# Examples for secondary school students

#### Number of problems found: 2028

• Find the sum Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• Vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
• Find the 13 Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
• Peaches There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
• Find the 3 Find the distance and midpoint between A(1,2) and B(5,5).
• Alice Alice spent 5/11 of her money on a back pack. She has \$42 dollars left. How much was her back pack?
• Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
• HP - harmonic progression 2 Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively.
• Angles of a hexagon Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence and the smallest angle is 70°.
• Imaginary numbers Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
• Four sides of trapezoid Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
• Garden The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.
• Sum-log The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
• Half life Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes. It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points. Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4) How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
• Dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
• Infinite decimal Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
• Without Euclid laws Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.

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