# Examples for secondary school students - page 60

- Minimum of sum

Find a positive number that the sum of the number and its inverted value was minimal. - Variation equation

Solve combinatorics equation: V(2, x+8)=72 - Imaginary numbers

Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum? - Series and sequences

Find a fraction equivalent to the recurring decimal? 0.435643564356 - Third member

Determine the third member of the AP if a4=93, d=7.5. - Parabola 3

Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ? - Folded square

ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD - Mother and daughter

The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now? - Wagons and cranes

Several of the same cranes unloaded 96 wagons. If there were 2 more cranes there would be less 8 wagons for each crane. How many cranes were here? - Solve equation

solve equation: ? - Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm. - Big number

hat is the remainder when dividing number 10 to 47 - 111 by number 9? - ABCD

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Combinations

How many elements can form six times more combinations fourth class than combination of the second class? - Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ? - Free fall

How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss? - Diagonals

A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal. - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Trapezium internal angles

A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D. - Circle - AG

Find the coordinates of circle and its diameter if its equation is: ?

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