# Examples for secondary school students

- Functions f,g

Find g(1) if g(x) = 3x - x^{2}Find f(5) if f(x) = x + 1/2 - 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. - Ladder slope

What is the slope of a ladder 6.2 m long and 5.12 m in height. - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - US GDP

Consider the following dataset , which contsins the domestic US gross in millions of the top grossing movie over the last 5 years. 300,452,513,550,780 I. Find the Mean of the Dataset II. Find the Squared deviation of the second observation from the mean I - The mast

A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Geometric seq

Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient. - Exponential equation

Solve for x: (4^x):0,5=2/64. - ABCD

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

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Pool

If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately? - Bonus

Gross wage was 1762 USD including 22% bonus. How many USD were bonuses? - Logic

A man drinks a barrel of water for 31 days, woman for 58 days, for how many days they drink barrel together? - Beer

After three 10° beers consumed in a short time there are 5.2 g of alcohol in 6 kg adult human blood. How much is it per mille? - Cube in a sphere

The cube is inscribed in a sphere with volume 6598 cm^{3.}Determine the length of the edges of a cube. - Axial section

Axial section of the cone is equilateral triangle with area 300 m^{2.}Calculate volume of the cone. - River

Calculate how many promiles river Hudson average falls, if on section long 921 km flowing water from 1224 m AMSL to 154 m AMSL. - Circle chord

What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm? - Clock

How many times a day hands on a clock overlap? - Trigonometric functions

In right triangle is: ? Determine the value of s and c: ? ?

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