The most difficult problems
- Geometric progression 4
If x+y=5, find xy (find the product of x and y if x+y = 5)
- Simplify 3
Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
- Adding mixed numerals
3 3/4 + 2 3/5 + 5 1/2 Show your solution.
The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when we 10% is waste?
- 15 teachers
15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage?
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?
- Equilateral cylinder
A hectolitre of water will fit in an equilateral cylinder. What are its dimensions?
- Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. At what rate are the volumes of cube, cuboid, and sphere?
- Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a² (ii) a3+1/a3
A taxi ride costs $3 plus $2.50 per mile. Write and Graph an equation in two variables that represent the total cost of a taxi ride.
- Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
- Normal distribution GPA
The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
- The Scout Tent
The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high pyramid roof?
- Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
- Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
- The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
- Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
- Water flow 2
How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the water flows at a speed of 30 km per hour