# Examples for secondary school students

#### Number of problems found: 2186

• Big numbers
How many natural numbers less than 10 to the sixth can be written in numbers: a) 9.8.7 b) 9.8.0
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
• Derivation
Exists a function whose derivation is the same function?
• Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
• Nineteenth member
Find the nineteenth member of the arithmetic sequence: a1=33 d=5 find a19
• Angle
Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
• Sum of series
Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
• Seedbeds
The father wants to plant 2 seedbeds of carrot and 2 seedbeds of onion. Use a tree chart to find how many different options for placing the seedbeds he has.
• As shown
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE
• Calculate 6
Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
• Sixty
Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?
• Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
• Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
• 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
• Crowns
1180 crowns are divided into three people: A got 20% less than B and C by 15% more than B. How many got A, B, and C?
• Friends in cinema
5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter?
• Diagonals
Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°.
• Lock
A combination lock will open when the right choice of 3 numbers (from 1 to 16 inclusive) is selected. A. How many different lock combinations are possible? B. Is the combination lock named appropriately?
• Confectionery
The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.

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