answer

4xcos(2x²)

Answer

4sin(2x2)

Answer

2xcos(2x²)

Answer

xcos(4x2)

Question 40

$$\frac{ ext{d}}{ ext{d}x}\left[x^2\cdot\sin\left(x ight) ight]$$

Accepted Answer

$$x^2\cos\left(x\right)+2x\sin\left(x\right)$$

Answer

$$x^2\cos\left(x\right)-2x\left(\sin x\right)$$

Answer

$$-x^2\sin\left(x\right)+2x\cos\left(x\right)$$

Answer

$$x^2\sin\left(x\right)+2x\cos\left(x\right)$$

Question 41

$$\frac{ ext{d}}{ ext{d}x}\left[x^2\left(x+1 ight)\left(2x-3 ight) ight]$$

Accepted Answer

$$8x^3-3x^2-6x$$

Answer

$$8x^3+3x^2-6x$$

Answer

$$8x^3-3x^2+6x$$

Answer

$$8x^3+3x^2+6x$$

Question 42

$$\frac{ ext{d}}{ ext{d}x}\left[\frac{1}{x}\cdot\frac{1}{2x^2}\cdot\frac{-1}{3x^3} ight]$$

Accepted Answer

$$\frac{1}{x^7}$$

Answer

$$\frac{1}{x^6}$$

Answer

$$-\frac{1}{x^7}$$

Answer

$$\frac{-1}{x^6}$$

Question 43

Given $$y=\ln\ \left(3x\right).\ \frac{dy}{dx}=?$$

Accepted Answer

$$\frac{1}{x}$$

Accepted Answer

$$\frac{3}{3x}$$

Answer

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

Question 44

$$y=-3\ln\left(x^2+3x-1\right).\ \frac{dy}{dx}=?$$

Accepted Answer

$$\frac{-6x-9}{x^2+3x-1}$$

Answer

$$\frac{-3}{x^2+3x-1}$$

Answer

$$\frac{2x+3}{x^2+3x-1}$$

Answer

$$\frac{1}{x^2+3x-1}$$

Question 45

$$y=\ln\sqrt[]{2+x}$$ . $$\frac{dy}{dx}=?$$

Accepted Answer

$$\frac{1}{2\left(2+x\right)}$$

Answer

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

Answer

$$\sqrt[]{2+x}$$

Answer

$$\frac{1}{2}\ln\left(2+x\right)^{-\frac{1}{2}}$$

Question 46

Given $$y=\left(\ln\ 2x\right)^3.\ \frac{dy}{dx}=?$$

Accepted Answer

$$3\left(\ln2x\right)^2\left(\frac{1}{x}\right)$$

Answer

$$3\left(\ln2x\right)^2$$

Answer

$$3\left(\ln2x\right)^2\left(\frac{1}{2x}\right)$$

Question 47

Given $$y=2x\ln\ 3x,\ \ \frac{dy}{dx}=?$$

Accepted Answer

$$2\ln3x+2$$

Answer

$$2\ln3x+\frac{2}{3}$$

Answer

$$2\left(\frac{1}{x}\right)$$

Answer

$$2x\ln3x+\frac{2}{x}$$

Question 48

Given $$y=\frac{e^{2x}}{\ln x}$$ . What is $$\frac{dy}{dx}=?$$

Accepted Answer

$$\frac{2e^{2x}-\frac{e^{2x}}{x}}{\left(\ln x\right)^2}$$

Answer

$$\frac{\frac{e^{2x}}{x}-2e^{2x}\ln x}{\left(\ln x\right)^2}$$

Answer

$$\frac{2e^{2x}}{\frac{1}{x}}$$

Answer

$$\frac{e^{2x}-\frac{e^{2x}}{x}}{\left(\ln x\right)^2}$$

Question 49

Given $$y=\ln\left(5x^3-1\right)^2\left(\sqrt[]{x^2+1}\right)$$ . Which shows the correct use of law of log and ready to obtain $$y$$ ?

Accepted Answer

$$y=2\ln\left(5x^3-1\right)^{ }+\frac{1}{2}\ln\left(x^2+1\right)$$

Answer

$$y=\ln\left(5x^3-1\right)^2+\ln\sqrt[]{x^2+1}$$

Answer

$$y=2\ln\left(5x^3-1\right)^{ }+\ln\sqrt[]{x^2+1}$$

Answer

$$y=\ln\left(5x^3-1\right)^2+\ln\left(x^2+1\right)^{\frac{1}{2}}$$

Question 50

Given $$y=\ln\left(\frac{\sqrt[]{x-2}}{\left(x^2+2\right)^2}\right)$$ .Which shows the correct use of law of log and READY to obtain $$y$$ ?

Accepted Answer

$$y=\frac{1}{2}\ln\left(x-2\right)-2\ln\left(x^2+2\right)^{ }$$

Answer

$$y=\ln\sqrt[]{x-2}-\ln\left(x^2+2\right)^2$$

Answer

$$y=\ln\sqrt[]{x-2}-2\ln\left(x^2+2\right)^{ }$$

Answer

$$y=\frac{1}{2}\ln\left(x-2\right)+2\ln\left(x^2+2\right)^{ }$$

Question 51

Given $$y=\ln\left(\frac{x^2-1}{x^2\left(1-2x^3\right)}\right).$$ Which shows the correct use of law of log and READY to obtain $$y$$ ?

Accepted Answer

$$y=\ln\left(x^2-1\right)-2\ln\left(x^{ }\right)-\ln\left(1-2x^3\right)$$

Answer

$$y=\ln\left(x^2-1\right)-\ln\left[x^2\left(1-2x^3\right)\right]$$

Answer

$$y=\ln\left(x^2-1\right)-\ln\left(x^2\right)+\ln\left(1-2x^3\right)$$

Answer

$$y=\ln\left(x^2-1\right)-\ln\left(x^2\right)-\ln\left(1-2x^3\right)$$

Question 52

Given $$y=\ln\left(\frac{\sqrt[]{x-2}}{\left(x^2+2\right)^2}\right)$$ . $$\frac{dy}{dx}=?$$

Accepted Answer

$$\frac{1}{2}\left(\frac{1}{x-2}\right)-2\left(\frac{2x}{x^2+2}\right)$$

Answer

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

Answer

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

Answer

$$\frac{1}{2x-4}-\frac{4x}{2x^2+4}$$

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics