Examples for secondary school students - page 44
- Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
It is true that the lines that do not intersect are parallel?
We throw 2 times with 2 dices. What is the probability that the first roll will fall more than sum of 9 and the second throw have sum 3 or does not have the sum 4?
Determine the smallest integer p for which the equation 4 sin x = p has no solution.
- Coffee shop
To the coffee shop brought 2 types of coffee totally 50 kg. The first type was CZK 220 per kilogram, coffee second type 300 CZK per 1 kg. For all the coffee trader earned CZK 12,000. How many kilograms of coffee of first type and how many kilograms of cof
Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
How many cans must be put in the bottom row if we want 182 cans arrange in 13 rows above so that each subsequent row has always been one tin less? How many cans will be in the top row?
Peter, Martin and Jirka were fire in a special target, which had only three fields with values of 12, 18 and 30 points. All boys were firing with the same number of arrows and all the arrows hit the target, and the results of every two boys differed in one
Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
- Quadrangular prism
The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
- Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
- Three dice
When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
- Right angled triangle
Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
- Vector - basic operations
There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w.
- 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.
Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
Calculate value of expression log |3 +7i +5i2| .
Joe and Caryl have a debt of $100,500. Joe makes $90,000 per year, and Caryl makes $35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries?