Free Printable Maths A

1.

Given $z_1=2+3i$ and $z_2=4-4i$ . Express $\frac{z_2}{\overline{z_1}}+\left(\frac{i^3}{-z_2}\right)$ in Cartesian form .

a)

$\frac{147}{104}+\frac{45}{104}i$

b)

$\frac{-147}{104}+\frac{45}{104}i$

c)

$\frac{147}{104}-\frac{45}{104}i$

d)

$-\frac{147}{104}-\frac{45}{104}i$

2.

Solve the equation $\log_2x-\log_4\left(3x+4\right)=0$

a)

4

b)

-1,4

c)

-1

d)

-1,-4

3.

Find the set of values of x for which $\left|\left(2x-3\right)\left(x+2\right)\right|+3x>6$

a)

$x<-1-\sqrt{7}\cup0<x<1\cup x>-1+\sqrt{7}$

b)

$x<-1+\sqrt{7}\cup0<x<1\cup x\ge-1+\sqrt{7}$

c)

$x<-1-\sqrt{7}\cup0<x<1\cup x>1-\sqrt{7}$

d)

$x<-1-\sqrt{7}\cup x<1\cup x>-1+\sqrt{7}$

4.

a)

$a=19,\ b=-9$

b)

$a=-19,\ b=-9$

c)

$a=19,\ b=9$

d)

$a=-19,\ b=9$

5.

A function is defined by $f\left(x\right)=-e^{2x}+5$ . Find $f^{-1}\left(x\right)$ and its domain and range.

a)

$f^{-1}\left(x\right)=\frac{\ln\left(5-x\right)}{2},\ \left(-\infty,5\right),\ \left(-\infty,\infty\right)$

b)

$f^{-1}\left(x\right)=\frac{\ln\left(x-5\right)}{2},\ \left(5,\infty\right),\left(-\infty,\infty\right)$

c)

$f^{-1}\left(x\right)=\frac{\ln\left(5-x\right)}{2},\ \left[5,\infty\right],\left(-\infty,\infty\right)$

d)

$f^{-1}\left(x\right)=\frac{\ln\left(x-5\right)}{2},\ \left[5,\infty\right],\left(-\infty,\infty\right)$

6.

The polynomial $P\left(x\right)=x^4+ax^3-7x^2-4ax+b$ has a factor $\left(x+3\right)$ and remainder 60 when divided by $\left(x-3\right)$ . Find the values of a and b. Hence, factorise $P\left(x\right)$ completely.

a)

$a=2,\ b=12,\$
$P\left(x\right)=\left(x+3\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)$

b)

$a=2,\ b=-12,\$
$P\left(x\right)=\left(x+3\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)$

c)

$a=-2,\ b=12,\$
$P\left(x\right)=\left(x+3\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)$

d)

$a=2,\ b=12,\$
$P\left(x\right)=\left(x-3\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)$

7.

By using $t=\tan\frac{\theta}{2}$ , solve $\sin\theta+7\cos\theta=-3$ for $0\degree<\theta<360\degree$

a)

$\theta=123.2\degree,\ 253\degree$

b)

$\theta=123.2\degree,\ 246.4\degree$

c)

$\theta=61.6\degree,\ 126.5\degree$

d)

$\theta=123.2\degree,\ 126.5\degree$

8.

Express $12\cos\theta+7\sin\theta$ in the form of $R\cos\left(\theta-\alpha\right)$ , where $R>0\ \ \ and\ \ \ \ 0\degree<\alpha<90\degree$ .

a)

$\sqrt{193}\cos\left(\theta-30.3\degree\right)$

b)

$193\cos\left(\theta-30.3\degree\right)$

c)

$\sqrt{193}\cos\left(\theta-1.04\degree\right)$

d)

$\sqrt{95}\cos\left(\theta-30.3\degree\right)$

9.

Find $\lim_{x\rightarrow4^-}\left(\frac{\sqrt{x}-2}{\left|x-4\right|}\right)$

a)

$-\frac{1}{4}$

b)

$\frac{1}{4}$

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

10.

Find $\lim_{x\rightarrow-\infty}\left(\frac{\sqrt{x^2+6x}}{3-2x}\right)$

a)

$\frac{1}{2}$

b)

$\frac{-1}{2}$

c)

2

d)

-2

11.

a)

A=4, B=3

b)

A=3, B=4

c)

A=-4, B=3

d)

A=3, B=-4

12.

The parametric equations of a curve are $x=t+\frac{2}{t}\ \ \ \ \ and\ \ \ \ \ y=2t-\frac{4}{t},t\ne0$ . Find $\frac{dy}{dx}\ \ \ and\ \ \ \ \frac{d^2y}{dx^2}$ .

a)

$-\frac{2t^2+4}{t^2-2}\ ,\ -\frac{16t^3}{\left(t^2-2\right)^3}$

b)

$-\frac{2t^2+4}{t^2-2}\ ,\ \frac{16t^3}{\left(t^2-2\right)^3}$

c)

$-\frac{2t^2+4}{t^2-2}\ ,\ -\frac{16t^3}{\left(t^2-2\right)^2}$

d)

$-\frac{2t^2+4}{t^2-2}\ ,\ -\frac{16t^{ }}{\left(t^2-2\right)^3}$

Maths A

Total questions: 12

Worksheet time: 44mins

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