# Examples for secondary school students - page 76

1. Domains of functions F(x)=x2-7x and g(x)=5-x2 Domain of (fg)(x) is. .. . . Domain of (f/g)(x). ..
2. Midpoint 4 If the midpoint of a segment is (6,3) and the other end point is (8,-4) what are thw coordinate of the other end?
3. Blocks There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
4. Linear system Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2
5. Find the 2 Find the term independent of x in the expansion of (4x3+1/2x)8
6. Expression with powers If x-1/x=5, find the value of x4+1/x4
7. Profit growth The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?
8. Journey 5 A man has to do a journey of 84km in 3 hours. He travels the first 30km at 20km/hr. At what rate must he travel the remaining distance to complete his journey on time?
9. Rectangular field A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
10. Loan 5 Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out the loan? C
11. Earth's circumference Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
12. Inverse matrix Find out inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3]
13. Brakes The braking efficiency of a passenger car is required to stop at 12.5 m at an initial speed of 40 km/h. What is the acceleration braking by brakes?
14. Odd/even number Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time. Prove. ..
15. Bonuses Five employees of the company were paid bonuses so that each successor received a 550 USD less than the previous employee. How much did everyone get, if a total of USD 11,000 has paid?
16. Mumbai A job placement agency in Mumbai had to send ten students to five companies two to each. Two of the companies are in Mumbai and others are outside. Two of the students prefer to work in Mumbai while three prefer to work outside. In how many ways assignment
17. Commission 2 Mr gomez sells used cellphones. His commission for every cellphone sold is 20%. If his total sales is Php 33850, how much is his commission? Please, please, please show your solution.
18. A rectangular patio A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
19. The crime The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2025.
20. Find the sum Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5

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