# 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 m^{2}. 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. - Quadratic function

It is given a quadratic function y = -4x^{2}+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. - Quadratic function

Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4) - Birthday paradox

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.

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.