Assignments

The following assignments relate to all kinds of basic skills. Some parts are dealt with separately in the other topics.

1. Simplify:

$\displaystyle\frac{x^3(x^{\frac{1}{3}})^6}{\sqrt[4]{x^{12}}}$

2. Factorize:

$(x-2)^2-5(x-2)+4$

3. Factorize:

$(x^2-h)$ als $h\geq0$

4. Calculate the value of the following fraction as $h$ approaches to $0$ :

$\displaystyle\frac{\sqrt{x+h}-\sqrt{x}}{h}$

Note that if you just substitute $h =0$ the result is $\frac{0}{0}$ which is not defined. The solution of this assignment is used in determining the derivative of the function $f(x)=\sqrt{x}$ , see also the subject Differentiating basic functions.

5. Calculate without the aid of a calculator:

$\displaystyle\frac{639^2-312^2}{951}$

6. Solve the following equation:

$(2x-1)(x+2)+4x-3=x^2+x(x-3)$

7. Solve the following equations with the sum-product method:

$x^2-12x-85=0$

$3x^2-12x+9=0$

$x^2-10x+21=0$

8. Solve the following equations:

$(x-3)^2+2(x-3)=0$

$(x-5)^2-16=0$

$x^2+x-1=0$

9. Factorize:

$9a^3b^2+3a^2b^3+12ab^2$

10. Calculate without the aid of a calculator:

$\displaystyle\frac{13}{7}.\frac{12}{5}.\frac{4}{9}.\frac{21}{26}.\frac{10}{36}$ .

0

Web Design Bangladesh Web Design Bangladesh Mymensingh