1. Using Dr. Racket to compute the following expressions. [5 points]

1.1 9 2 + 5

1.2 5 * ( 6 + 12 + 5 ) 25

1.3 7 * (( 5 - ( 1 * 3 )) + ( 2 * 4 ) )

1.4 3 * ( 4 + ( ( ( 6 * 6 ) + ( 6 * 6 ) ) / ( 10 + 2 ) ) )

1.5 ( ( ( ( ( ( 4 + 6 ) * ( 6 + 4 ) ) / 2 ) / 2 ) 5 ) / 2 ) + ( ( ( ( 4 * 5 ) + ( 5 * 4 ) ) / 2 ) + ( 4 * 5 ) )

2. Bind (define) each value in 1.5 above to its English text and then change the expression using the defined names. [5 points] For example, the values in 1.1 should be replaced with names three, five, and seven, and the correct corresponding expression is (eight + two - ten).

3. Define a procedure Add that takes parameters and returns the sum of them.

[5 points]

	> (Add 20 30) 50

4. Define a recursive procedure called Square that will compute the square amount of a value by additions. [15 points]

4.1 You must use the Add procedure defined above.

4.2 You will need to account for negative values as well.

Hint: This will require a conditional and possibly the (abs x) procedure. You may not use

multiplication in this procedure definition. Note n2 = 1+3+5+ + (2n-1).

> (Square 5)

25

5. Define a procedure ReadForSquare to read a value for the Square procedure defined above.

This procedure takes no values and will pass an input value to the Square procedure. [5 points]

> (ReadForSquare - 5)

25

6. Define a procedure DiffSquares that will compute the difference between the square values of 2 inputs. You must implement the ReadForSquare procedure defined above. This procedure should never return a negative value, as it should return the absolute value. [10 points]

> (DiffSquares)

5

10

75

7. Re-implement the procedure Add and call it AddLet. In this procedure, you must implement let-form to bind values. You may name the variables whatever youd like. [5 points]

> (AddLet 60 40)

100