Articles

1.2E: Basic Concepts (Exercises)


1. Find the order of the equation.

a. ( {d^2yover dx^2}+2 {dyover dx} {d^3yover dx^3}+x=0)

b. (y''-3y'+2y=x^7)

c. (y'-y^7=0)

d. (y''y-(y')^2=2)

2. Verify that the function is a solution of the differential equation on some interval, for any choice of the arbitrary constants appearing in the function.

a. (y=ce^{2x}; quad y'=2y)

b. (y= {x^2over3} +{cover x}; quad xy'+y=x^2)

c. (y= {1over2}+ce^{-x^2}; quad y'+2xy=x)

d. (y=(1+ce^{-x^2/2}) (1-ce^{-x^2/2})^{-1} ;quad 2y'+x(y^2-1)=0)

e. (y= { anleft( {x^3over3}+c ight)}; quad y'=x^2(1+y^2))

f. (y=(c_1+c_2x)e^x+sin x+x^2; quad y''-2y'+y=-2 cos x+x^2-4x+2)

g. (y=c_1e^x+c_2x+ {2over x}; quad (1-x)y''+xy'- y=4(1-x-x^2)x^{-3})

h. (y=x^{-1/2}(c_1sin x+c_2 cos x)+4x+8); (x^2y''+xy'+ {left(x^2-{1over4} ight)}y=4x^3+8x^2+3x-2)

3. Find all solutions of the equation.

a. (y'=-x) b. (y'=-x sin x)

c. (y'=x ln x) d. (y''=x cos x)

e. (y''=2xe^x) f. (y''=2x+sin x+e^x)

g. (y'''=-cos x) h. (y'''=-x^2+e^x)

i. (y'''=7e^{4x})

4. Solve the initial value problem.

a. (y'=-xe^x, quad y(0)=1)

b. ( {y'=x sin x^2, quad yleft({sqrt{piover2}} ight)=1})

c. (y'= an x, quad y(pi/4)=3)

d. (y''=x^4, quad y(2)=-1, quad y'(2)=-1)

e. (y''=xe^{2x}, quad y(0)=7, quad y'(0)=1)

f. (y''=- x sin x, quad y(0)=1, quad y'(0)=-3)

g. (y'''=x^2e^x, quad y(0)=1, quad y'(0)=-2, quad y''(0)=3)

h. (y'''=2+sin 2x, quad y(0)=1, quad y'(0)=-6, quad y''(0)=3)

i. (y'''=2x+1, quad y(2)=1, quad y'(2)=-4, quad y''(2)=7)

5. Verify that the function is a solution of the initial value problem.

a. (y=xcos x; quad y'=cos x-y an x, quad y(pi/4)= {piover4sqrt{2}})

b. ( {y={1+2ln xover x^2}+{1over2}; quad y'={x^2-2x^2y+2over x^3}, quad y(1)={3over2}})

c. (y= { anleft({x^2over2} ight)}; quad y'=x(1+y^2), quad y(0)=0)

d. ( {y={2over x-2}; quad y'={-y(y+1)over x}}, quad y(1)=-2)

6. (y=x^2(1+ln x); quad y''= {3xy'-4yover x^2}, quad y(e)=2e^2, quad y'(e)=5e)

b. (y= {x^2over3}+x-1; quad y''= {x^2-xy'+y+1over x^2}, quad y(1)= {1over3}, quad y'(1)= {5over3})

c. (y=(1+x^2)^{-1/2}; quad y''= {(x^2-1)y-x(x^2+1)y'over (x^2+1)^2}, quad y(0)=1, ; y'(0)=0)

d. (y= {x^2over 1-x}; quad y''= {2(x+y)(xy'-y)over x^3}, quad y(1/2)=1/2, quad y'(1/2)=3)

7. Suppose an object is launched from a point 320 feet above the earth with an initial velocity of 128 ft/sec upward, and the only force acting on it thereafter is gravity. Take (g=32) ft/sec(^2).

  1. Find the highest altitude attained by the object.
  2. Determine how long it takes for the object to fall to the ground.

8. Let (a) be a nonzero real number.

  1. Verify that if (c) is an arbitrary constant then [y=(x-c)^a ag{A}] is a solution of [y'=ay^{(a-1)/a} ag{B}] on ((c,infty)).
  2. Suppose (a<0) or (a>1). Can you think of a solution of (B) that isn’t of the form (A)?

9. Verify that [egin{aligned}y= left{ egin{array}{cl} e^x-1,& x ge 0, [6pt] 1-e^{-x},& x < 0, end{array} ight.end{aligned}]

is a solution of

[egin{aligned}y'=|y|+1end{aligned}] on ((-infty,infty)).

10.

(a) Verify that if (c) is any real number then [y=c^2+cx+2c+1 ag{A}] satisfies [y'={-(x+2)+sqrt{x^2+4x+4y}over2} ag{B}] on some open interval. Identify the open interval.

(b) Verify that [egin{aligned}y_1={-x(x+4)over4}end{aligned}] also satisfies (B) on some open interval, and identify the open interval. (Note that (y_1) can’t be obtained by selecting a value of (c) in (A).)


1.2E: Basic Concepts (Exercises)

"Two conceptual frameworks, Laban theory and the anatomical base of muscle function in PT enabled me to take a new look at the simple basic exercises established in either area, asking, raising the question: what is fundamental in basic actions?"
(Irmgard Bartenieff, Duke lecture notes)

From Bartenieff we have the principles of movement, Laban's common factors, on which to base our study of human motion. For Bartenieff, the totality of human movement analysis expanded on Laban’s theories to include four elements: Body, Effort, Shape, and Space (BESS). Bartenieff based her work on what she perceived as universal truths as far as the body and its connection to the world: to self, to space, to other bodies. Sequencing and initiation, breath support, spatial intent, rotation, attitude and effort (dynamics), and themes of expression-function, inner-outer, stability-mobility, exertion-recuperation support the Fundamentals. In addition to those principles Bartenieff developed exercises for body awareness, changes in level, and means of locomotion. These exercises are based on those common factors and principles, and can be accomplished – in some form – by almost everyone. The principles rely on basic, fundamental, themes and patterns of movement and are discernible by others (and the self). Laban and Bartenieff, then, created a system within which we can recognize these themes and patterns as representative of inherent mind/body connections.

"Bartenieff Fundamentals℠ is a construct that focuses on movement integration and harmony." When moving, our coordination is affected by body connections, center of weight and the relationship to initiation and follow through of a given action. Bartenieff Fundamentals℠ was developed by Irmgard Bartenieff in applying Rudolf Laban’s movement theories to the physical/kinesiological functioning of the human body. In developing the principles of Fundamentals, Bartenieff was concerned with support of the body to facilitate functional, expressive and efficient movement experiences."


1.2E: Basic Concepts (Exercises)

Introduction to Practical Life

Practical: means basic, useful, purposeful
Life: means the way of living.

Practical life Exercises are just that, they are Exercises so the child can learn how to do living activities in a purposeful way.

Meaning and Purpose of Practical Life

The purpose and aim of Practical Life is to help the child gain control in the coordination of his movement, and help the child to gain independence and adapt to his society. It is therefore important to &ldquoTeach teaching, not correcting&rdquo (Montessori) in order to allow the child to be a fully functionional member in hios own society. Practical Life Exercises also aid the growth and development of the child&rsquos intellect and concentration and will in turn also help the child develop an orderly way of thinking.

Practical Life Exercises can be categorized into four different groups: Preliminary Applications, Applied Applications, Grace and Courtesy, and Control of Moment.

In the Preliminary Exercises, the child learns the basic movements of all societies such as pouring, folding, and carrying.

In the Applied Exercises, the child learns about the care and maintenance that helps every day life. These activities are, for example, the care of the person (i.e the washing of the hand) and the care of the environment (i.e dusting a table or outdoor sweeping).

In the Grace and Courtesy Exercises, the children work on the interactions of people to people.

In the Control of Movement Exercises, the child learns about his own movements and learns how to refine his coordination through such activities as walking on the line.


Reason for Practical Life Exercises

Children are naturally interested in activities they have witnessed. Therefore, Dr. Montessori began using what she called &ldquoPractical Life Exercises&rdquo to allow the child to do activities of daily life and therefore adapt and orientate himself in his society.

It is therefore the Directress&rsquos task to demonstrate the correct way of doing these Exercises in a way that allows the child to fully observe the movements. Montessori says, &ldquoIf talking don&rsquot move, if moving don&rsquot talk&rdquo.

The directress must also keep in mind that the goal is to show the actions so that the child can go off and repeat the activity in his own successful way. Montessori says, &ldquoOur task is to show how the action is done and at the same time destroy the possibility of imitation&rdquo. The child must develop his own way of doing these activities so that the movements become real and not synthetic.

During the child&rsquos sensitive period between birth and 6, the child is constructing the inner building blocks of his person. It is therefore important for the child to participate in activities to prepare him for his environment, that allow him to grow independently and use his motor skills, as well as allow the child to analyze difficulties he may have in the exercise and problem solve successfully.

Montessori also saw the child&rsquos need for order, repetition, and succession in movements. Practical Life Exercises also helps to aid the child to develop his coordination in movement, his balance and his gracefulness in his environment as well as his need to develop the power of being silent.


Characteristics of Practical Life

Because Practical Life Exercises are meant to resemble everyday activities, it is important that all materials be familiar, real, breakable, and functional. The materials must also be related to the child&rsquos time and culture. In order to allow the child to fully finish the exercise and to therefore finish the full cycle of the activity, the material must be complete.

In the environment, the Directress may want to color code the materials as well as arrange the materials based on difficulties in order to facilitate the classification and arrangements of the work by the children.

The attractiveness is also of utmost importance as Montessori believed that the child must be offered what is most beautiful and pleasing to the eye so as to help the child enter into a &ldquomore refined and subtle world&rdquo.


C# Sharp Basic Declarations and Expressions : Exercises, Practice, Solution

[An editor is available at the bottom of the page to write and execute the scripts.]

1. Write a C# Sharp program to print Hello and your name in a separate line. Go to the editor
Expected Output :
Hello: Alexandra Abramov
Click me to see the solution

2. Write a C# Sharp program to print the sum of two numbers. Go to the editor
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3. Write a C# Sharp program to print the result of dividing two numbers. Go to the editor
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4. Write a C# Sharp program to print the result of the specified operations. Go to the editor
Test data:

5. Write a C# Sharp program to swap two numbers. Go to the editor
Test Data:
Input the First Number : 5
Input the Second Number : 6
Expected Output:
After Swapping :
First Number : 6
Second Number : 5
Click me to see the solution

6. Write a C# Sharp program to print the output of multiplication of three numbers which will be entered by the user. Go to the editor
Test Data:
Input the first number to multiply: 2
Input the second number to multiply: 3
Input the third number to multiply: 6
Expected Output:
2 x 3 x 6 = 36
Click me to see the solution

7. Write a C# Sharp program to print on screen the output of adding, subtracting, multiplying and dividing of two numbers which will be entered by the user. Go to the editor
Test Data:
Input the first number: 25
Input the second number: 4
Expected Output:
25 + 4 = 29
25 - 4 = 21
25 x 4 = 100
25 / 4 = 6
25 mod 4 = 1
Click me to see the solution

8. Write a C# Sharp program that takes a number as input and print its multiplication table. Go to the editor
Test Data:
Enter the number: 5
Expected Output:
5 * 0 = 0
5 * 1 = 5
5 * 2 = 10
5 * 3 = 15
.
5 * 10 = 50
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9. Write a C# Sharp program that takes four numbers as input to calculate and print the average. Go to the editor
Test Data:
Enter the First number: 10
Enter the Second number: 15
Enter the third number: 20
Enter the four number: 30

Expected Output:
The average of 10 , 15 , 20 , 30 is: 18
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10. Write a C# Sharp program to that takes three numbers(x,y,z) as input and print the output of (x+y).z and x.y + y.z. Go to the editor
Test Data:
Enter first number - 5
Enter second number - 6
Enter third number - 7

Expected Output:
Result of specified numbers 5, 6 and 7, (x+y).z is 77 and x.y + y.z is 72
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11. Write a C# Sharp program that takes an age (for example 20) as input and prints something as "You look older than 20". Go to the editor
Test Data:
Enter your age - 25
Expected Output:
You look older than 25
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12. Write a C# program to that takes a number as input and display it four times in a row (separated by blank spaces), and then four times in the next row, with no separation. You should do it two times: Use Console. Write and then use <0>. Go to the editor
Test Data:
Enter a digit: 25
Expected Output:
25 25 25 25
25252525
25 25 25 25
25252525
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13. Write a C# program that takes a number as input and then displays a rectangle of 3 columns wide and 5 rows tall using that digit. Go to the editor
Test Data:
Enter a number: 5
Expected Output:
555
5 5
5 5
5 5
555
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14. Write a C# program to convert from celsius degrees to Kelvin and Fahrenheit. Go to the editor
Test Data:
Enter the amount of celsius: 30
Expected Output:
Kelvin = 303
Fahrenheit = 86
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15. Write a C# program remove specified a character from a non-empty string using index of a character. Go to the editor
Test Data:
w3resource
Sample Output:
wresource
w3resourc
3resource
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16. Write a C# program to create a new string from a given string where the first and last characters will change their positions. Go to the editor
Test Data:
w3resource
Python
Sample Output:
e3resourcw
nythoP
x
Click me to see the solution

17. Write a C# program to create a new string from a given string (length 1 or more ) with the first character added at the front and back. Go to the editor
Sample Output:
Input a string : The quick brown fox jumps over the lazy dog.
TThe quick brown fox jumps over the lazy dog.T
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18. Write a C# program to check two given integers and return true if one is negative and one is positive. Go to the editor
Sample Output:
Input first integer:
-5
Input second integer:
25
Check if one is negative and one is positive:
True
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19. Write a C# program to compute the sum of two given integers, if two values are equal then return the triple of their sum. Go to the editor
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20. Write a C# program to get the absolute value of the difference between two given numbers. Return double the absolute value of the difference if the first number is greater than second number. Go to the editor
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21. Write a C# program to check the sum of the two given integers and return true if one of the integer is 20 or if their sum is 20. Go to the editor
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22. Write a C# program to check if an given integer is within 20 of 100 or 200. Go to the editor
Sample Output:
Input an integer:
25
False
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23. Write a C# program to convert a given string into lowercase. Go to the editor
Sample Output:
write a c# sharp program to display the following pattern using the alphabet.
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24. Write a C# program to find the longest word in a string. Go to the editor
Test Data: Write a C# Sharp Program to display the following pattern using the alphabet.
Sample Output:
following
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25. Write a C# program to print the odd numbers from 1 to 99. Prints one number per line. Go to the editor
Sample Output:
Odd numbers from 1 to 99. Prints one number per line.
1
3
5
7
9
.
95
97
99
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26. Write a C# program to compute the sum of the first 500 prime numbers. Go to the editor
Sample Output:
Sum of the first 500 prime numbers:
824693
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27. Write a C# program and compute the sum of the digits of an integer. Go to the editor
Sample Output:
Input a number(integer): 12
Sum of the digits of the said integer: 3
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28. Write a C# program to reverse the words of a sentence. Go to the editor
Sample Output:
Original String: Display the pattern like pyramid using the alphabet.
Reverse String: alphabet. the using pyramid like pattern the Display
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29. Write a C# program to find the size of a specified file in bytes. Go to the editor
Sample Output:
Size of a file: 31
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30. Write a C# program to convert a hexadecimal number to decimal number. Go to the editor
Sample Output:
Hexadecimal number: 4B0
Convert to-
Decimal number: 1200
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31. Write a C# program to multiply corresponding elements of two arrays of integers. Go to the editor
Sample Output:
Array1: [1, 3, -5, 4]
Array2: [1, 4, -5, -2]
Multiply corresponding elements of two arrays:
1 12 25 -8
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32. Write a C# program to create a new string of four copies, taking last four characters from a given string. If the length of the given string is less than 4 return the original one. Go to the editor
Sample Output:
Input a string : The quick brown fox jumps over the lazy dog.
dog.dog.dog.dog.
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33. Write a C# program to check if a given positive number is a multiple of 3 or a multiple of 7. Go to the editor
Sample Output:
Input first integer:
15
True
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34. Write a C# program to check if a string starts with a specified word. Go to the editor
Note: Suppose the sentence starts with "Hello"
Sample Data: string1 = "Hello how are you?"
Result: Hello.
Sample Output:
Input a string : Hello how are you?
True
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35. Write a C# program to check two given numbers where one is less than 100 and other is greater than 200. Go to the editor
Sample Output:
Input a first number( 100): 250
True
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36. Write a C# program to check if an integer (from the two given integers) is in the range -10 to 10. Go to the editor
Sample Output:
Input a first number: -5
Input a second number: 8
True
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37. Write a C# program to check if "HP" appears at second position in a string and returns the string without "HP". Go to the editor
Test Data: PHP Tutorial
Sample Output:
P Tutorial
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38. Write a C# program to get a new string of two characters from a given string. The first and second character of the given string must be "P" and "H", so PHP will be "PH". Go to the editor
Test Data: PHP
Sample Output:
PH
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39. Write a C# program to find the largest and lowest values from three integer values. Go to the editor
Test Data:
Input first integer:
15
Input second integer:
25
Input third integer:
30
Sample Output
Largest of three: 30
Lowest of three: 15
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40. Write a C# program to check the nearest value of 20 of two given integers and return 0 if two numbers are same. Go to the editor
Test Data:
Input first integer:
15
Input second integer:
12
Sample Output
15
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41. Write a C# program to check if a given string contains ‘w’ character between 1 and 3 times. Go to the editor
Test Data:
Input a string (contains at least one 'w' char) : w3resource
Test the string contains 'w' character between 1 and 3 times:
Sample Output
True
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42. Write a C# program to create a new string where the first 4 characters will be in lower case. If the string is less than 4 characters then make the whole string in upper case. Go to the editor
Test Data:
Input a string: w3r
Sample Output
W3R
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43. Write a C# program to check if a given string starts with "w" and immediately followed by two "ww". Go to the editor
Test Data:
Input a string : www
Sample Output
False
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44. Write a C# program to create a new string of every other character (odd position) from the first position of a given string. Go to the editor
Test Data:
Input a string : w3resource
Sample Output
wrsuc
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45. Write a C# program to count a specified number in a given array of integers. Go to the editor
Test Data:
Input an integer: 5
Sample Output
Number of 5 present in the said array: 2
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46. Write a C# program to check if a number appears as either the first or last element of an array of integers and the length is 1 or more. Go to the editor
Test Data:
Input an integer: 25
Sample Output
False
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47. Write a C# program to compute the sum of all the elements of an array of integers. Go to the editor
Test Data:
Array1: [1, 2, 2, 3, 3, 4, 5, 6, 5, 7, 7, 7, 8, 8, 1]
Sample Output
Sum: 69
Click me to see the solution

48. Write a C# program to check if the first element and the last element are equal of an array of integers and the length is 1 or more. Go to the editor
Test Data:
Array1: [1, 2, 2, 3, 3, 4, 5, 6, 5, 7, 7, 7, 8, 8, 1]
Sample Output
True
Click me to see the solution

49. Write a C# program to check if the first element or the last element of the two arrays ( length 1 or more) are equal. Go to the editor
Test Data:
Array1: [1, 2, 2, 3, 3, 4, 5, 6, 5, 7, 7, 7, 8, 8, 1]
Array2: [1, 2, 2, 3, 3, 4, 5, 6, 5, 7, 7, 7, 8, 8, 5]
Check if the first element or the last element of the two arrays ( leng th 1 or more) are equal.
Sample Output
True
Click me to see the solution

50. Write a C# program to rotate an array (length 3) of integers in left direction. Go to the editor
Test Data:
Array1: [1, 2, 8]
After rotating array becomes: [2, 8, 1]
Click me to see the solution

51. Write a C# program to get the larger value between first and last element of an array (length 3) of integers. Go to the editor
Test Data:
Array1: [1, 2, 5, 7, 8]
Highest value between first and last values of the said array: 8
Click me to see the solution

52. Write a C# program to create a new array of length containing the middle elements of three arrays (each length 3) of integers. Go to the editor
Test Data:
Array1: [1, 2, 5]
Array2: [0, 3, 8]
Array3: [-1, 0, 2]
New array: [2, 3, 0]
Click me to see the solution

53. Write a C# program to check if an array contains an odd number. Go to the editor
Test Data:
Original array: [2, 4, 7, 8, 6]
Check if an array contains an odd number? True
Click me to see the solution

54. Write a C# program to get the century from a year. Go to the editor
Click me to see the solution

55. Write a C# program to find the pair of adjacent elements that has the largest product of an given array which is equal to a given value. Go to the editor
Click me to see the solution

56. Write a C# program to check if a given string is a palindrome or not. Go to the editor
Sample Example:
For 'aaa' the output should be true
For 'abcd' the output should be false
Click me to see the solution

57. Write a C# program to find the pair of adjacent elements that has the highest product of an given array of integers. Go to the editor
Click me to see the solution

58. Write a C# program which will accept a list of integers and checks how many integers are needed to complete the range. Go to the editor
Sample Example [1, 3, 4, 7, 9], between 1-9 -> 2, 5, 6, 8 are not present in the list. So output will be 4.
Click me to see the solution

59. Write a C# program to check whether it is possible to create a strictly increasing sequence from a given sequence of integers as an array. Go to the editor
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60. Write a C# program to calculate the sum of all the integers of a rectangular matrix except those integers which are located below an intger of value 0. Go to the editor
Sample Example:
matrix = [[0, 2, 3, 2],
[0, 6, 0, 1],
[4, 0, 3, 0]]
Eligible integers which will be participated to calculate the sum -
matrix = [[X, 2, 3, 2],
[X, 6, X, 1],
[X, X, X, X]]
Therefore sum will be: 2 + 3 + 2 + 6 + 1 = 14
Click me to see the solution

61. Write a C# program to sort the integers in ascending order without moving the number -5. Go to the editor
Click me to see the solution

62. Write a C# program to reverse the strings contained in each pair of matching parentheses in a given string and also remove the parentheses within the given string. Go to the editor
Click me to see the solution

63. Write a C# program to check if a given number present in an array of numbers. Go to the editor
Click me to see the solution

64. Write a C# Sharp program to get the file name (including extension) from a given path. Go to the editor
Click me to see the solution

65. Write a C# Sharp program to multiply all of elements of a given array of numbers by the array length. Go to the editor
Click me to see the solution

66. Write a C# Sharp program to find the minimum value from two given two numbers, represented as string. Go to the editor
Click me to see the solution

67. Write a C# Sharp program to create a coded string from a given string, using specified formula. Go to the editor
Replace all 'P' with '9', 'T' with '0', 'S' with '1', 'H' with '6' and 'A' with '8'.
Sample Output:
969
J8V81CRI90
Click me to see the solution

68. Write a C# Sharp program to count a specified character (both cases) in a given string. Go to the editor
Click me to see the solution

69. Write a C# Sharp program to check if a given string contains only lowercase or uppercase characters. Go to the editor
Click me to see the solution

70. Write a C# Sharp program to remove the first and last elements from a given string. Go to the editor
Sample Output:
Original string: PHP
After removing first and last elements: H
Original string: Python
After removing first and last elements: ytho
Original string: JavaScript
After removing first and last elements: avaScrip
Click me to see the solution

71. Write a C# Sharp program to check if a given string contains two similar consecutive letters. Go to the editor
Sample Output:
Original string: PHP
Test for consecutive similar letters! False
Original string: PHHP
Test for consecutive similar letters! True
Original string: PHPP
Test for consecutive similar letters! True
Original string: PPHP
Test for consecutive similar letters! True
Click me to see the solution

72. Write a C# Sharp program to check whether the average value of the elements of a given array of numbers is a whole number or not. Go to the editor
Sample Output:
nums = < 1, 2, 3, 5, 4, 2, 3, 4 >
Check the average value of the said array is a whole number or not: True
nums1 = < 2, 4, 2, 6, 4, 8 >
Check the average value of the said array is a whole number or not: False
Click me to see the solution

73. Write a C# Sharp program to convert the letters of a given string (same case-upper/lower) into alphabetical order. Go to the editor
Sample Output:
Original string: PHP
Convert the letters of the said string into alphabetical order: HPP
Original string: javascript
Convert the letters of the said string into alphabetical order: aacijprstv
Original string: python
Convert the letters of the said string into alphabetical order: hnopty
Click me to see the solution

74. Write a C# Sharp program to check the length of a given string is odd or even. Return 'Odd length' if the string length is odd otherwise 'Even length'. Go to the editor
Sample Output:
Original string: PHP
Convert the letters of the said string into alphabetical order: Odd length
Original string: javascript
Convert the letters of the said string into alphabetical order: Even length
Original string: python
Convert the letters of the said string into alphabetical order: Even length
Click me to see the solution

75. Write a C# Sharp program which takes a positive number and return the nth odd number. Go to the editor
Sample Output:
1st odd number: 1
2nd odd number: 3
4th odd number: 7
100th odd number: 199
Click me to see the solution

76. Write a C# Sharp program to get the ASCII value of a given character. Go to the editor
Sample Output:
Ascii value of 1 is: 49
Ascii value of A is: 65
Ascii value of a is: 97
Ascii value of # is: 35
Click me to see the solution

77. Write a C# Sharp program to check whether a given word is plural or not. Go to the editor
Sample Output:
Is 'Exercise' is plural? False
Is 'Exercises' is plural? True
Is 'Books' is plural? True
Is 'Book' is plural? False
Click me to see the solution

78. Write a C# Sharp program to find sum of squares of elements of a given array of integers. Go to the editor
Sample Output:
Sum of squares of elements of the said array: 14
Sum of squares of elements of the said array: 29
Click me to see the solution

79. Write a C# Sharp program to convert an integer to string and a string to an integer. Go to the editor
Sample Output:
Original value and type: 50, System.String
Convert string to integer:
Return value and type: 50, System.Int32
Original value and type: 122, System.Int32
Convert integer to string:
Return value and type: 122, System.String
Click me to see the solution

80. Write a C# Sharp program to convert all the values of a given array of mixed values to string values. Go to the editor
Sample Output:
Printing original array elements and their types:
Value-> 25 :: Type-> System.Int32
Value-> Anna :: Type-> System.String
Value-> False :: Type-> System.Boolean
Value-> 4/15/2021 10:37:47 AM :: Type-> System.DateTime
Value-> 112.22 :: Type-> System.Double
Printing array elements and their types:
Value-> 25 :: Type-> System.String
Value-> Anna :: Type-> System.String
Value-> False :: Type-> System.String
Value-> 4/15/2021 10:37:47 AM :: Type-> System.String
Value-> 112.22 :: Type-> System.String
Click me to see the solution

81. Write a C# Sharp program to swap a two digit given number and check whether the given number is greater than its swap value. Go to the editor
Sample Output:
Input an integer value:
Check whether the said value is greater than its swap value: True
Click me to see the solution

82. Write a C# Sharp program to remove all characters which are non-letters from a given string. Go to the editor
From Wikipedia,
A letter is a segmental symbol of a phonemic writing system. The inventory of all letters forms the alphabet. Letters broadly correspond to phonemes in the spoken form of the language, although there is rarely a consistent, exact correspondence between letters and phonemes
Sample Output:
Orginal string: [email protected]
Remove all characters from the said string which are non-letters: Python
Orginal string: Python 3.0
Remove all characters from the said string which are non-letters: Python
Orginal string: 2^sdfds*^*^jlljdslfnoswje34u230sdfds984
Remove all characters from the said string which are non-letters: sdfdsjlljdslfnoswjeusdfds
Click me to see the solution

83. Write a C# Sharp program to remove all vowels from a given string. Go to the editor
Sample Output:
Orginal string: Python
After removing all the vowels from the said string: Pythn
Orginal string: C Sharp
After removing all the vowels from the said string: C Shrp
Orginal string: JavaScript
After removing all the vowels from the said string: JvScrpt
Click me to see the solution

84. Write a C# Sharp program to get the index number of all lower case letters in a given string. Go to the editor
Sample Output:
Orginal string: Python
Indices of all lower case letters of the said string:
1 2 3 4 5
Orginal string: JavaScript
Indices of all lower case letters of the said string:
1 2 3 5 6 7 8 9
Click me to see the solution

85. Write a C# Sharp program to find the cumulative sum of an array of number. Go to the editor
A cumulative sum is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence , are x , x+y , x+y+z
Sample Output:
Orginal Array elements:
1 3 4 5 6 7
Cumulative sum of the said array elements:
1 4 8 13 19 26
Orginal Array elements:
1.2 -3 4.1 6 -5.47
Cumulative sum of the said array elements:
1.2 -1.8 2.3 8.3 2.83
Click me to see the solution

86. Write a C# Sharp program to get the number of letters and digits in a given string. Go to the editor
Sample Output:
Original string:: Python 3.0
Number of letters: 6 Number of digits: 2
Original string:: dsfkaso230samdm2423sa
Number of letters: 14 Number of digits: 7
Click me to see the solution

87. Write a C# Sharp program to reverse a boolean value. Go to the editor
Sample Output:
Original value: False
Reverse value: True
Original value: True
Reverse value: False
Click me to see the solution

88. Write a C# Sharp program to find the sum of the interior angles (in degrees) of a given Polygon. Input number of straight line(s). Go to the editor
From Wikipedia,
In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit. The solid plane region, the bounding circuit, or the two together, may be called a Polygon.
Sample Output:
Input number of straight lines of the polygon:
Sum of the interior angles (in degrees) of the said polygon: -360
Click me to see the solution

89. Write a C# Sharp program to count positive and negative numbers in a given array of integers. Go to the editor
Sample Output:
Original Array elements:
10 -11 12 -13 14 -18 19 -20
Number of positive numbers: 4
Number of negative numbers: 4
Original Array elements:
-4 -3 -2 0 3 5 6 2 6
Number of positive numbers: 5
Number of negative numbers: 3
Original Array elements:
Number of positive numbers: 0
Number of negative numbers: 0
Click me to see the solution

90. Write a C# Sharp program to count number of ones and zeros in the binary representation of a given integer. Go to the editor
Sample Output:
Original number: 12
Number of ones and zeros in the binary representation of the said number:
Number of ones: 2
Number of zeros: 2
Original number: 1234
Number of ones and zeros in the binary representation of the said number:
Number of ones: 5
Number of zeros: 6
Click me to see the solution

91. Write a C# Sharp program to remove all the values except integer values from a given array of mixed values. Go to the editor
Sample Output:
Original array elements:
25 Anna False 4/24/2021 11:43:11 AM -112 -34.67
After removing all the values except integer values from the said array of mixed values: 25 -112
Click me to see the solution

92. Write a C# Sharp program to find the next prime number of a given number. If the given number is a prime number, return the number. Go to the editor
From Wikipedia,
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
Sample Output:
Original number: 120
Next prime number/Current prime number: 127
Original number: 321
Next prime number/Current prime number: 331
Original number: 43
Next prime number/Current prime number: 43
Original number: 4433
Next prime number/Current prime number: 4441
Click me to see the solution

C# Sharp Code Editor:

More to Come !

Do not submit any solution of the above exercises at here, if you want to contribute go to the appropriate exercise page. 


1.2E: Basic Concepts (Exercises)

Lessons and Worksheets

Teach and learn basic insurance policy types, concepts, and principles.

Insurance helps provide financial protection for unforeseen losses for you and your family. There are many different types of insurance including health and medical, auto, life, travel, homeowners, and rental insurance. Insurance is an important tool for all individuals managing and planning their personal finances.

Here students will learn about the importance of insurance, and also basic concepts. Teach and learn all about important terms, principles, rules, and procedures.

In addition, we also have included informative articles, helpful tips, and other topics related to insurance.

Insurance Lesson Plans and Worksheets

INTRODUCTION TO INSURANCE

An introduction to insurance, the different types of insurance, and terminology.

CAR INSURANCE

An introductory lesson on basic car insurance terminology. Learn about car insurance monthly premiums and answer the questions about choosing car insurance. Teaching focus is on price comparison, and early understanding of basic liability insurance.

HEALTH INSURANCE

Learn about health insurance monthly premiums and answer the questions about choosing a company's health insurance plan.

ADDITIONAL LESSONS

Students learn about risk and insurance.

Students learn about different types of insurance.

Students learn how insurance can be used to manage risk.

INFORMATION AND ARTICLES ON INSURANCE

An Overview of Permanent Health Insurance Coverage
Permanent health insurance provides you and your family with peace of mind and protection, providing access to an array of health services. Here is an overview of what permanent health insurance provides.

Types of Family Health Insurance
Information on the basic types of family health insurance.

Which Benefit Plan is Right for Me?
Learn the basics on companies employee health benefit plans.

Choosing the Right Level of Auto Insurance
Learn about the different types of auto insurance coverage, and what types of insurance you may need for your car.

Different Types of Auto Insurance
Information on the different types of auto insurance policies available.

An Overview of Life Insurance
We don't know what the future may bring. Here is an overview and information on life insurance.

The Importance of Homeowner Insurance Coverage
Your home and property are at risk from dangers beyond your control. You can help eliminate these financial risks with homeowner insurance coverage.

Here are some tips to help cut and lower your insurance costs.

MORE INSURANCE INFORMATION

Additional information and advice on health insurance, auto insurance, life insurance, and more.

BUSINESS MATH

Business Math
Teach and learn the concepts of basic business math. These lesson plans, business lessons, interactive material, and worksheets will introduce your students to these basic math concepts. Topics include earning money, income and wages, taxes, checking accounts, bank savings accounts, and more consumer math skills, examples and problems.

Additional Lesson Categories

INSURANCE LESSON PLAN WORKSHEETS TEACHING BEGINNING BUSINESS SKILLS FREE STUDENTS BASIC EDUCATION 101 SYLLABUS ONLINE COURSE STEPS CREATING ACTIVITY CLASS PROJECTS TUTORIAL CURRICULUM UNIT RESOURCES

Lessons appropriate for: 7th 8th 9th 10th 11th 12th Graders - Seventh Grade - Eighth Grade - Ninth Grade - Tenth Grade - Eleventh Grade - Twelfth Grade - K12 - High School Students - Middle School - Adults - Special Education - Teens - Teenagers - Young People

Teaching Insurance Skills - Sample Reference Form Work Education


1.2E: Basic Concepts (Exercises)

The Quantum Katas are a collection of self-paced tutorials and programming exercises to help you learn quantum computing and Q# programming.

Each kata is a separate set of exercises that includes:

  • A sequence of tasks progressing from easy to hard. Each task requires you to fill in some code. The first task might require just one line, and the last one might require rather complicated code.
  • A testing framework that sets up, runs, and validates your solutions. Each task is covered by a unit test which initially fails. Once you write the code to make the test pass, you can move on to the next task.
  • Links to quantum computing and Q# reference material you might need to solve the tasks.
  • Hints, reference solutions and detailed explanations to help you if you're stuck.

The Quantum Katas also include tutorials that introduce the learner to the basic concepts and algorithms used in quantum computing, starting with the necessary math (complex numbers and linear algebra). They follow the same pattern of supplementing the theory with Q# demos and hands-on programming exercises.

Here is the learning path we suggest you to follow if you are starting to learn quantum computing and quantum programming. Once you're comfortable with the basics, you're welcome to jump ahead to the topics that pique your interest!

Quantum Computing Concepts: Qubits and Gates

    Complex arithmetic (tutorial). Learn about complex numbers and the mathematics required to work with quantum computing.
  • Linear algebra (tutorial). Learn about vectors and matrices used to represent quantum states and quantum operations.
  • The qubit (tutorial). Learn what a qubit is.
  • Single-qubit gates (tutorial). Learn what a quantum gate is and about the most common single-qubit gates.
  • Basic quantum computing gates. Learn to apply the most common gates used in quantum computing.
  • Multi-qubit systems (tutorial). Learn to represent multi-qubit systems.
  • Multi-qubit gates (tutorial). Learn about the most common multi-qubit gates.
  • Superposition. Learn to prepare superposition states.

Quantum Computing Concepts: Measurements

  • Single-qubit measurements (tutorial). Learn what quantum measurement is and how to use it for single-qubit systems.
  • Measurements. Learn to distinguish quantum states using measurements.
  • Distinguish unitaries. Learn to distinguish unitaries by designing and performing experiments with them.
  • Joint measurements. Learn about using joint (parity) measurements to distinguish quantum states and to perform state transformations.

Q# and Microsoft Quantum Development Kit Tools

  • Random number generation (tutorial). Learn to generate random numbers using the principles of quantum computing.
  • Teleportation. Implement standard teleportation protocol and its variations.
  • Superdense coding. Implement the superdense coding protocol.

Quantum Oracles and Simple Oracle Algorithms

  • Quantum oracles (tutorial). Learn to implement classical functions as equivalent quantum oracles.
  • Exploring Deutsch–Jozsa algorithm (tutorial). Learn to implement classical functions and equivalent quantum oracles, and compare the quantum solution to the Deutsch–Jozsa problem to a classical one.
  • Deutsch–Jozsa algorithm. Learn about quantum oracles which implement classical functions, and implement Bernstein–Vazirani and Deutsch–Jozsa algorithms.
  • Simon's algorithm. Learn about Simon's algorithm.
  • Implementing Grover's algorithm. Learn about Grover's search algorithm and how to write quantum oracles to use with it.
  • Exploring Grover's search algorithm (tutorial). Learn more about Grover's search algorithm, picking up where the Grover's algorithm kata left off.
  • Solving SAT problems using Grover's algorithm. Explore Grover's search algorithm, using SAT problems as an example. Learn to implement quantum oracles based on the problem description instead of a hard-coded answer. Use Grover's algorithm to solve problems with an unknown number of solutions.
  • Solving graph coloring problems using Grover's algorithm. Continue the exploration of Grover's search algorithm, using graph coloring problems as an example.

Tools and libraries/Building up to Shor's algorithm

  • Quantum Fourier transform. Learn to implement quantum Fourier transform and to use it to perform simple state transformations.
  • Phase estimation. Learn about phase estimation algorithms.
  • Truth tables. Learn to represent and manipulate Boolean functions as truth tables and to implement them as quantum operations.
  • Ripple-carry adder. Build a ripple-carry adder on a quantum computer.
  • BB84 protocol. Implement the BB84 key distribution algorithm.
  • Bit-flip error correcting code. Learn about a 3-qubit error correcting code for protecting against bit-flip errors.
  • Unitary patterns. Learn to implement unitaries with matrices that follow certain patterns of zero and non-zero elements.
  • Quantum classification (tutorial). Learn about circuit-centric classifiers and the quantum machine learning library included in the QDK.

For a Q# programming language quick reference sheet, see Q# Language Quick Reference.

Run the katas and tutorials online

The Quantum Katas are now available as Jupyter Notebooks online! See index.ipynb for the list of all katas and tutorials, and instructions for running them online.

While running the Katas online is the easiest option to get started, if you want to save your progress and enjoy better performance, we recommend you to choose the local option.

To use the Quantum Katas locally, you'll need the Quantum Development Kit, available for Windows 10, macOS, and Linux. If you don't already have the Quantum Development Kit installed, see the install guide for the Quantum Development Kit.

If you want to run the katas and tutorials locally as Jupyter Notebooks:

  1. Follow the steps in the QDK install guide for Python and the QDK install guide for Jupyter Notebooks.
  2. Several tutorials require installing additional Python packages:
    • "Complex arithmetic" and "Linear algebra" require the pytest package.
    • "Exploring Grover's search algorithm" requires the matplotlib package.
    • "Quantum classification" requires matplotlib and numpy packages.

If you want to run the katas and tutorials locally as Q# projects:

Follow the steps in the QDK install guide for Visual Studio, Visual Studio Code or other editors.

Download the Quantum Katas

If you have Git installed, clone the Microsoft/QuantumKatas repository:

Run a kata as a Jupyter Notebook

The best way to run the katas as Jupyter Notebooks is to navigate to the root folder of the repository and to open index.ipynb using Jupyter:

This will open the notebook that contains a list of all katas and tutorials, and you will be able to navigate to the one you want using links.

Note that this will start Jupyter Notebooks server in the same command line window you used to run the command. If you want to keep using that window for navigation, you can launch Jupyter Notebooks server in a new window using the following commands (on Windows):

You can also open an individual notebook directly, but this might render internal links invalid:

Each kata is in its own directory as a self-contained Q# project, solution and Jupyter Notebook triplet. For instance, the BasicGates directory structure is:

To open the BasicGates kata in Visual Studio 2019, open the QuantumKatas/BasicGates/BasicGates.sln solution file.

To open the BasicGates kata in Visual Studio Code, open the QuantumKatas/BasicGates/ folder. Press Ctrl + Shift + P (or ⌘ + Shift + P on macOS) to open the Command Palette. Type Open Folder on Windows 10 or Linux or Open on macOS.

[!TIP] Almost all commands available in Visual Studio Code are in the Command Palette. If you get stuck, press Ctrl + Shift + P (or ⌘ + Shift + P on macOS) and start typing to search through all available commands.

You can also launch Visual Studio Code from the command line:

Once you have a kata open, it's time to run the tests using the following instructions. Initially all tests will fail. Don't panic! Open Tasks.qs and start filling in the code to complete the tasks. Each task is covered by a unit test. Once you fill in the correct code for a task, rebuild the project and re-run the tests, and the corresponding unit test will pass.

  1. Build the solution.
  2. From the main menu, open Test Explorer (Test > Windows) and select Run All to run all unit tests at once.
  3. Work on the tasks in the Tasks.qs file.
  4. To test your code changes for a task, rebuild the solution and re-run all unit tests using Run All, or run just the test for that task by right-clicking the test and selecting Run Selected Tests.
  1. Press Ctrl + ` (or ⌘ + ` on macOS) to open the integrated terminal. The terminal should open to the kata directory. If it doesn't, navigate to the folder containing the *.csproj file for the kata using cd command.
  2. Run dotnet test in the integrated terminal. This should build the kata project and run all of the unit tests. All of the unit tests should fail.
  3. Work on the tasks in the Tasks.qs file.
  4. To test your code changes for a task, from the integrated terminal run dotnet test again.

For convenience, a tasks.json configuration file exists for each kata. It allows Visual Studio Code to run the build and test steps from the Command Palette. Press Ctrl + Shift + P (or ⌘ + Shift + P on macOS) to open the Palette and type Run Build Task or Run Test Task and press Enter.

You can use the included Dockerfile to create a docker image with all the necessary tools to run the katas from the command line or Jupyter.

  1. Run the image in the container named katas-container with interactive command-line and redirect container port 8888 to local port 8888 (needed to run Jupyter):
  1. From the same command line that you used to run the container, run the C# version of the BasicGates kata:
  1. Once Jupyter has started, use your browser to open the kata in notebook format. You will need a token generated by Jupyter when it started on the previous step:

To exit a docker container without killing it (daemon mode), press Ctrl+P, Ctrl+Q


Lessons and Worksheets

PRINTABLE BUDGET WORKSHEETS

Use these budgeting worksheets with our lesson plan or for teaching your own budget lesson plans. Monthly and daily student budget sheets. Personal budget form.

STARTING A BUDGET INTRODUCTION

Printable budget lesson starter worksheets for a lesson introducing budgeting. Includes creating a personal budget for yourself, and earning money while prioritizing needs and wants.

HOW DO I BUDGET?

Students learn what a budget is, why they should budget, and how to set up a simple budget.

INTRODUCTION TO BUDGETING LESSON:

FIXED AND VARIABLE EXPENSES

This is an introductory worksheet.

Students learn and identify fixed and variable expenses to help understand how to create a budget.

EARLY MONEY BUDGET WORKSHEET:

CHILDREN'S BUDGET

Use these worksheets to teach basic budget concepts. Even a child should understand basic personal finance concepts.

ESTIMATING YOUR GROCERIES

Students practice their skills at estimation while shopping for groceries.

NEEDS OR WANTS

An important budgeting money concept is understanding the difference between needs and wants.

UNDERSTANDING YOUR MONEY HABITS

In this lesson, students learn to understand and identify what are their money habits.Every money decision you make either reinforces good or bad money habits. The first step toward creating good money habits is to first identify the money habits you currently have.

SPENDING LOG

In this lesson, students keep a log of all their spending for products and services for a week to help identify their spending habits and patterns.

COMPARISON SHOPPING WORD PROBLEMS

Learn about comparison shopping with this word problem worksheet.

MAKING A BUDGET WORD PROBLEMS

This is a word problem worksheet for a lesson in basic budget concepts.

BUDGET LESSON PLAN

Learn what a budget is how to put one together activity.

BUDGET PLAN

Put together and categorize a budget.

This is a good introductory worksheet showing what a simple one looks like. This worksheet is random, so every time you choose the link, a new worksheet is created.

SIMPLE BUDGET

This worksheet takes a predetermined budget and the student is asked to fill in the monthly items and determine if they are above or below their estimates. It also teaches and reinforces basic math skills.

BUDGETING WORD PROBLEMS

Test basic math skills while answering related questions.

SPENDING PLAN

Students will use given information to create a monthly spending plan, also known as a budget. In this lesson, they will develop the abilities needed to make an effective plan to budget monthly spending goals.

GROCERY SHOPPING WITH COUPONS

Use the coupons and answer the questions about grocery shopping with coupons. An introduction lesson on using coupons and discounts. Basic money math.

STUDENT BUDGETING: ESTABLISHING A REALISTIC BUDGET

Students learn about creating a realistic budget.

PLANNING EFFECTIVE FINANCIAL GOALS

In this lesson, students learn to figure out their desired financial objectives by planning smart and effective financial goals that will help them achieve their goals. They will set financial goals that are specific, measurable, attainable, relevant, and time-bound.

COLLEGE BUDGET LESSON

Many college students discover too late that they need to learn how to budget their money. Use this budget lesson plan and worksheet on the subject of college budgeting to help teach related principles.

BUYING A CAR LOAN INTRODUCTION

A car is often one of the more expensive items we purchase.

Read the car advertisements and answer the questions about taking a car loan with this loan worksheet. Learn about down payments and finance charges.

PURCHASING AND FINANCING A CAR

Learn about purchasing and financing a car by filling in the missing financing calculations.

CAR INSURANCE LESSON

An introductory lesson on basic car insurance terminology. Learn about car insurance monthly premiums and answer the questions about choosing car insurance. Teaching lesson focus is on price comparison, and early understanding of basic liability insurance.

RENTING AN APARTMENT

Learn to read the apartment advertisements and answer the questions about choosing an apartment to rent.

Lesson focus is on rent comparison.

MORTGAGE LOAN CALCULATION

A worksheet introducing students to the concept of a mortgage loan. Also introduces the concepts of down payment and closing costs.

CREDIT CARDS

Credit cards, credit, and paying interest.

A fundamental understanding of credit cards is important since people often exceed their budget by overspending on their credit card. Use these lessons to help with your understanding of credit and credit cards.

REAL WORLD BUDGETING - COTTAGE BUDGET

Students must design a cottage and stay within the specified budget. Practice real-word budgeting problems, while actively applying logic and algebraic knowledge. Students must understand evaluating alternatives, cost/benefit analysis, work with a budget, and substantiate their analysis.

VACATION AND TRAVEL

Costs for vacation and travel can often be more than we anticipate. Use this lesson to help teach and learn about budgeting and spending for vacation travel.

SPENDING MONEY

Worksheets and Lessons with a spending money theme. Learn about spending money issues to help with budgeting lessons.

ADDITIONAL LESSONS

Money Responsibility
This lesson introduces students to the concept of being responsible for managing money through accurate record-keeping.

Budget to Save—The Balance Sheet
This lesson begins with dispelling common myths about millionaires. Students then have an opportunity to give their opinions of wealth in a brainstorming activity that culminates in a formalizing of the definition of wealth through the equation of “assets – liabilities = net worth.”

Developing a Budget
With financial goals in mind, students work in pairs to complete a budget analysis for a fictitious high school senior who needs to save money. The lesson concludes with a personal budget development activity that uses the information on expenditures that was collected during the two-week data gathering period.

Your Budget Plan – Spending Behaviors
Students work in pairs to participate in a “Track Star” game that illustrates positive and negative spending behaviors. Each pair analyzes the game results, identifies effective and ineffective budgeting behaviors, and generates a list of budgeting principles.

BUDGET RELATED INFORMATIONAL ARTICLES

Creating a Budget by Tracking Expenses
The first step towards creating a budget is monitoring and categorizing your spending.

Sample Budget
A sample monthly household budget.

How to find your Dream Apartment
Finding your dream apartment starts with understanding your "must haves" and
wants.

5 Steps to Budgeting Success
Some helpful advice on achieving budgeting success.

4 Budgeting Pitfalls to Avoid
Having a budget is an important part of disciplined money management. Here are some tips to help you stick to your budget.

Effective Budgeting
Here are a few tips to help you budget effectively, practice good money management, and lead a debt-free life.

More Budgeting and Budget Planning Information
Information, tips, and advice on how to budget.

SUGGESTIONS OR NEED HELP?

Do you have a recommendation for an enhancement to this budgeting money lesson page, or do you have an idea for a new lesson? Then leave us a suggestion.

To teach and learn money skills, personal finance, money management, business, careers, and life skills please go to the Money Instructor home page.


Exercises that could be harmful

Bouncing while stretching

It is mistakenly believed that 'bouncing' as you stretch (ballistic stretching) helps muscles to stretch further. Sudden overstretching stimulates the stretch reflex causing the muscles to contract even tighter in an attempt to prevent injury. Bouncing is counterproductive as it can cause small tears to the muscle tissue, which are experienced as muscle soreness or tenderness.

  • concentrating on slow, sustained stretches
  • holding the stretch for 10 to 20 seconds
  • once the muscle feels comfortable, gently increasing the stretch and then holding again.

Standing toe-touches

Avoid standing toe-touches altogether. Bending down to touch the toes, with straight legs, can overstretch the lower back muscles and hamstrings, and stress the vertebrae, discs and muscles of the lower back and hamstrings. Adding a twisting movement to the toe-touch can cause damage to the joints.

  • Stretch the hamstrings and lower back muscles by placing one foot on a low bench or chair, with both legs slightly bent so as not to stress the knee joints and, keeping your back straight, gently reach forward with your arms.
  • An alternative hamstring stretch involves lying on your back with both knees bent. Straighten one leg by lifting it towards the ceiling, keeping the knee slightly bent. Support this leg by clasping both hands behind the knee. Hold. Repeat for the other leg. You should feel the stretch on the back thigh of the straight leg.
  • For an alternative lower-back stretch, sit cross-legged on the floor then slowly lean forward, keeping your back straight while reaching your arms out to the floor. Hold.

Deep (full) squat

Full squats push the knee joint past 90 degrees. Whether they are done with or without weights (a barbell or a weight held across the shoulders or in the hands) this can strain the ligaments, cartilage and muscle of the knee joint and lower back, and create problems with the tracking (movement) of the kneecap.

  • Perform half-squats instead (45-degree bend of the knee).
  • Use a mirror to check when your knee joint is at 90 degrees. You could also ask someone else to watch you or seek instruction from a qualified fitness professional.

Sit-ups

Two common but potentially harmful variations of the sit-up include anchoring the feet (where your training partner holds your feet) or keeping the legs straight along the floor. The hands are held behind the head or neck, and the upper body lifted. These types of sit-ups strain the lower back and tend to target the muscles of the hips and thighs rather than the abdomen. Avoid this style of sit-up altogether.

Instead, perform abdominal curls. Lie on your back with your knees bent, feet flat on the floor and arms folded across your chest or alongside your body. Breathe out and curl your ribcage towards your pelvis.

Double leg raises

Behind the neck press


What is the Diffie-Hellman key exchange?

Suppose, there are two people Alice and Bob and they want to attack a bank. However, they are on either sides of the bank and they can only communicate with each other via a shared line which is being tapped by the bank.

Something like this.

Keep in mind, everything that Alice and Bob say to each other will be eavesdropped upon by the bank. So, how can they both decide on a date to attack the bank without the bank getting to know about it and without Alice and Bob explicitly exchanging that information?

This conundrum can be answered by the Diffie-Hellman key exchange it is a concept by which two parties can get hold of secret information without sharing it.

To understand how the Diffie-Hellman works, we need to use one of the most famous applications of this theory, the secret colour exchange.

For this there are 3 things that you need to keep in mind:

  • Alice and Bob both publicly agree that yellow is going to be the common paint that they are both going to use.
  • Alice then secretly keeps to herself that she is also going to use orange along with yellow.
  • Bob secretly decides that he is going to use aqua along with yellow.

Since it was publicly declared that yellow is going to be the colour of choice:

Now Alice mixes in her private colour aka orange with yellow and gets a composite colour which we will call CA.

At the same time, Bob mixes his private colour aqua with yellow and creates composite colour CB.

So, at the end of stage two this is what things look like:

Stage Three

Now, Alice and Bob will send each other their respective colours, which will promptly get tapped by the bank. However, the bank now faces a problem.

Colour combinations are a trapdoor function.

While it is easy for someone to combine two colours and generate a third colour, it is infeasible for them to determine the first two colours from the given third colour. So, the bank will get hold of CA and CB but will have no idea which are the colours that has gone into its creation.

So, this is what things are looking like right now:

Now, Alice and Bob are once again going to mix their secret colours into the mix that they have received from the other person, so now both of them are going to have a mix of yellow, orange and aqua which is brown. The bank, however, will only have CA and CB because they have no idea what the secret colours are.

So, this is what things look like now:

And this is where the trick lies, by not revealing their secret colours, both Bob and Alice have, in their possession, the colour brown, even though they never explicitly exchanged brown with each other.

This is what the diagram of this entire exchange looks like:

This is the representation of the Diffie-Hellman exchange, but a mathematical means was needed to make sure that there could be practical applications of this as well. For this reason, the modulus function was used.


BASIC MOVEMENT PATTERNS

This article discusses how most S&C coaches categorise exercises and use them for exercise prescription.

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By Owen Walker
6 Feb 2016 | 5 min read

Contents of Article

  1. Summary
  2. Introduction
  3. What are the Basic Movement Patterns?
  4. How are they classified?
  5. Examples of the Basic Movement Patterns
  6. Conclusion
  7. References
  8. About the Author
  9. Comments

Summary

Basic movement patterns are realistically just a way of categorising exercises based on their biomechanical demands. Classifying exercises into these categories makes it easier for the strength and conditioning coach to identify which exercise is most appropriate for the athlete.

Introduction

For decades gym-based training has revolved around the concept of training muscle groups in isolation. Though nobody knows exactly, it is commonly agreed that this very concept has stemmed primarily from bodybuilding. However, strength training pioneers such as Prof. Yuri Verkhoshansky and Dr. Michael Yessis began to popularise gym-based training for athletes during the mid-20 th century (1, 2). Since then, global developments on how to train athletes, and how to make it functional* for their sport has accelerated – particularly in recent years. Perhaps these advancements are associated with the immense commercial growth of sport (3) and thus the increase in sports science related degrees and courses worldwide. Regardless, strength and conditioning coaches and exercise specialists all over the world now appreciate the significant difference between training athletes and training others (e.g. bodybuilders).

*Functional, by definition, means something that is ‘designed to be practical and useful, rather than attractive’ (4). Though this has become a huge buzzword in recent years with trainers using any form of ‘fancy’ or ‘attractive’ equipment they can get their hands on, it simply refers to any training methods that are applicable and useful for that sport, regardless of complexity or attractiveness. For example, a simple barbell deadlift is practical and useful for athletic development in rugby, therefore this may be referred to as ‘functional’.

What are the Basic Movement Patterns?

Basic exercise movement patterns are, quite simply, exercise classifications, which due to popularity have formed the foundations of exercise selection. Once a strength and conditioning coach determines which basic movement patterns are essential for the athlete, they will they devise a battery of exercises forged from those movement patterns (i.e. exercise classifications). For example, a primary movement pattern of a rowing athlete is a horizontal pulling action, as a result, a ‘horizontal pulling’ movement (e.g. Prone Rows) may become a vital component of their training programme. On the other hand, a leg extension exercise would be classified as a ‘knee dominant’ movement, as the knee joint is the prime lever. Although there are thousands of different exercises, a large majority of them can be categorised into the following movement patterns.

  • Hip Hinge
  • Hip Dominant
  • Knee Dominant
  • Vertical Push
  • Vertical Pull
  • Horizontal Push
  • Horizontal Pull
  • Rotational and Diagonal
  • Anti-Rotation
  • Anti-Flexion
  • Anti-Extension
  • Anti-Lateral Flexion

How are they classified?

At present, this is normally done by anecdotal evidence and purely based on the opinion of the strength and conditioning coach and their scientific knowledge of each exercise. However, there are common rules of thumb that are followed to categorise each exercise. These are segregated by one of three things:

  1. The movement direction of the exercise (e.g. flat bench press is a horizontal press).
  2. The primary joint lever (e.g. during the knee extension, the knee joint is the primary lever).
  3. Or, by the joint deemed to experience the largest ‘relative’ forces (e.g. let’s just suggest that the hip is capable of handling higher joint forces than the knee. During a pistol squat, whilst the forces exerted on the hip may be larger than those on the knee, the knee might be enduring its maximal tolerance. In which case, this may be deemed as a knee-dominant movement because the knee is experiencing the largest ‘relative’ forces). Note that this is purely a fictitious example.

Examples of the Basic Movement Patterns

This category of exercises is comprised of exercises that involve a hinging motion at the hip joint, with little to no knee movement. These hip dominant exercises are initiated by a contraction of the hip extensors (e.g. glutes, hamstrings) and spinal erectors to extend the hip. These exercises tend to be more of a pulling action as opposed to a push.

The following are examples of hip hinge exercises:

Hip Dominant

Though this category can include hip hinging movements, it is used to identify all exercises in which the hip joint plays the primary role. For example, whilst the Glute Bridge is a hip dominant movement, it is not reflective of a hip hinging movement. Similarly, the High-Box Step-Up is also a hip dominant movement that is not reflective of a hip hinge.

The following are examples of hip dominant exercises:

  • Glute Bridges
  • High-Box Step-Ups
  • Leg Press (position-specific)
  • Romanian Deadlift (RDL) and its variations (e.g. single-leg)
  • Kettlebell Swing
  • Squat (Bilateral variations) However, this is really a misnomer as it is not really either knee or hip dominant -it’s both.

Knee Dominant

This category is classified by movements in which the knee is the dominant lever during the exercise.

The following are examples of knee dominant exercises:

  • Single-Leg Squats (Pistol, Bulgarian, Knee-Tap, Elevated)
  • Low-Box Step up
  • Lunge (Forward, Backward, Lateral)
  • Leg Press (position-specific)
  • Squat (Bilateral variations) However, this is really a misnomer as it is not really either knee or hip dominant -it’s both.

Vertical Push

This category of exercises include all exercises that move the load/weight vertically in relation to the torso, or at least in that direction. It usually consists of movements in the sagittal plane (shoulder flexion) or frontal planes (shoulder abduction). Furthermore, this normally means its movements create shoulder abduction and/or flexion and extension of the elbow (i.e. pushing).

The following are examples of vertical push exercises:

  • Push Press
  • Military Press
  • Overhead Dumbbell Press
  • Seated Shoulder Press
  • Jammer Press

Vertical Pull

This category of exercises also includes moving a load/weight vertically in relation to the torso, or at least in that direction. However, it usually consists of movements in the sagittal (shoulder extension), frontal, or transverse planes (shoulder adduction). Furthermore, this normally means its movements create shoulder extension and/or adduction with elbow flexion (i.e. pulling).

The following are examples of vertical pull exercises:

  • Pull-Ups (Close-Grip, Wide-Grip, Supinated Grip etc)
  • Lat Pull-Downs
  • Kneeling Pull-Downs
  • Plank Rows

Horizontal Push

This category of exercises involves moving a weight straight out in front of you, away from the torso. Therefore, it consists of movements in the sagittal (shoulder flexion) and/or transverse plane (shoulder horizontal adduction) with elbow extension (i.e. pushing).

The following are examples of horizontal push exercises:

  • Press-Ups
  • Bench Press
  • Standing Chest Press
  • Single-Arm Dumbbell Press
  • Kneeling Single-Arm Press

Horizontal Pull

This category of exercises involves moving a weight towards the torso. Therefore, it consists of movements in the sagittal (shoulder extension) and/or transverse plane (shoulder horizontal abduction) with elbow flexion (i.e. pulling).

The following are examples of horizontal pull exercises:

  • Inverted Row
  • Bench Row
  • Bent Over Row (Bilateral, Unilateral, Barbell, Dumbbell, Kettlebell etc)
  • T-Bar Row
  • Seated Row
  • Kneeling Single-Arm Row

Rotational and Diagonal

This category of exercises are primarily associated with movements of a rotational nature, typically within the transverse plane. These movements may also incorporate some form of pushing and/or pulling movements.

The following are examples of Rotational/Diagonal exercises:

  • Russian Twist
  • Barbell Torque
  • Cable Rotations
  • Woodchops
  • Lateral Medicine Ball Throw

Anti-Rotation

Anti-rotation exercises are designed to challenge the lumbo-pelvic complex muscles (i.e. the core) to prevent rotation in the transverse plane and improve stiffness and stability of the spine (5) – hence the term ‘anti-rotation’. NOTE: Some exercises in this category also fall into other categorises, meaning some exercises can have dual purposes and therefore potentially more ‘bang for your bucks’.

The following are anti-rotation exercises:

Anti-Flexion

Anti-flexion exercises are designed to challenge the lumbo-pelvic complex and spinal erector muscles to prevent flexion and improve stiffness and stability of the spine (5) – hence the term ‘anti-flexion’. Most exercises in this category are associated with common exercises and therefore they are not often referred to as anti-flexion.

The following are anti-flexion exercises:

Anti-Extension

Anti-extension exercises are designed to challenge the lumbo-pelvic complex and spinal flexor muscles to prevent extension in the sagittal plane and improve stiffness and stability of the spine (5) – hence the term ‘anti-extension.

The following are anti-extension exercises:

  • The Plank and its variations
  • Press-Ups
  • Supermans
  • Crocodile Crawls
  • Commando Crawls

Anti-Lateral Flexion

Anti-lateral flexion exercises are designed to challenge the lumbo-pelvic complex and spinal erector muscles to prevent lateral flexion and improve stiffness and stability of the spine (5) – hence the term ‘anti-lateral flexion.

The following are anti-lateral flexion exercises:

  • Vertical Palov Press
  • Single-Arm Overhead Press
  • Imbalance Lunges
  • Imbalance Step-Ups
  • Imbalance Farmer Walks

Like anything, there are numerous ways to ‘cook an egg’, so although there are various other ways to classify fundamental movement patterns other than those shown above, a large amount of strength and conditioning coaches appear to divide their exercises based upon these categories.

Conclusion

Functional simply refers to practicality and usefulness. Therefore, during programme design, it is essential that exercises are selected based on their function and usefulness to the athlete and not on the attractiveness or difficulty of the movement. Although exercise professionals may select their exercises using a different battery of movement patterns, or perhaps none at all, a large number of coaches currently use those presented in this article.

What now?

Some coaches believe that reading one article will make them an expert on strength and conditioning. Here’s why they’re wrong…

Strength and conditioning entails many, many topics. By choosing to simply read up on Basic Movement Patterns and ignore the sea of other crucial S&C topics, you run the risk of being detrimental to your athlete’s success and not realising your full potential.

To make you an expert coach and make your life as easy as possible, we highly suggest you now check out this article on Agility.

References

Reference List (click here to open)

  1. CV & Bibliography . 2015. CV & Bibliography . [ONLINE] Available at: [Link] [Accessed 08 November 2015].
  1. Michael Yessis – Wikipedia, the free encyclopedia. 2015. Michael Yessis – Wikipedia, the free encyclopedia. [ONLINE] Available at: [Link]. [Accessed 08 November 2015].
  1. Slack, T. (2003). The Commercialisation of Sport (Sport in the Global Society). 1 Edition. Routledge. [Link]
  1. Functional Meaning in the Cambridge English Dictionary. 2015. Functional Meaning in the Cambridge English Dictionary. [ONLINE] Available at: [Link]. [Accessed 09 November 2015].
  2. Fenwick, CMJ, Brown, SHM, and McGill, SM. Comparison of different rowing exercises: Trunk muscle activation and lumbar spine motion, load and stiffness. J Strength Cond Res 23(5): 1408–1417, 2009 [PubMed]

About the Author

Owen Walker MSc CSCS
Founder and Director of Science for Sport

Owen is the founder and director of Science for Sport. He was formerly the Head of Academy Sports Science and Strength & Conditioning at Cardiff City Football Club, and an interim Sports Scientist for the Welsh FA. He also has a master’s degree in strength and conditioning and is a NSCA certified strength and conditioning coach.