The Algerian English foreign language (EFL) baccalaureate is a high stake exam that assesses both students' learning and their critical thinking skills. Thus, devising appropriate and effective exam questions may be a problematic issue for tests designers. Under the requirements of the current Algerian English curriculum, the exam questions must cover the lower and higher-order thinking skills of Bloom's taxonomy. On this basis, this research paper seeks to investigate the effectiveness of the EFL baccalaureate exam papers, and aims to answer the research question: 'To what extent does the Algerian EFL Baccalaureate exam paper cover the lower and higher-order thinking skills of Bloom's taxonomy?' This research is a descriptive content analysis; the researcher analyzed the exam questions of the Algerian EFL Baccalaureate under the cognitive domains of Bloom's taxonomy. This study is significant as it helps tests' designers to design practical EFL exams that develop students' thinking skills and language competencies. The findings of this study revealed that the EFL baccalaureate exam does not establish the students' higher-order thinking skills and does not assess their communicative abilities. Accordingly, some recommendations are suggested to hopefully help test designers to improve the quality of the EFL Baccalaureate questions.