Math Competition

Algebra

100

((-2)^-1)³

-1/8

200

Find the roots of quadratic equation:

2x²+3x+1=0

-1,  -1/2

300

Multiplication of two consecutive numbers is 12. Find the numbers

-4, 3

400

Find a quadratic equation whose roots are 1/3 and 3/2.

6x²-11x+3=0

500

A man climbing up a mountain climbs 800 m in the first hour and 25 m less than the previous hour in each subsequent hour. In how many hours can he climb 5700 m?

8 hours

Function and Graphs

100

If f(x) = 2x², find f(-3)=?

18

200

Find the domain of this function:
f(x)=(2x+1)/(x²-16)

(-∞, -4) U (-4, 4) U (4, ∞)

300

For the function ff(x)=−x²+4:
Does the graph open upward or downward?

downward

400

Find the function of this graph

x²+y²=16

500

Two functions are given:

f(x)=3x+3,g(x)=7x−9

At which point do their graphs intersect?

(3, 12)

Word problems

100

A fruit seller has 80 apples. He sells 25% on Monday and 30% of the remainder on Tuesday. How many apples are left?

42 apples

200

Five friends share a total of 15,000 tenge equally for a boat trip. At the last minute, two friends decide not to pay.How much more does each of the remaining friends have to pay?

2000 more each

300

Three numbers are in ratio 4:5:6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers?

44, 55, 66

400

Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting number is greater than the original number by 27. What is the two digit number?

36

500

The distance between two stations is 425km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of the other by 5km/h. If the distance between the two trains after 3h of their start is 20km, find the speed of each train.

65, 70

Geometry

100

In a triangle, a line segment joining a vertex to the midpoint of the opposite side is called a _____ of the triangle.

median

200

What is the sum of interior angles of octagon?

1080 degrees

300

Find the measure of angle A in the figure below.

87 degrees

400

Find the area of the given shape.

270 cm²

500

The vertices of the inscribed (inside) square bisect the sides of the second (outside) square. Find the ratio of the area of the outside square to the area of the inscribed square.

2

Logic/ Brain Teasers

100

In a class of 24 students, 12 know English and 15 know German. How many students know both languages?

3

200

How many times does the digit 5 appear from 1 to 100?

20

300

Find the pattern 

10

400

Find a?

0,5

500

If the shapes in the equations are equal to some numbers:

12