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9000104805

Level:

C

Find the slope of a line through the center of the hyperbola

\frac{(x - 2)^{2}}{4} - \frac{(y + 3)^{2}}{9} = 1

which has a unique intersection with this hyperbola.

There is no solution, the line with these properties does not exist.

\frac{3}{2}

- \frac{3}{2}

\frac{2}{3}

1

0

9000104809

Level:

C

Among the following lines (which all pass through the point

[- 1; 3]

) identify a line which is tangent to the following hyperbola.

(x + 2) \cdot (y - 2) = 1

k : y = - x + 2

p : y = 3

q : x = - 1

r : y = x + 4

None of the given answers is correct.

9000101610

Level:

C

Simplify using long division of polynomials.

(2 x^{3} - x^{2} - 3 x - 1) : (2 x + 1)

x^{2} - x - 1

x^{2} - x + 1

x^{2} + x + 1

x^{2} - 2 x - 1

9000101609

Level:

C

Simplify using long division of polynomials.

(3 x^{3} + 17 x^{2} + 23 x + 5) : (x^{2} + 4 x + 1)

3 x + 5

3 x - 5

3 x + 1

3 x - 1

9000101708

Level:

C

Factor the following polynomial.

8 x^{3} - 27

(2 x - 3) (4 x^{2} + 6 x + 9)

(2 x - 3) (4 x^{2} - 6 x + 9)

(2 x + 9) (4 x^{2} - 6 x + 9)

(2 x - 3) (4 x^{2} + 6 x - 9)

9000101709

Level:

C

Factor the following polynomial.

27 x^{6} z - 8 y^{3} z

z (3 x^{2} - 2 y) (9 x^{4} + 6 x^{2} y + 4 y^{2})

z (3 x^{2} + 2 y) (9 x^{4} + 6 x^{2} y - 4 y^{2})

z (3 x^{2} + 2 y) (9 x^{4} - 6 x^{2} y + 4 y^{2})

z (3 x^{2} - 2 y) (9 x^{4} + 6 x^{2} y^{2} + 4 y)

9000101707

Level:

C

Factor the following polynomial.

x^{6} - 1

(x - 1) (x + 1) (x^{2} + x + 1) (x^{2} - x + 1)

(x - 1) (x + 1) (x^{2} + x + 1) (x^{2} - x - 1)

(x - 1) (x + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

(x - 1) (x + 1) (x^{2} + x - 1) (x^{2} - x + 1)

9000089004

Level:

C

Students in a university are allowed to buy either lunch or dinner in a student's canteen. There are

129

freshmen students in total. Altogether

116

freshmen students buy the lunch or dinner. From this amount,

62

students buy just one meal. The number of freshmen students which buy lunch is bigger by

46

than the number of freshmen students which buy dinner. How many freshmen students buy only the dinner?

8

54

62

9000089002

Level:

C

Students from a class decided to order books for forthcoming holiday. The book-shop in the neighborhood had two bestsellers on the stock: a crime novel and a horror stories. There were

31

students in the class in total. From this total,

22

students bought horror stories. Altogether

12

students bought just one of the books. Two students did not buy any of these books. How many students bought the crime novel?

24

7

5

9000089005

Level:

C

There are two types of cheese in a shop. Altogether

153

customer were in the shop during a day. From this total,

65

customers bought the first cheese. From the same total,

49

customers bought the second cheese.

20 %

of customers which bought at least one of the types of cheese bought actually both types. How many customers did not buy any of these two cheeses?

58

39

19

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