# Examples for secondary school students

1. Intercept with axis
F(x)=log(x+4)-2, what is the x intercept
2. Blocks
There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
3. Diagonals
What x-gon has 54 diagonals?
4. Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
5. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
6. Rectangles
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
7. Find the 3
Find the distance and mid-point between A(1,2) and B(5,5).
8. 2 pipes
2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone?
9. Same area
There is a given triangle. Construct a square of the same area.
10. Dice
We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
11. Three students
Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolve
12. The length
The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
13. The sum 2
The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer.
14. Minute average
In a factory, four workers are assigned to complete an order received for dispatching 1400 boxes of a particular commodity. Worker A takes 4 mins per box, Worker B takes 6 minutes per box, C takes 10 mins per box, D takes 15 mins per box. Find the average
15. Solid cuboid
A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
16. Bottles
The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
17. Bridge cards
How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
18. Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increa
19. Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
20. Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3

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