# Examples for secondary school students

- Boys to girls

The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally? - Flowers 2

Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there? - Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm - Pyramid cut

We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm^{2}. Find the area of the - Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Account operations

My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year? - Square root 2

If the square root of 3m^{2}+22 and -x = 0, and x=7, what is m? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Associative law multiplication

In a warehouse, you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first) - Expressions 3

If k(x+6)= 4x^{2}+ 20, what is k(10)=? - The pond

We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond? - Octane value

I loaded 10L 95 octane gasoline and 5L 100 octane gasoline. What is the resulting octane value of the gasoline in the tank? - Sum of two primes

Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers. - SSA and geometry

The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer. - Median and modus

Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell. - Electric input power

Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =? - Transformer

Solve the textbook problems - transformer: a) N1 = 40, N2 = 80, U2 = 80 V, U1 =? b) N1 = 400, U1 = 200 V, U2 = 50 V, N2 =? - Reciprocal equation 2

Solve this equation: x + 5/x - 6 = 4/11 - A book

A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253. - Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.

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