#### Solving linear equations.

Solve the following linear equations with brackets or denominator.

# Linear equations

Training
7

#### Find the value_3

Evaluate the following algebraic expression if $x=−4$ and $y=−2$ $x\cdot\frac{y+1}3-2y\frac{2(x+3)+3}7$

# Equations & Inequations

Training
9

#### Solve an equation or inequality with arcsin

Consider $f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$ with domain $D_f=[0, 1]$ and let $f^{-1}(x)= \dfrac{1}{2} -\dfrac{1}{2} \sin\left(\dfrac{\pi}{4}-\dfrac{x}{2}\right)$ be the analytic expression of the inverse function whose domain is $D_f^{-1}=\left[-\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right]$. The solution of the equation $f\left( \dfrac{1-x}{2}\right) +\dfrac{1}{2}\cos\left(\dfrac{\pi}{4}\right) +f^{-1}(0) = \dfrac{1}{2}$ is:
# Equations
# Trigonometry

Training
13

#### Differential - approximate arcsin

Use differential to approximate the change in $y=\arcsin(2x+1)$ when $x$ changes from $−0.5$ to $−0.49$.

# Functions of one variable

Training
13

#### 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 $1)y= - 3x²$ $2) y=\frac{1}{2}x²$ $3) y=4x^2$ $4) y= -\ \frac{1}{2}x²$