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9000089003

Level:

Students from a class bought a snack in the school lunch-room. There were

31

students in the class in total. Altogether

8

students had snack from their home and they did not buy anything. Altogether

12

students bought hamburger and

15

students bought hot-dog. How many students bought both hamburger and hot-dog?

4

19

8

9000090905

Level:

Given lines

p

and

q

, find

m \in R

such that the lines

p

and

q

are parallel.

p : x - 2 y + 7 = 0, q : x + 3 y + m = 0

does not exist

m = - 7

m = - \frac{2}{7}

m = 2

m = 7

9000090906

Level:

Given lines

p

and

q

, find

m \in R

such that the lines

p

and

q

are parallel.

\begin{aligned} p : x & = 1 + t, \\ y & = - 3 t; t \in R, \end{aligned} \begin{aligned} q : x & = 3 - 2 u, \\ y & = 1 + m u; u \in R \end{aligned}

m = 6

m = \frac{3}{2}

m = - \frac{2}{3}

does not exist

9000090907

Level:

Given points

A = [2; m]

and

B = [- 1; 0]

, find

m \in R

such that the line

p

is parallel to the line passes through the points

A

B

\begin{aligned} p : x & = 3 + 2 t, \\ y & = 5 - t; t \in R \end{aligned}

m = - \frac{3}{2}

m = \frac{3}{2}

m = - \frac{2}{3}

m = 2

does not exist

9000090908

Level:

Given points

A = [2; 1]

and

B = [m; 0]

, find

m \in R

such that the line

p

is parallel to the line passes through the points

A

B

p : 3 x - y + 17 = 0

m = \frac{5}{3}

m = 4

m = \frac{5}{2}

m = - 1

another solution

9000090909

Level:

Given lines

p

and

q

, find

m \in R

such that the lines

p

and

q

are parallel.

p : 2 x + m y - 3 = 0, \begin{aligned} q : x & = 1 + t, \\ y & = 2 - t; t \in R \end{aligned}

m = 2

m = - 2

m = 11

m = - \frac{1}{11}

does not exist

9000090910

Level:

Given lines

p

and

q

, find

m \in R

such that the line

p

is parallel to

q

p : x + 4 y - 3 = 0, \begin{aligned} q : x & = 1 + m t, \\ y & = 2 - 3 t; t \in R \end{aligned}

m = 12

m = - \frac{1}{12}

m = 4

m = \frac{5}{2}

m = - 1

9000090903

Level:

Given the line

p : 3 x - 2 y + 11 = 0,

find

m \in R

such that the point

C = [m; 0]

is on the line

p

m = - \frac{11}{3}

m = - 1

m = 11

m = - \frac{1}{11}

m = 2

9000090902

Level:

Given the parametric line

p

, find

m \in R

such that the point

C = [m; 3]

is on the line

p

\begin{aligned} p : x & = 1 - t, \\ y & = - 3 + 2 t; t \in R \end{aligned}

m = - 2

m = 4

m = 11

m = - \frac{11}{3}

m = \frac{3}{2}

9000089001

Level:

Students from a class have a possibility to work in mathematical and physical hobby groups. There are

31

students in the class. From the total,

21

students are members of mathematical group. Some of the students are members of both groups, but there are

10

which are members of just one group. There are

3

students which are not members of any of those groups. How many students are members of both mathematical and physical groups?

18

16

19

C

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