#### Chapter 1 Elementary Arithmetic

Section 1.5 Final Test

# 1.5.1 Final Test Module 1

This is a test for submission:
• Unlike open exercises, no hints for formulating mathematical expressions are provided.
• The test can be restarted or interrupted at any time.
• The test can be terminated and submitted using the buttons at the end of the page, or reset.
• The test can be attempted several times. Only the last version will be included in the statistics.

##### Exercise 1.5.1
Check the box in each case to indicate whether the mathematical expressions are equations, inequalities, terms, or numbers (multiple checks are possible):

 Mathematical expression Equation Inequality Term Number $1+\frac{1}{2}-3\left(3-\frac{1}{2}\right)$ ${5}^{x}-{x}^{5}$ ${x}^{2}<\sqrt{x}$ $xyz-1$ ${b}^{2}=4ac$

##### Exercise 1.5.2
Simplify the compound fraction $\frac{3+\frac{3}{2}}{\frac{1}{12}+\frac{1}{4}}$ to a reduced simple fraction:
For example, enter $\frac{11}{12}$ as 11/12.

##### Exercise 1.5.3
Expand the following term completely and collect like terms:
$\left(x-1\right)·\left(x+1\right)·\left(x-2\right)$ = .
For example, enter $\left(x+1\right)\left(x+2\right)$ = x^2+3*x+2 or alternatively as x*x+3*x+2.

##### Exercise 1.5.4
Apply one of the binomial formulas to transform the term:
1. $\left(x-3\right)\left(x+3\right)$ = .
2. $\left(x-1{\right)}^{2}$ = .
3. $\left(2x+4{\right)}^{2}$ = .
For example, enter $\left(x+1{\right)}^{2}$ = x^2+2*x+1 or alternatively as x*x+2*x+1.

##### Exercise 1.5.5
Rewrite the following expression containing powers and roots as a simple power with a rational exponent:
$\frac{{x}^{3}}{{\left(\sqrt{x}\right)}^{3}}$$=$ .
For example, enter $\sqrt{x}·{x}^{2}$ = x^(5/2) or alternatively as x^(2.5),
mind the brackets around the fraction.

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