Examples for secondary school students - page 155 of 237
Number of problems found: 4730
- The mast
A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Determinant Product Matrices
The determinant of the product of 2 square matrices has the value 3. What is the product's value of the respective determinants of these matrices? - Geometric seq
Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient. - Exponential equation
Solve for x: (4^x):0,5=2/64. - Part-timer payment
Three part-timers have a total of CZK 2,850. The first received 20% less than the second part-timer, and the third part-timer received CZK 50 more than the second part-timer. How much CZK did the first, second, and third part-timers get? - Pyramid intersection
Given a regular quadrilateral pyramid ABCDV, point M is inside its edge AV, and point N is on the long line DC beyond point C. Construct the intersection of the plane MNV with the plane BCV and the intersection of the line MN and the plane BCV. - The pool
The pool has a volume of 40 m3, and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C? - ABCD
AC= 40 cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Debt
Joe and Caryl have a debt of $100,500. Joe makes $90,000 annually, and Caryl makes $35,000 annually. Based on their salaries, how much should both pay to zero out the debt fairly? - ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 110 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the average train speed for both journeys woul - Triangle KLM
In the rectangular triangle KLM, where |KL|=m is the hypotenuse (sketch it!). Find the length of the leg k and the height of triangle h if the hypotenuse's segments are known MK = 5 cm and ml = 15 cm. - Diagonal 20
The rectangular town plaza's diagonal pathway is 20 m longer than the width. Suppose the pathway is 20 m shorter than twice the width. How long should the pathway be? - Sum on dice
We have two dice. What is the greater likelihood of falling a total sum of 7 or 8? (write 7, 8, or 0 if the probabilities are the same)? - Perimeter of triangle
In the triangle, ABC angle A is 60°, angle B is 90°, and side size c is 15 cm. Calculate the triangle circumference. - Isosceles triangle
The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at a ratio of 5:6. Find the triangle area. - Sum or product
What is the probability that two dice fall will have the sum of seven or product 12? - Arithmetic progression
Determine the difference and the first term of AP if a3 + a4 = 48, a7 = 80. - Matrix Row Operation Rank The rank of matrix A is 3. What rank will this matrix have if we add twice the second row to its first row?
- Lines
How many lines can be drawn with 8 points if three points lie on one line and the other any three points do not lie on the same line? - Digits
How many five-digit numbers can be written from numbers 0.3,4, 5, and 7 divided by 10, and digits are repeated?
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