22a. Practice++

A few more practice problems.

Parabola

Using the parabola $$f(x) = (x+8)(x-6),$$ find the sum of all of the y-coordinates on the graph of $y=f(x)$ with x an integer between left and right (“inclusive”: see first example).

 (check-expect (parabola-ys 2 2) (* 10 -4))
 (check-expect (parabola-ys 2 3) (+ (* 10 -4) (* 11 -3)))

Sevenths

The function add-sevenths: number(start) number(end) -> number finds the sum of all of the sevenths with integer numerator between start and end (inclusive).

(define (add-sevenths start end) 0)
(check-expect (add-sevenths 1 4) (+ 1/7 2/7 3/7 4/7))
(check-expect (add-sevenths 2 4) (+ 2/7 3/7 4/7))
(check-expect (add-sevenths 3 4) (+ 3/7 4/7))
(check-expect (add-sevenths 4 4) 4/7)

Add Odd

Sum all of the odd numbers between start and end (inclusive).

(define (add-odd start end) 0)
(check-expect (add-odd 12 12) 0)
(check-expect (add-odd 11 11) 11)
(check-expect (add-odd 10 11) 11)
(check-expect (add-odd 9 11)  (+ 9 11))
(check-expect (add-odd 8 11)  (+ 9 11))
(check-expect (add-odd 7 11)  (+ 7 9 11))

Add 5s

Sum all of the multiples of five between the start and end number.

(define (add-5s start end) 0)
(check-expect (add-5s 3 17) (+ 5 10 15))