Maths practice for 14 year olds - page 356 of 362
Number of problems found: 7226
- Root
Use the law of square roots: cbrt (sqrt[2] (sqrt[4] (6))) = sqrt[n] (6) - Quadratic equation
Determine the numbers b and c that the numbers x1 = -8 and x2 = -1 were roots of the quadratic equation: -3x ² + b x + c = 0 - Rates
When gas consumption, the consumer may choose one of two rates: rate A - which pays 0.4 € per 1 m³ of gas a flat monthly fee of 4.2 € (regardless of consumption) rate B - which pays 0.351 € per 1 m³ of gas a flat monthly fee of 10.1 € From what monthly co - Trigonometric functions
In a right triangle, it holds that: tg α= frac(4) 2 Find the values of s and k: sin α= (s)/(√ 20) cos α= (k)/(√ 20) - Center traverse
Does the midsegment of a triangle bisect its area? - Diagonals of the rhombus
Calculate the height of a rhombus whose diagonals are 18 cm and 6 cm. - Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length? - Pipes
A water pipe has a cross-section of 1903 cm². In one hour, 859 m³ of water flows through it. How much water flows through a pipe with a cross-section of 300 cm² in 11 hours, if the water flows at the same speed? - Chord
In a circle with radius r = 60 cm, there is a chord that is 4 times longer than its distance from the centre. What is the length of the chord? - Trigonometry
Is true equality? sin(x +13 π)= sin(x) - Rotating cone II
Calculate the lateral surface area of a cone with base radius r = 20 cm and height h = 10 cm. - Gold wire
A wire of length 1.4 km was drawn from one gram of gold. What is its diameter if the density of gold is ρ = 19.5 g/cm³? - Energy saving
Three independent inventions were released, each saving 15%, 17%, and 16% of energy respectively. Some people assumed that using all three would save 15% + 17% + 16% = 48% of energy. Is this correct? What is the actual total percentage of energy saved by - Bulbs
A box contains 16 bulbs of 75 W, 14 bulbs of 40 W, and 10 bulbs of 50 W. Calculate the probability that a randomly selected bulb is: a) 40 W b) 75 W or 40 W - The angle of lines
Calculate the angle between the two lines y = x-8 and y = +12. - Median
In the right triangle are sides a=96 dm b=31 dm. Calculate the length of the medians tc to the hypotenuse. - Rectangles
How many rectangles with an area of 8855 cm² have sides that are natural numbers? - Secret number
Find the secret number n, which reversed decreases by 15.4 if the number increases by 15.4. - Rectangle SS
The perimeter of a rectangle is 154 dm and its diagonal is 62.36 dm. Find the dimensions of the rectangle. - Track arc
Two straight railway tracks meet at an angle of 126°. They are joined by a circular arc with radius r = 1110 m. How long is the connecting arc (L)? How far is the centre of the arc from the intersection of the tracks (x)?
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