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Algebra · Math Test #3

Math Test #3 Template saved · 28 variants ready

Template

Quadratic equation

a x^{2} + b x + c = 0

a ∈ [2; 9] b ∈ [−12; 12] c prime

3 pt

Vieta's formula

x_{1} \cdot x_{2}, x_{1} + x_{2} for x^{2} + b x + c = 0

D > 0 integer roots

2 pt

Single root

x^{2} + k x + c = 0, D = 0

c = 9, 16, 25…

3 pt

Preview · Variant V07

Math Test

V07

Algebra & Calculus45 min · 10 problems

#	Instructions	Problem	Answer
1	Find 25% of	$\frac{3}{5} + \frac{1}{4}$	$=$
2	Solve the equation	$4 x + 7 = x - 5$	$x =$
3	Solve the system	${\begin{matrix} 2 x + y = 7 \\ x - y = 2 \end{matrix}$	$x =$ $y =$
4	Solve the equation	$x^{2} + 2 x - 8 = 0$	$x_{1} =$ $x_{2} =$
5	Solve, state the domain	$\frac{3 x + 2}{x - 5} = 2$	$x =$ Domain:
6	Solve the equation	$\sqrt{x + 7} = x - 1$	$x =$
7	Solve the equation	$\sin x = \frac{\sqrt{2}}{2}$	$x =$
8	Solve the equation	$\log_{3} (2 x - 1) = 2$	$x =$
9	Find the local min of	$f (x) = x^{3} - 6 x^{2} + 9 x + 2$	$x =$
10	Compute	$\int_{0}^{2} (3 x^{2} - 4 x + 2) d x$	$=$

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#	Instructions	Problem	Answer
1	Find 50% of	$\frac{1}{2} + \frac{1}{3}$	$\frac{5}{12}$
2	Solve the equation	$5 x - 2 = 2 x + 7$	$x = 3$
3	Solve the system	${\begin{matrix} x + 2 y = 8 \\ x - y = 2 \end{matrix}$	$x = 4, y = 2$
4	Solve the equation	$2 x^{2} - 3 x - 2 = 0$	$x_{1} = - \frac{1}{2}, x_{2} = 2$
5	Solve, state the domain	$\frac{4 x + 2}{x - 1} = 7$	$x = 3, x \neq 1$
6	Solve the equation	$\sqrt{2 x + 1} = x - 1$	$x = 4$
7	Solve the equation	$\cos x = \frac{1}{2}$	$x = \pm \frac{π}{3} + 2 π n$
8	Solve the equation	$\log_{2} (x + 5) = 3$	$x = 3$
9	Find the local min of	$f (x) = x^{3} + 3 x^{2} - 9 x + 1$	$x = 1$
10	Compute	$\int_{0}^{2} (3 x^{2} + 2) d x$	$12$

Instructions

Problem

Answer

Find 50% of

\frac{1}{2} + \frac{1}{3}

\frac{5}{12}

Solve the equation

5 x - 2 = 2 x + 7

x = 3

Solve the system

{\begin{matrix} x + 2 y = 8 \\ x - y = 2 \end{matrix}

x = 4, y = 2

Solve the equation

2 x^{2} - 3 x - 2 = 0

x_{1} = - \frac{1}{2}, x_{2} = 2

Solve, state the domain

\frac{4 x + 2}{x - 1} = 7

x = 3, x \neq 1

Solve the equation

\sqrt{2 x + 1} = x - 1

x = 4

Solve the equation

\cos x = \frac{1}{2}

x = \pm \frac{π}{3} + 2 π n

Solve the equation

\log_{2} (x + 5) = 3

x = 3

Find the local min of

f (x) = x^{3} + 3 x^{2} - 9 x + 1

x = 1

Compute

\int_{0}^{2} (3 x^{2} + 2) d x

12

#	Instructions	Problem	Answer
1	Find 75% of	$\frac{3}{4} + \frac{3}{5}$	$\frac{81}{80}$
2	Solve the equation	$5 x - 3 = 2 x + 6$	$x = 3$
3	Solve the system	${\begin{matrix} x + y = 5 \\ x - y = 1 \end{matrix}$	$x = 3, y = 2$
4	Solve the equation	$x^{2} + 3 x - 4 = 0$	$x_{1} = - 4, x_{2} = 1$
5	Solve, domain	$\frac{5 x + 17}{x + 3} = 3$	$x = - 4, x \neq - 3$
6	Local min of	$x^{3} - 3 x + 5$	$x = 1$
7	Compute	$\int_{1}^{2} (3 x^{2} + 4 x + 1) d x$	$14$

Instructions

Problem

Answer

Find 75% of

\frac{3}{4} + \frac{3}{5}

\frac{81}{80}

Solve the equation

5 x - 3 = 2 x + 6

x = 3

Solve the system

{\begin{matrix} x + y = 5 \\ x - y = 1 \end{matrix}

x = 3, y = 2

Solve the equation

x^{2} + 3 x - 4 = 0

x_{1} = - 4, x_{2} = 1

Solve, domain

\frac{5 x + 17}{x + 3} = 3

x = - 4, x \neq - 3

Local min of

x^{3} - 3 x + 5

x = 1

Compute

\int_{1}^{2} (3 x^{2} + 4 x + 1) d x

14

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