Dude. This will not work. First of all, an ordinary kitchen knife won't even pierce to the skull so using it as a spearhead would require high accuracy. You may go for the eye sockets or other openings of the skull but if the zombie can move in the same way as a human then it would be a very difficult task. Secondly, taping the kitchen knife to a stick isn't actually gonna fix the knife to the stick. After 1 or 3 uses it'll start to get out of place. Lastly, this type of weapon will only be lethal when you do piercing attacks. Problem is piercing attacks isn't that effective against a group of 5 to 7 zombies. You'll probably need a shield if you want to hold out longer with a spear or polearm or whatever you want to call this weapon.
Is it meant to be thrown or to be used as a stabbing device?
Not sure about this...
1). Bike mace
Remove the main or largest gear from a bicycle, Cut a grove into a 2 -3 ft long broom handle incert gear into handle and screw the gear inplace, use duct tape if you want to, then sharpen if you wish, as this will kill (or re-kill) even if it is blunt
2) Tooth Bat
Have a chain saw but no fuel or power? remove the chain then wrap it round the bat and screw into place, the added weight and cutting teeth should do some serious damage.
3) Cooks bar
8" (or bigger) cooks knife? remove the wooden handle, and incert into a stick or broom handle and fix into place, not only is this a spear but you can use as a long slashing weapon.
4) Wolverines fist
small 3" round of wood, push in 3 long nails or screws, now go and be the zombie killing wolverine you know you want to be!