# Examples for secondary school students

1. The book
If one day you read p pages, you will read the book 24 days. If you read each day 10 pages more, you would read a book in 16 days. How many pages have the book?
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
3. Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6
4. Two triangles SSA
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
5. Scouts
Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together?
6. Triangle
Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
8. Find the area
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
9. Vacation
Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When gran
10. Football league
In the football league is 16 teams. How many different sequence of results may occur at the end of the competition?
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
12. Annual income
The annual incomes (in thousands of \$) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
13. Cubes - diff
Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
14. Two boxes-cubes
Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years.
16. Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
17. Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
18. Box and whisker plot
Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
19. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
20. Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

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