# Grade - examples

- Two chords

There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure. - Sweater

Dana confuses sweater and wool has a choice of seven colors. In how many ways she can choose from three colors to the sleeves? - Ophelia

Ophelia recorded the temperature of a cold store every two hours. 1. At 6am it was -4°C and at 8am it was -1°C. By how much did the temperature rise? 2. The temperature went up by 5°C in the next two hours. .What was the temperature at 10am? - Double ladder

The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach? - Tropical, mild and arctic

How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'. - Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste. - Digit sum

How many are three-digit numbers that have a digit sum of 6? - Hemispherical hollow

The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm? - Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible. - Right triangle

Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'. - Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm^{2.}What dimensions can this large rectangle have? Write all options. Explain your calcu - Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - CuSO4 mixture

How many grams of solid CuSO4 we have to add to 450g of 15% CuSO4 solution to produce a 25% solution? - Sum of inner angles

Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees. - The big clock

The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00. - Sandbox

Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox. - Digits

Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z. - Geometric progression 4

8,4√2,4,2√2 - Algebra

X+y=5, find xy (find the product of x and y if x+y = 5) - 5 people

5 people have $122000 and 1 person has $539000 How much should each person (equally) pay?

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