Free Printable Set 2: Clash of KMSw Mathematicians

1.

Insert your full name here

(a)

2.

Solve $\left|4x^2-8x+3\right|\le1$

a)

$\left(-\infty,\frac{2-\sqrt{2}}{2}\right]\cup\left[\frac{2-\sqrt{2}}{2},+\infty\right)$

b)

$\left[\frac{2-\sqrt{2}}{2},\frac{2+\sqrt{2}}{2}\right]$

c)

$\left[\frac{2-\sqrt{2}}{2},1\right]\cup\left[1,\frac{2+\sqrt{2}}{2}\right]$

d)

$\left[\frac{2-\sqrt{2}}{2},1\right]$

3.

Solve the inequality $\frac{6-5x-x^2}{x-3}\ge0$

a)

$\left[-6,1\right]\cup\left[3,+\infty\right)$

b)

$\left[-6,1\right]\cup\left(3,+\infty\right)$

c)

$\left(-\infty,-6\right]\cup\left[1,3\right]$

d)

$\left(-\infty,-6\right]\cup\left[1,3\right)$

4.

Given $f\left(x\right)=3x^2+5$ and $g\left(x\right)=\sqrt{x-1}$ . Find $\left(f\ \circ\ g\right)\left(5\right)$ .

a)

7

b)

17

c)

80

d)

11

5.

Find the inverse of $f\left(x\right)=\frac{e^x-e^{-x}}{2}$

a)

$f^{-1}\left(x\right)=x-\sqrt{x^2+1}$

b)

$f^{-1}\left(x\right)=x+\sqrt{x^2+1}$

c)

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

d)

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

6.

Given that $f\left(x\right)=3x-5$ and $\left(g\ \circ\ f\right)\left(x\right)=\frac{1}{6x-10}+1$ . Find $g\left(x\right)$ .

a)

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

b)

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

c)

$g\left(x\right)=\frac{3x-5}{6x-10}$

d)

$g\left(x\right)=\frac{1}{2x-20}+1$

7.

a)

$A=-\frac{3}{4}$ , $B=2$

b)

$A=\frac{3}{4}$ , $B=2$

c)

$A=\frac{3}{4}$ , $B=-2$

d)

$A=-\frac{3}{4}$ , $B=-2$

8.

Given the complex numbers $z_1=\frac{a}{1+i}$ and $z_2=\frac{b}{1+2i}$ , where $a$ and $b$ are real such that $z_1+z_2=1$ . Find the values of $a$ and $b$ .

a)

$a=4,\ b=-5$

b)

$a=4,\ b=5$

c)

$a=-4,\ b=-5$

d)

$a=-4,\ b=5$

9.

$\log_8\left(x+3\right)+\log_8\left(9-x\right)=\frac{2}{3}$

Solve the equation

a)

$x=1,\ x=-5$

b)

$x=1$

c)

$x=5$

d)

$x=1,\ x=5$

10.

Given that $y^4=\ln\left(x^5y^3\right)\$ where $x>0,\ y>0$

. Find the value of $\frac{dy}{dx}$ when $y=1$ .

a)

$5e^{\frac{1}{5}}$

b)

$\frac{e^{-\frac{1}{5}}}{5}$

c)

$5e^{-\frac{1}{5}}$

d)

$\frac{1}{5}e^{\frac{1}{5}}$

11.

Find $\frac{\text{d}^2y}{\text{d}x^2}$ for the parametric $y=3e^{t^2}$ and $x=3\ln t^2$ .

a)

$t^2e^{t^2}$

b)

$2t^2e^{t^2}\left(t^2+1\right)$

c)

$\frac{2t^2e^{t^2}\ \left(t^2+1\right)}{3}$

d)

$\frac{t^2e^{t^2}\left(t^2+1\right)}{3}$

12.

The curve $f\left(x\right)=-x^3+3x^2$ have 2 stationary points with coordinates $\left(0,0\right)$ and $\left(2,4\right)$ . Determine the interval where $f\left(x\right)$ is increasing.

a)

$\left(-\infty,\ 0\right)$

b)

$\left(0,2\right)$

c)

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

d)

$\left(0,\infty\right)$

13.

A man 1.8m tall is walking at speed $2\ ms^{-1}$ away from a lamp post. If the lamp is 6m above the ground, find the rate of the change in the length, $\frac{dx}{dt}$ , of this man's shadow.

a)

$0.8571\ ms^{-1}$

b)

$0.4286\ ms^{-1}$

c)

$1.4286\ ms^{-1}$

d)

$2.0\ ms^{-1}$

14.

Usually, what is your feeling/emotions when doing Maths? You may select more than one answer. (Ungraded)

a)

Nervous

b)

Excited

c)

Disappointed

d)

Relaxed

e)

Frustrated

Set 2: Clash of KMSw Mathematicians

Total questions: 14

Worksheet time: 45mins

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