# Examples for secondary school students

#### Number of problems found: 2059

• 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.
• Function 3 Function f(x)=a(x-r)(x-s) the graph of the function has x- intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s.
• Pairs of socks Ferdinand has twelve pairs of socks, one sock is leaky. What is the probability of putting on a leaky sock?
• Hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
• The length The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
• Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
• Square If we increase side of the square, increase its area of 63%. What is the percentage we increase side of the square?
• Acceleration The car accelerates at rate 0.5m/s2. How long travels 400 meters and what will be its speed?
• Wind drift The plane flies at 900 km/h, passing distance 1800 kilometers with the wind and once again against the wind for 4 h 1 min. What is the wind speed?
• Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
• Angle at the apex In an isosceles triangle, the angle at the apex is 30° greater than the angle at the base. How big are the internal angles?
• Population The town has 65,000 inhabitants. 40 years ago, there were 157,000. How many people will live in a city in 10 years if the population's average rate is as in previous years?
• Honored students Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them?

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