using recursion to create a new list

I've written a function that takes a number and returns a list of all
the integer multiples of that number from 1 to 10, in as simple a way
as I can think of. Given the number 3, my function returns the list:

(define (multiples-list num)
(append (list num)
(map (lambda (x) (* num x))
'(2 3 4 5 6 7 8 9 10))))

==> (3 6 9 12 15 18 21 24 27 30)

How do I go about thinking recursively to do this by making a new list?
I.e., using a mapping function ala

;; Return a list of the square roots of the numbers in a list
(define (square-roots a-list)
(if (null? a-list)
'()
(cons (sqrt (car a-list))
(square-roots (cdr a-list)))))

.

Relevant Pages

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