diff --git a/kernel/proc.c b/kernel/proc.c
index f7652f6..cf7f260 100644
--- a/kernel/proc.c
+++ b/kernel/proc.c
@@ -20,6 +20,7 @@ static void wakeup1(struct proc *chan);
 
 extern char trampoline[]; // trampoline.S
 
+// initialize the proc table at boot time.
 void
 procinit(void)
 {
@@ -145,8 +146,8 @@ freeproc(struct proc *p)
   p->state = UNUSED;
 }
 
-// Create a page table for a given process,
-// with no user pages, but with trampoline pages.
+// Create a user page table for a given process,
+// with no user memory, but with trampoline pages.
 pagetable_t
 proc_pagetable(struct proc *p)
 {
diff --git a/kernel/proc.h b/kernel/proc.h
index c257eb7..9c16ea7 100644
--- a/kernel/proc.h
+++ b/kernel/proc.h
@@ -97,7 +97,7 @@ struct proc {
   // these are private to the process, so p->lock need not be held.
   uint64 kstack;               // Virtual address of kernel stack
   uint64 sz;                   // Size of process memory (bytes)
-  pagetable_t pagetable;       // Page table
+  pagetable_t pagetable;       // User page table
   struct trapframe *trapframe; // data page for trampoline.S
   struct context context;      // swtch() here to run process
   struct file *ofile[NOFILE];  // Open files
diff --git a/kernel/vm.c b/kernel/vm.c
index 3004bb3..4f65d4e 100644
--- a/kernel/vm.c
+++ b/kernel/vm.c
@@ -16,9 +16,7 @@ extern char etext[];  // kernel.ld sets this to end of kernel code.
 extern char trampoline[]; // trampoline.S
 
 /*
- * create a direct-map page table for the kernel and
- * turn on paging. called early, in supervisor mode.
- * the page allocator is already initialized.
+ * create a direct-map page table for the kernel.
  */
 void
 kvminit()
@@ -70,7 +68,7 @@ kvminithart()
 //   21..39 -- 9 bits of level-1 index.
 //   12..20 -- 9 bits of level-0 index.
 //    0..12 -- 12 bits of byte offset within the page.
-static pte_t *
+pte_t *
 walk(pagetable_t pagetable, uint64 va, int alloc)
 {
   if(va >= MAXVA)
@@ -278,7 +276,7 @@ uvmdealloc(pagetable_t pagetable, uint64 oldsz, uint64 newsz)
 
 // Recursively free page-table pages.
 // All leaf mappings must already have been removed.
-static void
+void
 freewalk(pagetable_t pagetable)
 {
   // there are 2^9 = 512 PTEs in a page table.
diff --git a/user/usertests.c b/user/usertests.c
index f83a060..aefbc9f 100644
--- a/user/usertests.c
+++ b/user/usertests.c
@@ -2251,9 +2251,12 @@ countfree()
   int n = 0;
 
   while(1){
-    if((uint64)sbrk(4096) == 0xffffffffffffffff){
+    uint64 a = (uint64) sbrk(4096);
+    if(a == 0xffffffffffffffff){
       break;
     }
+    // modify the memory to make sure it's really allocated.
+    *(char *)(a - 1) = 1;
     n += 1;
   }
   sbrk(-((uint64)sbrk(0) - sz0));