Examples for secondary school students - page 142 of 230

Number of problems found: 4597

Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.
Independent term
Find the term independent of x in the expansion of (4x³+1/2x)⁸
Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
Radioactive material
A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
Investment
1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
Principal 6066
After a year, little Katka was on a passbook of thousands of euros. What was the annual interest rate in the bank, and the principal was 957 euros?
Exponentially 6065
The intensity of daylight penetrating seawater decreases exponentially depending on its depth. At a depth of 6m, it is reduced by half. The underwater camera needs at least 75% of the daylight intensity for recording. To what depth can we use it under thi
Deposited 6059
On January 2nd, 2009, Janko's father deposited €3,000 in the bank's passbook. The bank provides an annual interest of 0.30% for deposits up to €5,000. However, Janko's father collected the money after eight months. What is interest in euros added to it?
Parallelogram - area
Calculate the area of the parallelogram if a = 57cm, the diagonal u = 66cm, and the angle against the diagonal is beta β = 57°43'
Interest 6047
Mr. Demikát took out a loan worth 5,000 euros from the bank with an interest rate of 12 percent. How many months will it repay if the monthly payment is 80 euros?
Interest 6043
Mr. Vysoky took out a mortgage on the house. He borrowed a total of 2 million for ten years. The interest rate was 2.3%. How much will Mr. Vysoky pay in total if the interest rate does not change?
Two chords
In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle.
Altitude difference
Between the resorts is 15 km, and the climb is 13 permille. What is the height difference?
Combinations 6
Six purses Nine flaps 12 straps Every combination must include one purse, one flap, and one strap. How many are possible combinations?
Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
Find two
Find two consecutive natural numbers whose product is one larger than their sum. Searched numbers are expressed by a fraction whose numerator is the difference between these numbers, and the denominator is their sum.
One-third 6009
In the forest nursery, children planted new trees for 3 days. They planted a total of 84. On the second day, they planted 75% of what they did on the third day. On the first day, they planted exactly one-third of all planted trees. How many trees did the
Equations 6005
Solve a system of two equations with two unknowns, x and y: 3x - 4y = 12 -x + 3y = 1 Will the sum of x + y be equal?
Right triangular prism
We have a cuboid with a base and dimensions of 12 cm and 5 cm and a height of 4 cm. The tablecloth is cut into two identical triangular prisms with right triangular bases. We painted the surface of the created prisms with color. Calculate the surface area
Supermarket 6000
The goods, whose original price was CZK 1,200, were discounted twice. First by 15%, later by 10% of the new price. Find the final price and the percentage by which the supermarket discounted the goods in total.

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