Free Printable Year 13 Starter Quiz 07/1/021

1.

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

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

2.

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

a)

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

b)

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

c)

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

d)

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

3.

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

a)

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

b)

$\frac{3x^2}{2}+7x+c$

c)

$\frac{x^4}{8}+7x+c$

d)

$\frac{x^4}{8}+c$

4.

Integrate $\int_{ }^{ }\sin x\ dx$

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

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

5.

$\int\tan x_{ }dx\$

a)

$\ln\left|\cos\right|+C$

b)

$-\ln\left|\cos x\right|+C$

c)

$\ln\left|\sin x\right|+c$

d)

$\frac{\tan^2x}{2}+c$

6.

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.

a)

3

b)

5.33

c)

1.97

d)

81

7.

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

a)

$3\cos3x-2\ln2x$

b)

$3\cos3x-\frac{1}{x}$

c)

$\cos3x-\frac{3}{x}$

d)

$-3\cos x+\ln2x$

Year 13 Starter Quiz 07/1/021

Total questions: 7

Worksheet time: 21mins

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