The study of chemistry among sciences has a direct effect on the nations' economy. It has been observed that students encounter difficulties in trying to solve chemical problems. This could be linked to their inability to learn adequately pre-requisite concepts. This research examined the cumulative effects of understanding learned pre-requisite chemistry concepts on problem solving ability among secondary school students. 394 students and 10 chemistry teachers took part. Three instruments; Modified two-tier multiple choice (M.T.M.C)test, Instances of difficult chemical concepts (I.D.C.C), and Teachers’ views on learning chemical concepts (T.V.L.C) were used. The findings of the research show that there is a wide gap between factual knowledge and problem solving among students. On difficult chemical concepts, teachers and students differ on perception of 13 fundamental chemistry concepts. The study recommends that teaching and learning of chemistry should emphasize inter-relatedness of concepts. Tests and examinations given to students should reflect understanding of chemistry concepts rather than simple recall of factual knowledge. This book can be useful to general public.