## All Tasks

#### Differential of the function arcsin

Find the differential of the function $y=\arcsin \sqrt{2x+1}$.

# Functions of one variable

Training

13

#### Recognition

Choose the correct answer with matching the parabola with her form
$ 1)y= - 3x² $
$ 2) y=\frac{1}{2}x² $
$3) y=4x^2 $
$4) y= -\ \frac{1}{2}x²$

# Quadratic functions

Reasoning

9

#### Linear equations strategy 1

Solve the linear equation by calculating backwards as in the example:
9a – 19 = 17

# Linear equations

Training

7

#### Solvable or not?

Which of the following equations is not solvable?

# Linear equations

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