9th grade (14y) + expression of a variable from formula - examples
- Sales off
The price has decreased by 20%. How many percents do I have to raise the new price to be the same as before the cut?
- Quadrangular pyramid
The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
- Collection of stamps
Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
- Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
- Circle described
The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
- Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
There are 32 pupils in the classroom, and girls are two-thirds more than boys. a) How many percents are more girls than boys? Round the result to a whole percentage. b) How many are boys in the class? c) Find the ratio of boys and girls in the class. Wr
- KLMN trapezoid
The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
- Final exam
There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage?
- The volume 2
The volume of a cube is 27 cubic meters. Find the height of the cube.
- Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
- Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
- Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
- Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
- Cube in a sphere
The cube is inscribed in a sphere with volume 8818 cm3. Determine the length of the edges of a cube.
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
- MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
- Square diagonal
Calculate length of the square diagonal if the perimeter is 476 cm.
- IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.