Year 13 Starter Quiz 07/1/021

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Tags

CCSS.HSA.APR.A.1

Integrate  $\sqrt{x}$  with respect to x

•  $x^{\frac{1}{2}}+c$  

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

•  $\frac{2}{3}x^{\frac{3}{2}}+\ c$  

•  $\frac{3}{2}x^{\frac{3}{2}}+\ c$  

Tags

CCSS.HSN.RN.A.2

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

•  $\frac{3x^2}{2}$  

•  $\frac{3x^2}{2}+7x+c$  

•  $\frac{x^4}{8}+7x+c$  

•  $\frac{x^4}{8}+c$  

Tags

CCSS.HSA.APR.A.1

Integrate $\int_{ }^{ }\sin x\ dx$  

•  $=\tan x+c$  

•  $=-\cos x+c$  

•  $=-\sec x+c$  

•  $=\operatorname{cosec}\ x\ +c$  

 $\int\tan x_{ }dx\$  

•  $\ln\left|\cos\right|+C$  

•  $-\ln\left|\cos x\right|+C$  

•  $\ln\left|\sin x\right|+c$  

•  $\frac{\tan^2x}{2}+c$  

In the expansion of $\left(4-px\right)^6$  , the coeffecient of the  $x^4$  term is 19,440. Give that p is a positive integer find the value of p.

• 3

• 5.33

• 1.97

• 81

The function f(x) is defined as  $f\left(x\right)=\sin3x-\ln2x\ \ \ \ \ \ \ \ \ \ \ \ x>0\ where\ x\ is\ in\ radians\$  a) Find f'(x)

•  $3\cos3x-2\ln2x$  

•  $3\cos3x-\frac{1}{x}$  

•  $\cos3x-\frac{3}{x}$  

•  $-3\cos x+\ln2x$