Examples for secondary school students - page 9
Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
In the market have 4 kinds of chocolates. How many ways can we buy 19 chocolates?
- Speed of Slovakian trains
Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
- Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
- Without Euclid laws
Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
- Diofant equation
In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
- Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
- Phone numbers
How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
- Area of RT
In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of this triangle.
On the tourist map at a scale of 1 : 50000 is distance between two points along a straight road 3.7 cm. How long travels this distance on a bike at 30 km/h? Time express in minutes.
- Triangle ABC
Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
- 4side pyramid
Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
- Two doctors
Doctor A will determine the correct diagnosis with a probability 86% and doctor B with a probability 87%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains.