Examples for secondary school students - page 24 of 237
Number of problems found: 4730
- Point plane distance
Calculate the distance of point A[ 4; 2; -3 ] from the plane : 2x - 2y + z + 5 = 0 - Triangle area angle
The area of a right triangle ABC is 346 cm2, and the angle at vertex A is 64°. Calculate the lengths of the overhangs a and b. - Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC. - PIN probability number
The mobile PIN has 4 characters. What is the probability that the PIN contains the number 7 and ends with the number 5? - Sound Doppler observer
A sound source emits a tone with an absolute pitch of 500 Hz and moves towards the observer at a speed of 5 m/s. Sound travels at a speed of 340 m/s. How fast is an observer moving who hears a tone with an absolute pitch of 522 Hz? - From experience
Based on the experience of an insurance company employee, it was found that an insurance payout under household insurance exceeds 25,000 CZK with a probability of 0.3. What is the probability that among the next ten insurance claims: a) at least 5 will ex - Function inverse square
The inverse function to the function f(x) = √(x-3) for x ≥ 3 is the function: - Cube small diagonal
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and space diagonals. - Point collinear coordinates
Given are points A [1;a2;a3], B [3;-4;-1], C [-3;-1;8]. Points A, B, and C lie in a straight line. Calculate the coordinates a2, a3 - Function graph intersection Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common.
- Centimeters - trapezoid
The area of the trapezoid is 132 cm². The difference in the length of both bases is 6 cm, and the height is 2 cm longer than the shorter base. Find the height of the trapezoid in centimeters. - Line perpendicular coordinate
The straight line p is given by the formula y = 1/2 x - 1 . The line q is perpendicular to the line p and passes through the point A [1; 5]. Determine the y-coordinate of the point that intersects the line q with the y-axis. - Avocado seed probability
The probability of sprouting each avocado pit is 0.9. We planted 3 stones. What is the probability that exactly two of them will grow? - Calculate cuboid
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - Cylinder express radius
Please express r from the formula for the surface of the cylinder. - Circle line intersection
Calculate the sum of the x-coordinates of the intersections of the circle given by the equation (x - 1)²+ y² = 1 and the line given parametrically x = t, y = t , where t∈R. - Radiation shield
Determine what thickness of the shielding material will be required if we reduce the radiation to 3% of the original value if we know that a thickness of 6 mm will reduce the level of the same radiation by 9%. Round up to the whole value in millimeters (t - Odd number sum
Determine the sum of all positive odd numbers less than 78 - Conductor charge transfer
Conductor A has an electrical potential of +140 V concerning the Earth; conductor B has a potential of -60 V. How much electric charge will we transfer from wire B to wire A if we do the work of 4.10-4 Joules?
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