# Examples for secondary school students

- 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? - Add vector

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - 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 - 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? - 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 - Airplane navigation

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)? - 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 - 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 - Football league

In the football league is 16 teams. How many different sequence of results may occur at the end of the competition? - Bearing - navigation

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. - 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. - Cubes - diff

Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm^{3}. Calculate the sizes of the edges of the two dice. - 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 and granddad

Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years. - 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? - Brass tube

The outer perimeter of brass tube (ρ = 8.5 g/cm^{3}) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness? - 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 - Euclid 5

Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height v_{c}= 5 cm. - 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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