# Examples for secondary school students

1. Sheep and cows
There are only sheep and cows on the farm. Sheep is eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm?
2. STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.
3. Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
4. Classroom
Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys
5. Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
6. Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace and 2 in the third?
7. Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
8. Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
9. Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
10. Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
11. A pizza
A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
12. Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long?
13. 600 pencils
600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
14. Two parallel chords
The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
15. Family
94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
16. Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
17. Completing square
Solve the quadratic equation: m2=4m+20 using completing the square method
18. Three numbers
We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
19. Company and employees
There are 370 employees in the company - women are 15% less than men. How many men work in the company?
20. KLM triangle
Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.

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