Quadratic equation + basic functions - practice problems - last page
Number of problems found: 158
- Sum-log
The sum of two numbers is 32, and the sum of their logarithms (base 10) is 2.2. Determine these numbers. - Circle
The circle is given by center on S[-7; 10] and maximum chord 13 long. How many intersect points have a circle with the coordinate axes? - Built-up area
John build-up area 5 x 7 = 35 m² with building with a wall thickness 30 cm. How many centimeters would he have to subtract from the thickness of the walls that the built-up area fell by 9%? - Root
The root of the equation (x-10)² +4 = x² +35x is (equal or greater or less than zero). ...
- Garden
The square garden area is 2/9 of triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing need to fence a square garden? - Similarity
The area of the regular 10-gon is 563 cm². The area of similar 10-gon is 606 dm². What is the coefficient of similarity? - Rectangular cuboid
The rectangular cuboid has a surface area 5447 cm², and its dimensions are in the ratio 2:4:1. Find the volume of this rectangular cuboid. - Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 3a +4b = 4.9c
- Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately? - Equation
Equation f(x) = 0 has roots x1 = 64, x2 = 100, x3 = 25, x4 = 49. How many roots have equation f(x²) = 0? - Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than the second one. How many minutes is filled with the first pump? - Euler problem
Someone buys 300 tolars towels. If it were for the same money of 5 more towels, it would be 5 tolars cheaper each. How many were towels? - Secret number
Find the secret number n, which reversed decreases by 16.4 if the number increases by 16.4.
- Right triangle
The legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle. - Golden ratio
Divide the line of length 14 cm into two sections so that the ratio of shorter to greater is the same as the ratio of the greater section to the whole length of the line. - Party
At the party, everyone clinked with everyone. Together, they clink $strng times. How many people were at the party? - Trolleybus
Trolleybus line No. 206 measured 24 km. If the trolley bus goes faster by 5 km/h, the way there and back would be shorter by 33 minutes. Calculate the trolley bus speed and the time it takes for a return trip.
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