diff --git a/code/os/02-memanagement/page.c b/code/os/02-memanagement/page.c
index b0f19246df37c9c11358c3cd039bb36e1a2b1a5f..fddddd40d02ef5a0d90cfccc35e53205c241f7b7 100644
--- a/code/os/02-memanagement/page.c
+++ b/code/os/02-memanagement/page.c
@@ -117,8 +117,8 @@ void *page_alloc(int npages)
 			 * meet a free page, continue to check if following
 			 * (npages - 1) pages are also unallocated.
 			 */
-			struct Page *page_j = page_i;
-			for (int j = i; j < (i + npages); j++) {
+			struct Page *page_j = page_i+1;
+			for (int j = i+1; j < (i + npages); j++) {
 				if (!_is_free(page_j)) {
 					found = 0;
 					break;
diff --git a/code/os/03-contextswitch/entry.S b/code/os/03-contextswitch/entry.S
index e952564bf60f1d4153370bd2a837d89ed88b7b99..d4b5818bd9fdc51b0efd32332f8cdd2782885a2f 100644
--- a/code/os/03-contextswitch/entry.S
+++ b/code/os/03-contextswitch/entry.S
@@ -89,8 +89,9 @@
 .align 4
 switch_to:
 	csrrw	t6, mscratch, t6	# swap t6 and mscratch
-	beqz	t6, 1f			# Notice: previous task may be NULL
-	reg_save t6			# save context of prev task
+	beqz	t6, 1f			# Notice: if this is the first time to run, t6 will be NULL,
+					# because after sched_init, mscratch is NULL
+	reg_save t6			# save context of current task
 
 	# Save the actual t6 register, which we swapped into
 	# mscratch
diff --git a/code/os/04-multitask/sched.c b/code/os/04-multitask/sched.c
index 85259df39672240de0cec02f809b3771d5ec4160..1bb3bfd1df19c14818bd51e9f45f57dff4f538c6 100644
--- a/code/os/04-multitask/sched.c
+++ b/code/os/04-multitask/sched.c
@@ -43,7 +43,7 @@ void schedule()
 /*
  * DESCRIPTION
  * 	Create a task.
- * 	- start_routin: task routune entry
+ * 	- start_routin: task routine entry
  * RETURN VALUE
  * 	0: success
  * 	-1: if error occured