## All Tasks

#### Solvable or not?

Which of the following equations is not solvable?

# Unassigned

Reasoning

9

#### Inverse function of arcsin

Consider $f(x)= a -2 \arcsin(1-2x)$ with domain $D_f=[0,1]$ and range $D'_f = \left[ 0, 2\pi\right] $.
Determine the analytic expression of the inverse function of $f$, $f^{-1}(x)$, and use that to calculate the value of $a \in \mathbb R$ knowing that $f^{-1}(0)=0$.

# Functions of one variable

Training

13

#### Find the coefficients of terms in algebraic expression_2

Find the number $a$ if the following algebraic expression is independent of $y$.
$A= a(x+y+2)-2(x+2y)+6$

# Linear equations

Reasoning

8

#### Find the value_1

Evaluate the following algebraic expression if $x=-2$ and $y=-3$
$A=\frac{x+3}3-2\frac{y+2}5$

# Unassigned

Training

8

#### Simplification of algebraic expression_1

If we simplify the following algebraic expression $A= 2x+3y+7-3x+5x-3+7y$ into the form $ax+by+c$, where the $a,b$ and $c$ are rational numbers, the A is

# Linear equations

Training

8

#### Chain rule arcsin

Determine the equation of the normal line to the graph of $y(x)=6\arcsin(f(x))$ at $x=0$, knowing that $f(0)=0.5$ and $f'(0)=1$

# Functions of one variable

Reasoning

13