Examples for secondary school students - page 63
- Saving 9
An amount if $ 2000 is invested at an interest of 5% per month. if $ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount have accumula
- Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
- The inverse
The inverse matrix for matrix A has a determinant value of 0.333. What value has a determinant of the matrix A?
- Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
- The room
The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
- The cruise ship
The cruise ship has a speed of 12 km / h at a calm surface. When we sail 45 km along the river and 45 km back, it took us exactly 8 hours. Which (constant) speed of flow of the river?
- Coordinate axes
Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?
- The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
- The determinant
The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.
The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers.
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?
- Cuboid walls
If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
- Inscribed circle
Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
- Inverse matrix
Find how many times is the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix.
- Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas